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Mechanical response of reconstituted, freeze-dried collagen under compression loads Khosla, Amardeep Singh 1981

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MECHANICAL RESPONSE OF RECONSTITUTED, FREEZE-DRIED COLLAGEN UNDER COMPRESSION LOADS by AMARDEEP SINGH KHOSLA B.A.Sc, The University of Br i t i sh Columbia, 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER-OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (CHEMICAL ENGINEERING) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1981 (c) Amardeep Singh Khosla, 1981 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y o f B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 D a t e P. — 10 - ^ gl ABSTRACT The mechanical response under uniaxial compression of collagen d i s c s , made from freeze-dr ied collagen reconstituted at acid pH, was inves-tigated at 22, 29.5, and 35°C ( ± 0 . 3 C ° ) . The pH during compression was maintained near the physiological level of 7.40-5. Connective t issues are known to be non-linear v iscoe las t ic mater ia ls . It was f e l t , however, that the l i near i zed , f l u i d transport-based model developed by Bert (1970) would adequately describe the behaviour of collagen "for small changes in hydration. [The model is l inear ized through the assumption that the d i f fus ion c o e f f i c i e n t , D(H), i s a weak function of hydration, and is therefore constant for small changes in hydration]. The average d i f fus ion c o e f f i c i e n t , D(H), and the flow c o n d i c t i v i t y , k / n , were found to be stronger functions of hydration than expected in the hydration range investigated [1.9 to 5.5 g H 20/g col lagen] , and this may have increased scatter in the r e s u l t s . Average values of D(H) and k/n at hydration 3.0 g H 2 0/g collagen [ i . e . skin hydration] were ^ 3.5xl0~ 7 cm 2 /s and ^6.0x10" 1 1 cmVdyne-s respect ive ly . The compressive response of collagen was only weakly influenced by temperature, and possible thermal degradation of the molecules was indicated at 35°C. Some creep was also noted at times >5 t, , but no attempt was made to quantify i t . TABLE OF CONTENTS 11i ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENT INTRODUCTION CHAPTER 1 BACKGROUND 1.1 Connective Tissue 1.2 Collagen Organization 1.3 Collagen Hydration 1.4 Reconstituted Collagen 1.5 Methods for Measuring Soft Tissue Response 1.6 The Mechanical Response of Collagenous Tissues Page i i i i i v vi v i i 1 2 2 3 12 13 15 17 CHAPTER 2 MATHEMATICAL 2.1 Formulation of the Model 2.2 Determination of Model Parameters 22 22 26 CHAPTER 3 EXPERIMENTAL 3.1 General 3.2 Collagen Preparation 3.2.1 Solutions 3.2.2 Procedure 3.3 Experiments 3.3.1 The Experimental System 3.3.2 The Apparatus 3.3.3 Procedure 29 29 31 31 31 33 33 36 39 CHAPTER 4 4.1 4.2 General Analysis DATA AND ANALYSIS 42 42 45 CHAPTER 5 RESULTS AND DISCUSSION 5.1 Results 5.2 Discussion 5.2.1 Sensit iv i ty of the Model to H 5.2.2 Significance of the Half-time 5.2.3 Compensation for Equilibrium 5.2.4 Accuracy of the Model 5.2.5 Val idity of D(H) 5.2.6 The Relationship of D(H) and k/n to Hydration 47 47 66 66 66 67 74 77 78 iv Page CONCLUSIONS 80 RECOMMENDATIONS FOR FURTHER WORK 81 NOMENCLATURE 82 REFERENCES 84 APPENDIX 1 EQUIPMENT 87 1.1 Linear Displacement Transducer 87 1.2 Carrier Amplifier 87 1.3 Strip Chart Recorder 87 1.4 Recirculating Constant Temperature Bath 87 1.5 Centrifuge 87 1.6 Blender 88 1.7 Digitizer 88 APPENDIX 2 SAMPLE CALCULATIONS 89 2.1 Calculation of Hydration 89 2.1.1 Determination of Sample Thickness 89 2.1.2 Determination of Hydration 89 2.2 Calculation of the Half-Time 91 2.3 The Least Squares Fit 91 2.4 Calculation of Model Parameters 94 2.4.1 The Diffusion Coefficient 94 2.4.2 The Flow Conductivity 94 APPENDIX 3 COMPUTER PROGRAMS 96 3.1 Program for Calculation and Plotting of 97 Dimensionless Hydration Curves for Individual Sampl es 3.2 Program for Calculation and Plotting of 102 Dimensionless Hydration Curves for Lumped Data APPENDIX 4 DATA FOR GRAPHS PRESENTED 104 APPENDIX 5 RAW DATA 143 V LIST OF TABLES Table T i t l e p a g e 1.2.1 Molecular formulae and distr ibution of various 5 collagen types 1.3.1 Hydration of collagen 12 3.2.1.1 Compositions of solutions used 31 3.3.3.1 Experiments performed 41 5.1.1 Least squares f i t for dimensionless hydration-time data 58 5.1.2 Model parameters for 22 C, sequence 1 61 5.1.3 Model parameters for 29.5 C, sequence 1 62 5.1.4 Model parameters for 35 C, sequence 1 63 5.1.5 Model parameters for 29.5 C, sequence 2 64 5.1.6 Model parameters for 35 C, sequence 2 65 5.2.3.1 Comparison between original and recalculated values of t^ 75 5.2.4.1 Errors due to approximation to the model 2 77 A2.2.1 Average half-times 92 A4.1 Data for figure 4.1.1 105 A4.2 Data for figure 5.1.1 106 A4.3 Data for figure 5.1.2 108 A4.4 Data for figure 5.1.3 110 A4.5 Data for figure 5.1.4 112 A4.6 Data for figure 5,1.5 114 A4.7 Data for figure 5.1.6 116 A4.8 Data for figure 5.1.7 119 A4.9 Data for figure 5.1.8 120 A4.10 Data for figure 5.1.9 122 A4. l l Data for figure 5.1.10 126 A4.12 Data for figure 5.2.3.1 127 A4.13 Data for figure 5.2.3.2 129 A4.14 Data for figure 5.2.3.3 132 A4.15 Data for figure 5.2.3.4 135 A4.16 Data for figure 5.2.3.5 138 A5.1 Raw data vi LIST OF FIGURES Figure T i t l e Page 1.1.1 Diagrammatic i l lu s t ra t ion of connective tissue matrix. 4 1.2.1 Schematic representation of the structure of the pro- 6 collagen molecule. 1.2.2 Schiff-base type bonds between adjacent collagen molecules 8 1.2.3 Current concept of the collagen molecule and p ro to f i b r i l . 10 1.2.4 Schematic drawing of a part of a tendon. 11 1.6.1 Comparison between Jamison et aj_. and Sakata models. 19 2.1.1 I l lustrat ion of the f lu id transport-based model of Bert. 23 3.2.1.1 Apparatus for neutralization of collagen/PBS mixture. 32 3.2.2.2 Test-tube prepared for centrifugation. 34 3.3.1.1 Schematic representation of the experimental system. 35 3.3.2.1 The main apparatus. 37 3.3.2.2 Mounting for the l inear transducer. 38 4.1.1 Swelling pressure/hydration relationship for samples 44 tested in sequence 2 at 29.5°C. 5.1.1 Response of sample tested in sequence 1, 29.5°C, 30 g 48 weight. 5.1.2 Response of sample tested in sequence 1, 29.5°C, 40 g 49 weight. 5.1.3 Response of sample tested in sequence 1, 29.5°C, 50 g 50 weight. 5.1.4 Response of sample tested in sequence 1, 29.5°C, 60 g 51 weight. 5.1.5 Response of sample tested in sequence 1, 22°C, 40 g 52 weight. 5.1.6 Response of sample tested in sequence 1, 35°C, 40 g 53 weight. 5.1.7 Response of sample tested in sequence 2, 29.5°C, 40 g 54 weight. 5.1.8 Response of sample tested in sequence 2, 29.5°C, 60 g 55 weight. 5.1.9 Response of sample tested in sequence 2, 29.5°C, 80 g 56 weight. 5.1.10 Response of sample tested in sequence 2, 35°C, 40 g 57 weight. 5.1.11 Relationship of D(H) to average hydration, H° 59 5.1.12 Relationship of k/n to average hydration, H° 60 5.2.3.1 Relationship of dimensionless hydration and time 69 (cut off at 5 t^) for sample #10. 5.2.3.2 Relationship of dimensionless hydration and time 70 (cut off at 6 t i j for sample #10. 5.2.3.3 Relationship of aimensionless hydration and time 71 (cut off at 7 t j j for sample #10. 5.2.3.4 Relationship of climensioniess hydration and time 72 (cut off at 5 and compensated for H°) for sample #10. 2 5.2.3.5 Relationship of dimensionless hydration (unsealed for 73 time) for sample #10. A2.1.1.1 Sample raw data curve. 90 v i i ACKNOWLEDGEMENTS I would l ike to express my thanks to the following individuals: Dr. K.L. Pinder, for his patience and help during the course of this work. Tony Paterson, for his support, and for timely help with various mathematical problems. Joel Bert, for le t t ing me draw on his considerable knowledge in the f i e l d . Marlene Woschee for her excellent typing under duress. My parents, for their love and support. In addition, I would l ike to express appreciation for the efforts of the staff of the Chemical Engineering Workshop and Stores. Financial support from the National Research Council of Canada is grateful ly acknowledged. 1 INTRODUCTION It is the purpose of this work to further the understanding of the mechanical behaviour of skin - and by extension, other connective tissues [Chapters 1.1, 1.2] - under uniaxial compression. The long term result of such studies should be to give a clearer understanding of how individual components of skin, and other connective tissues, interact in vivo, and what specific contributions to overall tissue response are made by these components [Chapters 1.5, 1.6]. The task is highly complex, and the present study is limited to the f i r s t of two stages: a) Analyzing the viscoelastic behaviour of samples, made from re-constituted, freeze-dried collagen [Chapters 1.3, 1.4], via the f lu id trans-port-based model developed by Bert [Chapter 2]. b) Investigating the interaction of collagen with other constituents of skin. This would involve adding, for example, elastin and proteoglycans to the collagen samples, and determining changes in the f lu id transport properties caused by such additions. Collagen was reconstituted at acid pH, neutralized to physiological pH, and cast into plexiglass rings via a centrifugation technique developed by the author [Chapters 3.1, 3.2]. The disc-shaped pellets were then sub-jected, at various temperatures, to several levels of uniaxial compression using the apparatus [modified by the author] designed by Sakata (1969) [Chapter 3.3]. Results from the experiments were then analyzed using stat ist ica l methods applied to the model derived by Bert (1970) [Chapters 4, 5]. 2 CHAPTER 1 BACKGROUND 1.1 Connective Tissue The structural protein, collagen, is the major constituent of connective tissue - a generic term that encompasses a variety of biologic materials. These vary from skin, tendon and carti lage, to the corneal stroma, spinal discs and arterial walls. A knowledge of the swelling behaviour of collagen is thus indispensable to an adequate understanding of such phenomena, among others, as edema, cartilage function in joints, peridontal membrane function, the e las t ic i ty of skin, and arterial blood flow. Connective tissue may be regarded as consisting of three function-a l l y dist inct substances: collagen f ibres, e last in, and the amorphous ground substance, or proteoglycans. Morphology [that i s , gross structure], composition and function vary greatly from tissue to tissue. Several types of connective tissue are to be found in both man and animals. Their specific functional properties - which allow the tissue to f u l f i l l specific biological functions - are largely dependent upon the macro-molecular organization of the collagen molecules within the tissue. For example, collagen fibre bundles in skin, tendon and bone are composed of collagen f i b r i l s of comparable diameter, but collagen in articular cartilage forms a fine meshwork of relat ively narrow f i b r i l s . Furthermore, although collagen may constitute up to 33% of skin [79% on a dry weight basis] i t only forms about 23-35% of cartilage (Lowther (.1963), Schubert and Hamermann (1968)). 3 In some connective tissues, both the collagen and the ground sub-stance swell under appropriate conditions. The degree of swelling of the collagen has been shown by Bert (1970) to be much lower than that of the proteoglycans at hydration levels above 0.2 g H20/g collagen. Hence, in most cases, the fibrous collagen network serves as a support structure which physically restrains the gel- l ike proteoglycans within the space between the f ibres, and provides the mechanical strength of the tissue [Figure 1.1.1]. This study is not concerned with the swelling of biological tissues in general, but only with measuring and modelling the swelling behaviour of their major constituent, collagen, in isolation. A discussion of the swell-ing behaviour of a l l connective tissues and their contributions to the overall response of specific tissues is c learly beyond the scope of this work. [The response of connective tissue as a lumped system has been dealt with by Sakata (1969), who used ramp function loads and cycl ical step func-tion loads]. An examination of the molecular level interactions within and between collagen molecules is likewise not necessary, since this work is primarily concerned with bulk convective flow through a collagen network, and the empirical confirmation of a parametric model based on continuity equations, and Darcy's law [Chapter 2]. A general understanding is impor-. tant insofar as i t provides an appreciation of the significant deviation from the in vivo state of the collagen used, and therefore a brief summary of collagen genesis and structure is presented below. 1.2 Collagen Organization Collagen chains are synthesized intracel1ulary (Scott (1979), Diamant et a l . (1972)) as single polypeptide chains - of molecular weight VL00 000 - each forming a left-handed helix with non-helical end regions. The helical regions typical ly contain 1011 amino acid residues and the end 4 FIGURE 1.1.1 Diagrammatic i l l u s t ra t ion of connective tissue matrix. (Scott (1979)) 5 regions from 9 to 25 residues (Fietzek and Ku'hn (1976)). Four morphological types of collagen, composed of f ive genetically d ist inct polypeptide chains [Table 1.2.1], have been identi f ied so far and al l are very similar (Scott (1979)). Fietzek and Kiihn (1976), in their excellent review of collagen structure, report that of these chains the structure of the a l ( I ) - and half of the a2-chain are known. Some preliminary data has also been obtained on the sequence of the al ( I I ) - and al( I I I ) -chains. Three of these polypeptide chains are brought together int ra -c e l l u l a r by a complex chain of events which includes the "hydroxylation of certain proline and lysine residues by specif ic hydroxylases and attachment of carbohydrate moieties to some of the hydroxylysine residues by galactosyl TABLE 1.2.1 Molecular formulae and distr ibut ion of various Collagen types (Fietzek and Kiihn (1976)) Morphological Molecular Distribution Type Formula I [al( I)] 2 a2 Skin, bone, tendon, aorta, lung, etc. II [ c d U I ) ] 3 Hyaline carti lage III [a l ( I I I ) ] 3 As type I, re t i cu l in IV [a l ( IV)] 3 Basement membrane and glycosyl transferases" (Fietzek and Kiihn (1976)). This coming together of three l e f t handed helical molecules produces a right handed super-helical molecule with non-helical procollagen peptides attached [Fig. 1.2.1]. The formation and correct alignment of this so-called 'tropocollagen' molecule is assumed to be fac i l i t a ted by the interaction of the pro-collagen peptides. After the t r i p l e helix is secreted into the extra-(MarOn GlcNac (20A) N-TERMINAL PROPEPTIDE (150 A) Globular Domain Triple - Helical Domain Nontriple- Helical Domain C O L L A G E N M O L E C U L E 3000 A ) Nontriple- Helical Domain Nontriple - Helical Domain ;,_C-TERMINAL PROPEPTIDE (100 A) (Man)n GlcNac (100A! FIGURE 1.2.1 Schematic representation of the structure of the procollagen molecule. Glc denotes glucose, Gal galactose, Man mannose, and GlcNac N-acetylglucosamine. (Prockop et a l . (1979)) 7 ce l lu la r f lu id the procollagen peptides are enzymatically cleaved off , thus giving the molecule the ab i l i t y to aggregate into f i b r i l s (Grant (1972), Prockop et al_. (1979)). It is important to note that a l l three * polypeptide chains have a characterist ic Gly-X-Y repeat sequence of amino acids throughout the t r i p l e hel ical region. This arrangement is necessary due to ster ic considerations encountered during formation of the t r i p l e helix and after. Glycine is the smallest of the amino acids and lacks any side chains, and is thus part icular ly suitable for occupying the positions located in the inter ior of the t r i p l e helix (Ramachandran and Kartha (1955), Rich and Crick (1955)). It is assumed that the higher order organization of the collagen molecules is also controlled by the sequence of amino acid residues. Constituent chains of f i b r i l s may be brought together in a way determined by the action of selective enzymes on segments of the chain. For example, certain lysine and hydroxylysine residues located in the non-triple helical regions at both ends of the helices are deaminated by oxidation via a lysine oxidase (Gallop et aj_. (1973), Robins et al_. (1973)). This results in interaction between the carbonyl compounds thus created and the lysine and hydroxylysine molecules in adjacent molecules via Schiff base-type intermolecular bonds [Fig. 1.2.2]. The non-triple helical regions are also notable for their high concentration of amino acids with hydrophobic side chains (Fietzek and Kiihn (1976)). Gross and Kirk (1958) have per-formed a series of experiments which involved the heating of di lute solutions of neutral salt-soluble collagen to 37°C. This was found to cause the spontaneous precipitation of collagen molecules and resulted * Glycine, an amino acid. 8 aldehyde = 0 + H2N - R" primary amine condensation R, H20 + R NR II Schiff base weakly basic hydrolysis (H20 + strong acid) carbonyl compound (aldehyde, ketone, etc.) + H2N - R II Fig. 1.2.2: Schiff-base type bonds between adjacent collagen molecules in the formation of a gel at concentrations as low as 0.2% by weight. [Neutral salt-soluble collagen is a group of proteins which aggregates to typical collagen f i b r i l s when solutions of i t are warmed to body temperature (Gross (1958), Harkness et a l . (1954), Jackson (1951)]. The rate of gel formation was found to be measurably reduced by the presence of sub-stances such as urea and arginine, which are known to prevent the formation of hydrogen bonds between molecules [in addition, they may also function as competitors for carboxyl and other charged groups]. The results of Van Duzee (1978) also confirm th i s . Both pH and ionic strength were also found, by Fessler (1960), to affect urea inhibit ion and this was held to suggest that there is a "part ic ipat ion of electrostat ic forces in addition to hydrogen bonding in f i b r i l formation in this [collagen/neutral salt solution] system." Furthermore, the established amino acid sequence 9 strongly suggests that hydrophobic interactions are also involved in estab-l i shing bonds in which the C-terminal of the collagen molecule is involved. The C-terminal is strongly hydrophobic, and the quarter-stagger arrangement within f i b r i l s [see below] ensures that i t wil l always be in contact with hydrophobic regions of the surrounding chains. Since the a2-chain contains many more hydrophobic residues than the cd(I)-chain, i t contributes greatly to the hydrophobic character of type I collagen (Fietzek and Klihn (1976)). .Current theory suggests that "the aggregation of the molecules into f i b r i l s represents a self-assembly process, regulated by the amino acid sequence of the collagen molecule" (Fietzek and Kuhn (1976)). Several review ar t i c les have covered the history of the investigation of collagen structure and properties. To quote Vi id ik (1973): "Recently, an idea that the tropocollagen molecule consists of f ive ident i f iab le segments, four of these having the length of the period (D)* seen in the native f i b r i l and the f i f t h being shorter (0.4D), has won support." [Fig. 1.2.3] Fietzek and Kuhn (1976) and also Scott (1979) quote studies - Chapman (1974), Chapman and Hardcastle (1974), and Holmes et al_. (1973) - that strongly support the above, and set the repeat period [D] at 233 amino acids in length. The non-triple hel ical regions of 16 and 25 residues respectively, f i t into the empty spaces of length 0.6D. This over-lapping arrangement gives r i se to the typ i ca l , regularly banded, appear-ance of collagen in electron micrographs. It is also generally held that tropocollagen molecules aggregate into f i b r i l s and these in turn clump together longitudinal ly to form fibres [Fig. 1.2.4]. Fibres may anasto-mose at acute angles in tissue in contrast with f i b r i l s which are generally * Repeat unit corresponding to 233 amino acid residues in length. 26.8 A (A) 0.4D 0.6D D \ ; / ; i 680 A i -) 1 1 1—• > 1 i - 1 1 • - 1 1 1 1—• »• 1 1 1 H • • 1 1 •—t 1 • • 1 1 H 1 • )» 1 1 1 1 • ^ 1 ( B ) FIGURE 1.2.3 Current concept of the collagen molecule and proto f ibr i l . (A) A section (black) of one of the three chains constituting the molecule wound around its own axis (white), which in turn is wound around the common axis of the molecule (dotted). (B) The concept of quarter-stagger of the molecules combined with overlaps and gaps as the length of the length of the molecule is 4.4 times that of a period (D). (Viidik (1973)) FIGURE 1.2.4 Schematic drawing of a part of a tendon. One of the primary fiber bundles is cut (arrow), showing the wavy course of the f ibers. The group of primary bundles shown is surrounded by a sheath (also cut). (Scott (1979)) 12 "not considered to branch at a l l in the native state". (Viidik (1973)). 1.3 Collagen Hydration The interaction between collagen and water has received consider-able attention late ly. Nomura and his coworkers (1977) have identif ied four regimes in collagen hydration, and these are l i s ted in Table 1.3.1. TABLE 1.3.1 Hydration of Collagen Water Content g H20/g collagen Characteristics 0 - 0.07 structural water 0.07 - 0.25 bound water 0.25 - 0.45 bound-free transition zone > 0.45 free water They have gone on to suggest that the structural water is incorporated into the t r ip le superhelix, the bound water is associated with the polar side chains within the interhelical regions of a f ibre, and that the free water corresponds with the i n te r f i b r i l l a r gel [along with the proteoglycans]. However, since the hydration ranges dealt with in the present work are always above 2 g H20/g collagen, i t is assumed that the movement of water into and out of the collagen matrix is re lat ively unaffected by i n te r f i b r i l l a r forces. 13 1.4 Reconstituted Collagen The collagen used for this work was commercially available lyophil ized [freeze-dried] bovine achi l les tendon or rat t a i l tendon collagen [U.S. Biochemical Corporation], and therefore, according to the c lass i f i cat ion system given in Table 1.2.1, primarily type I collagen. The method of preparation used by the manufacturers is that of Einbinder and Schubert (1951). This method involves extraction of cleaned collagenous tissue for 6 days at 0°C with 3% ^ H P C s to remove soluble proteins, further extraction for 6 days at 0°C with 25% KC1 solution to remove proteoglycans; and f i na l l y , washing with water and dehydration of the tissue using absolute alcohol. This is followed by .lyophilizing the tissue. Collagen prepared in such a manner has a dry, flaky appearance, with some comparatively large 'bundles' mixed in. Reconstitution of the collagen to a state approximating in vivo collagen, was subject to the following considerations: a) Dried collagen does not swell easi ly at the pH of physiological saline (Veis (1964)). It does, however, swell rapidly at acid pH. Accord-ing to Schubert and Hamermann (1968) the "effect of lowering pH appears to favor a shift of equi l ibr ia to the disordered forms because of the disruptive effect of the repulsions among the accumulated cationic charges on the ordered f ibres " . Flory and Weaver (1959) report that v i scos i t ies of di lute collagen solutions were considerably reduced by the addition of 0.4% acetic acid, and attributed this to the suppression of association of collagen molecules by electrolytes present in the acid. This was confirmed by Weissman and Cocks (1978). The mechanism involves: ^i) The concentration of reactive collagen residues such as the e-amine groups of lysine [this step is dependent on pH due to the ac id-base hydrolysis equi l ibr ia which exist for this side group]. 14 i i ) pH sensitive intermolecular forces. At pH levels below the i soelectr ic point of collagen, the net positive charge increases with decreasing pH and therefore, at low pH, the increased repulsive force between molecules along with freeing of ionic groups on collagen by the high H + concentration, establishes a Donnan potential inside the f ibres. Hence water flows in along i ts concentration gradient and equalizes the ion concentration inside the collagen and in the external solution (Ramachandran and Kartha (1955)). Low pH i s , therefore, desirable but strong acids damage the collagen structure by disrupting the matrix. 0.5M acetic acid has been used (Gross and Kirk (1958)) without damage to the tropocollagen molecule, and this concentration of acid was used in the present study. Damage done to the molecules at low pH can be reversed by neutralization and cooling to 4°C (Gustavson (1956)). b) The conditions under which the experiments are conducted should reproduce, where possible, in vivo conditions. While disruption of collagen at low pH during collagen reconstitution is necessary, the collagen sample once formed, must be kept at stable physiological pH [7.40-7.45] for up to 6 days at up to 37°C. In order to effect this a phosphate buffered physiological saline solution [PBS] was used (Dulbecco and Vogt (1954)). This solution is buffered with NaH2P0ii and KH 2 P0 Hi with an effective range centered near a pH of 6.8 (Hampel and Hawley (1973)). c) Proteins are open to thermal, biochemical and biological attack outside the body: i) Collagen is subject to thermal degradation at temperatures above 35°C, the maximum temperature encountered in this study (Gustavson (1956), Schubert and Hamermann (1968), Veis (1964)). 15 ii). The molecular organization of collagen can be severely disrupted by the lyotropic action of certain electrolytes and stabi l ized by the presence of others (Gustavson (1956), Veis (1964)). Of the salts, present in the PBS used in this study, only CaCl 2 has a moderately disrup-tive effect on collagen when present at high concentrations. This salt was present at a very low concentration [0.001M] in the PBS and could not have caused any s ignif icant disruption. i i i ) 0.2% w/w sodium azide, NaN3, was used to prevent bacterial growth in the PBS. 1.5 Methods for Measuring Soft Tissue* Response Soft tissues have been shown to be complex materials and their mechanical behaviour is the result of complex steric interactions within a matrix of extracel lu lar, largely collagen, fibres imbedded in an aqueous proteoglycan gel. To the response of the matrix must be added effects due to the movement of free i n te r s t i t i a l f lu id under the influence of osmotic and hydrostatic concentration and pressure gradients, and matrix deform-ation. Beyond the necessary complexity of any soft tissue model, l i e problems of experimental technique. In spec i f ic , for the case of skin, the following considerations ar ise: a) In i ts natural state, skin is b iax ia l ly , and unevenly stressed, with the degree of preloading varying from point to point on the body. Maps showing directions of minimum extens ib i l i ty - the so-called 'Langer's l i nes ' (Danielson (1971)) - have been produced, and are extensively v * 'Soft t issue ' is a term widely used to denote tissues with viscoelast ic properties similar to those of connective tissues. 16 used by surgeons. b) Whole skin is inhomogeneous. Skin properties vary not only with i ts location and thickness, but with hair density, race, age, sex and the presence of pathological states. c) If the experiment is to be done in vivo, i t is often not possible to determine skin thickness (Alexander and Cook (1977)). d) If the experiment is to be done in v i t ro , then i t is important to reproduce in vivo conditions as far as possible. The majority of the skin and tendon investigations done to date have involved characterization of tissue behaviour under tension and have generally been carried out using one of two experimental techniques: a) Use of tradit ional materials-testing apparatus such as that made by Instron, and other extensometer manufacturers (Fung (1967), Van Duzee (1978), Diamant et al_. (1972), Elden (1964)). b) Application of hydrostatic pressure via vacuum or manometer manipulation (Dick (1951), Alexander and Cook (1977), Grahame (1969)). These experiments can be done in vivo or in v i t ro , and are part icular ly useful in investigating behaviour of edematous tissues. Cartilage investigations, on the other hand, have been done primarily under compressive stresses, using indentation methods (Parsons and Black (.1977), Hayes and Bodine (1978), Schwartz et al_. (1966)). The indentation methods used for tests performed on carti lage are similar to that used in this paper. One of the major problems with extensometric studies is that they are often destructive in nature, and must therefore be carried out in v i t ro , with some care devoted to both extraction and preservation of the t issue. For studies with immediate c l i n i ca l applications, particular care must be taken to ensure close approximation to natural state conditions< [For 17 example, skin must be kept under tension as i t is in vivo]. Furthermore, due to the non-linear viscoelastic nature of the tissues involved, charac-terization of tissue behaviour based on stress [force per unit area] be-comes d i f f i cu l t due to changes in cross-sectional area during testing. Also, expression of f luids due to tight clamping of the samples can inter-fere with results, particularly where swelling behaviour is being invest i -gated . The hydrostatic pressure application method of Dick (1951), in its c l in ica l manifestation as a vacuum application technique, is also trouble-some (Grahame (1969)). To quote Alexander and Cook (1977): "Reducing the raw data from such a technique to quantitatively valuable stress-strain information is complicated by a' number of factors: the skin is already biaxial ly loaded in the natural state, the thickness of the test site is not known, and any characterization in terms of material constants requires a multiaxial stress-strain law that is generally valid for a range of skin types." 1.6 The Mechanical Response of Collagenous Tissues The mechanical response of collagenous tissue to extension and compression has been investigated in considerable detail over the last half century. The modelling of tissue response has been undertaken with a view to either: a) assisting in diagnosis of pathological conditions. Most of the work in this area has been done on skin (Kennedi et al_. (1975)) which is not only the most easily accessible of tissues, but also often reflects the state of health in the body [e.g. under rheumatoid conditions], or b) characterizing tissue behaviour in order to develop a r t i f i c i a l replacements. The highly variable and non-homogenous nature of most connective 18 tissues makes such characterization d i f f i c u l t , and inclusion of such factors as stress history dependency often leads to intractable mathematical formu-lations. L i t t l e attention has been paid to the behaviour of individual connective tissue components. The experiments performed for the present work are essentially an extension of those done by Wilkins and Pinder (1979) using the apparatus - with some modifications - designed by Sakata (1969). The data obtained was f i t ted to the water transport-based model derived by Bert (1970). Many attempts at modelling the mechanical behaviour of so-called "soft" biological tissues have involved the traditional spring and dashpot approach. The models suggested by Jamison et al_. (1968) and Sakata (1969) are presented below [Fig. 1.6.1] and consist of ideal elastic and viscous elements - represented by springs and dashpots, respectively. In the case of Sakata (1969), an idealized plastic or f r ic t ion element - the "ratchet" element - has also been included. Viidik (1973) provides an excellent introduction to the application of such mechanical analogies to tissue response. Although these models have often been successfully applied, i t must be born in mind that the ideal elements used in them have no clearly identif iable physical counterparts (Kennedi et_ al_. (1975)). Another type of model based on the theory of continuum mechanics has also been widely used. Such models are derived by one of two approaches: a,) stress and strain are related by proposing a strain energy function [or work function, or relaxation spectrum] of appropriate form and solved for the parameters via curve f i t t ing methods. For example, the model of Veronda and Westman, presented below: FIGURE 1.6.1 Comparison between Jamison et al_. ( left ) and Sakata (right) models. Left: n i»n 2 .= Viscous element. E 2 = Elastic element. Right: F = Force. A,C = Elastic elements. B = Viscous element. D = Elastic element with ratchet. X l s X 2, X3 = Displacement. A,B,C,D = Time dependent parameters. (Wilkins and Pinder (1979)) 20 3 W = Y, °i d A1 i=l where W is the stra in energy function per unit volume of the undeformed body a., i s the stress in the i d i rect ion X. is the ra t io between principal extensions of the deformed body and the corresponding i n i t i a l dimensions in the undeformed state , b) an integral equation is solved for the stra in energy function when oCt) and x(t) are known. Such a model was suggested by Gou (1970), and th is was tested by WiTkins and Pinder (1979) on various constituents of con-nective t issue in gelat in ge ls . This model involves the phenomenological treatment of continuum mechanics given by Mooney (1940), and the load exten-sion re la t ion for uniaxial stress proposed by Aubert (1955) for a soft t issue [sartorius muscle]. It is presented below: a = 3ck(x 6-X~3)exp[k(x6-3+2x)] 1.6-2 where c and k are parameters X is the uniaxial stra in and a is the corresponding uniaxial s t r e s s . Simi lar models have been proposed by others. These models have one drawback, however - they are usual ly very sensi t ive to X at low s t r a i n s , and very small errors in the measurement can lead to large errors in the predicted values of o. 1.6-1 21 Some authors have also f i t ted exponential and power series func-tions to the response curves of connective tissue fibres under uniaxial tension (Ridge and Wright (1965)). The water transport-based model of Bert (1970) was chosen for this work for the following reasons: a) -It avoids the large numbers of parameters inherent in the mechanical analogue models of Sakata (1969) and Jamison et_ al_. (1968). Given the considerable scatter associated with biological experiments, this excessive complexity is not jus t i f ied . b) The values of a l l parameters in the model can be experimentally determined once certain simplifying assumptions have been made [Chapter 2]. c) While mechanical analogue and strain energy-based models may be suitable for modelling fibers under extensional stresses, i t was fe l t that a model based on f lu id transfer through a porous membrane would more closely approximate real i ty for a highly hydrated tissue. d) It allows comparison of the swelling behaviour of different soft tissues based on a measurable quantity - the hydration of the tissue. In his work, which will be expanded upon in the next chapter, Bert (1970) investigated the swelling behaviour of several different con-nective tissues. These included corneal stroma, costal and articular carti lage, spinal discs, skin and aortic walls. He reports flow conduc-t i v i t i e s near 7 x 10~ 1 2 cm^s"^yne" 1 for skin at hydrations near 3 g H20 per gram of dry tissue. 22 CHAPTER 2 MATHEMATICAL 2.1 Formulation of the Model The following discussion is based on the formulation presented by Bert (1970). The space variable x [Fig. 2.1.1] has been defined as dm dm where dmw is the incremental amount of water in a segment of membrane with dry mass dm, and 6 and y are the densities of collagen and water, respectively. The above assumes that the volumes of f lu id and dry material are additive. Equation 2.1-1 can be rearranged to give 1 1 dm _ + _ . _ ! ! 6A yA dm dx HTT + • -TIT- V-m 2.1-2 or dm where is the hydration at a point, H g water/g collagen. Bert has defined e = ^ and & = ^~ , where is the thickness of dry material from o 6 A 0 to x. This allows the transformation of the space variable x to the variable which is based on the thickness of dry collagen in the sample: FIGURE'2.1.1 I l lustration of the f luid transport-based model of Bert. Hydration profiles are assumed to be symmetrical about the l ine ip = 0. ro co 24 dx = • o> 2.1-4 The continuity equation for the system can be shown to be 3 H Hm 9 f v dm = _ -^L . dm 2.1-5 3t A 9m where f is the water flux in the x d i rect ion, -rr • T ~ is---the rate of change x _ 3 f 3t A of mass of water in the segment dm, and • dm-is the rate of change of accumulation of water in the segment for uniaxial flow in the x d irect ion. Rearrangement of equation 2.1-5 gives 3 H 3 f x 2.1-6 9t . m 9 A where the rate of change of hydration is now given as a function of m/A, which is independent of the degree of swelling for the one-dimensional case. An equation of motion has also been derived by Bert from Darcy's law which states that: k 9P f = v . — • —— 2.1-7 c T n 9x where f is the convective flux g/cm2-s and- k/n is the flow conductivity The dif fus ive flux f d , associated with water ac t iv i ty gradients, is described by Fick's f i r s t law: 9a f . = - D — ^ 2.1-8 d 3X 25 For connective tissues at hydrations greater than 0.2 g water/g collagen, the diffusive flux has been shown by Bert to be negligible [less than 1% of the convective f lux] . The equations of interest to us, are thus reduced to i) The continuity equation: 9H 9f x x 2.1-6 at 4 i i ) The equation of motion: k 9 P C f = f = _ . — A 2.1-7 x c n 9x i i i ) An equation of state which is derived from experimental data and de-fines the swelling pressure as a function of the hydration of the system. Combining equations 2.1-6 and 2.1-7, and bearing in mind the definit ion of ^, gives 9H 1 9 f k YE 3 P C S 1 2.1-9 9t Y 9* I n (E+H) 3 T/J 9P dP 9H Using the relationship = • and substituting in equation 2.1-9 yields 9H 1 9 f k YE dP s 9H It = - Y 3* 1 n ' U+Hl * dlT * a* ^  2'1"10 But E = Y/<S and is independent of ty. Hence 26 9H d C k e 2 dP ' 3 K V 9t = 9^ 1" n ' Te+Hl ' ciTT ' 3^ J • 2.1-11 Bert has defined the diffusion coeff ic ient D(H) to be k E 2 dp -DCH) . - . ^ . ^ 2.1-12 and has rewritten equation 2.1-11 as •• f • ! * • • { " « < > 2-1-13 If i t is assumed that DCH) is a weak function of hydration for small change in hydration, then equation 2.1-13 can be l inearized to 9 H _ DTHT . 9£H at ----^ where DCH) is the coeff ic ient D(H) averaged over the hydration range in question. 2.2 Determination of Model Parameters Bert defines the dimensionless hydration H - H. o i where H.. is the i n i t i a l , and HQ the f i n a l , hydration. Equation 2.1-14 can be written for H: 27 Crank (1975) has solved the heat transfer analogue to equation 2.2-2 with the following i n i t i a l and boundary conditions: IC t=0 H=0 BC H=l BC where \p=0 is the centre of the membrane and ty=\p' the surface is thus half the dry thickness of the sample]. This system is depicted in Fig. 2.1.1. The solution is given (Crank (1975)) as: H - H. , ~ , ,*n - D ( n T ( 2 n + l ) 2 T r 2 t / 4 V 2 , o n + n , n=0 For n>0, a good approximation i s : 0 1 v or -D(HTTT2t/4f 2 H = H + (H.-H ) - e cos f f r 2.2-5 0 1 0 TT 2$ and at any time, the average hydration across the membrane, H g v , is given by _ =^^ ' -rKITTr 2t/4^ 2 f> H =H + (H.-H ) - e • V / cosffr dij; 2.2-6 a v o l o TT ^ ^ or 28 -D{hTir2t/V2 H = H + CH.-H ) \ e 2.2-7 av o i o T T Z H -H A plot of l n ( T j r - n — ) versus time wil l c lear ly give a straight l ine of slope i o l n (~z) - 4 " ^ ' ^ » a n d from this DCH) can easi ly be determined. dP Once DCH) is determined, jpp 1 S experimentally determined from the swelling pressure - hydration relationship [the hydration of the membrane at any time is calculated from measurements of i ts thickness, via the equation Ap j Hav = ~m~ 1 ~ 6 2 - 2 " 8 where A is the cross sectional area of the membrane, DW its dry weight, and T the thickness of the membrane]. k The parameter the flow conductivity, can then be calculated from equation 2.1-12. Note that D(H) as determined is considered to be the value H i + H o Also note that a l l values of H measured are in fact averages, H = w , av over i^ =0 to ^=^'. The subscript wil l be l e f t o f f , for the sake of c l a r i t y , from this point on. 29 CHAPTER 3 EXPERIMENTAL 3.1 General Experiments were performed to measure the mechanical response, under uniaxial compression, of discs made from reconstituted, freeze-dried, collagen f ibres. The results were compared to the f lu id transport-based model pro-posed by Bert (1970). Considerable effort was invested in the preparation of collagen discs. Two major objectives were ident i f ied in this regard: a) The discs produced have to be both easi ly reproducible, and homogeneous: i) The use of reconstituted collagen* eliminated some of the random errors associated with any experimentation involving soft t issues. [These large errors are a direct result of the large variations in structure and properties inherent in l i v ing tissues [Chapter 1.5]]. Also a r i g id procedure for preparing the collagen discs was developed and s t r i c t l y adhered to [see below]. i i ) The preparation of homogeneous samples was also d i f f i c u l t to accomplish due to the viscous nature of the collagen produced. In the preparation procedure [see below] di lute acetic acid was used to cause re-hydration of the collagen, and, after neutralization to the pH of ECF**, * Taken from re la t ive ly homogeneous, col lagen-r ich, tissues such as bovine achi l les tendon and rat t a i l s . * * Extracel lular or i n te r s t i t i a l f l u i d , pH 7.40-7.45. 30 the mixture of swollen collagen had a hydration much higher than that of skin*. Although such techniques as pressure or vacuum f i l t ra t ion could be used to remove much of the PBS suspending solution they were not adequate for the reduction of the collagen hydration to the skin hydration leve l . Centrifugation of the collagen/PBS mixture produced highly viscous pel-lets of collagen [at re lat ively low hydrations], which were d i f f i cu l t to deal with: the discs produced by manually packing this material into plexi -glass rings [see below] invariably contained air pockets. It was in order to circumvent such problems that the centrifugation method, described below, was developed. b) The stress history of the sample had to be eliminated, as far as possible, as a variable. This was accomplished by the standardization of the preparation procedure. Again, the use of reconstituted collagen rather than natural tissue allowed for better control of stress history. * The hydration of skin is about 3 g H20/g collagen. 31 3.2 Collagen Preparation 3.2.1 SOZ.UXA.OVU,: TABLE 3.2.1.1 Compositions of Solutions Used Solution Contents Amount Molarity (grams) acetic acid C H 3 C O O H 0, .50 sodium hydroxide NaOH 5, .00 phosphate buffered NaCl 8. .00 0, .1368 saline KCl 0. .20 0, .0027 NazHPO^ 1; .15 0, .0081 KH2P04 0. .20 0, .0015 CaCl 2 0. .10 0. .0009 MgCl2-6H20 0, .10 0, .0005 NaN3 0, .20 H20 990, .15 1000.2 PBS was f i l tered through a nucleopore membrane [pore size 0.45 ym], under vacuum, before use. 3.2.2 VnodoAiUtz: a) 4.50 g of collagen* was allowed to swell in 225 ml of 0.5 M acetic acid on a ball mill for 18 hours, at room temperature. b) The dilute collagen/acetic acid mixture was neutralized in a blender [Appendix 1; Figure 3.2.2.1] at maximum speed at room temperature to the pH of normal body ECF using 5.0 M NaOH. c) The mixture was centrifuged [Appendix 1] at 5200 g to remove a nearly clear supernatant f l u i d , which was then discarded. * U.S. Biochemical Corporation, freeze-dried bovine achil les tendon co l -lagen. 32 FIGURE 3.2.2.1 Apparatus for neutralization of collagen/PBS mixture. 33 d) The collagen pellets thus produced were resuspended, using the blender, in 200 ml of PBS at pH 7.40-7.45, and l e f t for 18 hours in a refrigerator at 4°C. e) Steps c) and d) were repeated to give a total of 160 g of the collagen/PBS mixture, which was suff ic ient for about 9 samples of collagen. The mixture was l e f t refrigerated overnight before using. f) 18 g of collagen suspension from e) were placed in a special ly prepared test tube [see below, and Figure 3.2.2.2] and centrifuged at 1650 g for h hour, 1100 g for a further h hour, and f i na l l y 1100 g for 10 minutes. The collagen was st irred with a spatula after each centrifuga-tion step to release a i r trapped under the porous disc, and also in order to prevent packing gradients from developing in the collagen disc. The f inal weight of a collagen sample was about 3 g. g) The disc was removed from the tube, and the membrane was re-moved, leaving only the plexiglass r ing. The disc was then placed on top of a porous metal disc in a covered glass beaker containing 1.5 ml of PBS, just enough to wet the top of the metal d isc. This was refrigerated for at least two days before using in the apparatus described below. 3.3 Experiments 3.3.1 The, ExpthAjmzYital. System-The experimental system is represented in Figure 3.3.1.1 and consists of f ive major elements [Appendix 1]: a.) The main apparatus, in which the collagen discs are subjected to uniaxial stress. b) A l inear transducer/carrier amplifier combination, the output of which is proportional to the thickness of the collagen disc under obser-vation. 34 POLYCARBONATE TUBE POROUS STEEL DISC FIGURE 3.2.2.2 Test-tube prepared for centrifugation. CONSTANT TEMPERATURE RECIRCULATING BATH STRIP CHART RECORDER MAIN APPARATUS CARRIER AMPLIFIER FIGURE 3.1:1.1 Schematic representation of the experimental system. 36 c) A str ip chart recorder, to record the output of the carrier amplifier, and hence the thickness of the disc, as a function of time. d) A constant temperature bath, to ensure that a chosen temperature is maintained in the main apparatus for the duration of a given experiment. e) Weights, to apply stress to the collagen discs. 3.3.2 Thu ApptVicutuA: a) The main apparatus used for compression testing of the collagen discs was that designed by Sakata (1969) with some modifications. The mod-if icat ions made were as follows [Figure 3.3.2.1]: i) The entire apparatus was mounted on a massive steel base [13] in order to reduce vibrations. The base, in turn, rested on a massive stone-topped table. i i ) A constant-temperature bath [9] was provided for the linear transducer coil in order to reduce fluctuations in output caused by changes in ambient temperature. The coil was mounted in a threaded copper cylinder that screwed into a solid copper base [Figure 3.3.2.2]. i i i ) The aluminum anvil [10] replaced the force transducer used by Sakata (1969) in his variable load tests. iv) The copper heating coil [6] used by Sakata was found to react mildly with the PBS, and was then replaced by one made of stainless steel. The apparatus consisted of a probe [1], an arm [2], an arm support [3], a l inear displacement transducer [4], a cyl indrical vessel [5], a heating coil [6], a support for the collagen disc [7], a restraining cylinder to keep the disc in place [8], a constant temperature bath for the transducer [9], an anvil [10], a screw-adjusted counterweight [11], vessel covers [12] and a heavy steel base [13]. FIGURE 3.3.2.1 The main apparatus. AM- numbers are referred to in the text. Everything within the cylindrical vessel [5] is shown in section. Figure is approximately to scale. FIGURE 3.3.2.2 Mounting for the l inear transducer. 39 c) Water at constant temperature was circulated through the bath surrounding the transducer [9], and also through a stainless steel heating co i l [6], immersed in the PBS tank [5], by means of a constant temperature bath. d) Calibrated weights were placed on the arm, d i rect ly over the probe, to apply pressure to the collagen discs. 3.3.3 ?fL0C.2.duAZ: a) Calibration of l inear transducer i) The temperature bath control was set to produce the required temperature, as measured by a thermometer inserted with the bulb at the level of the collagen sample, in the cy l indr ica l vessel. Temperatures used were 22, 29.5 and 37°C. i i ) PBS was added to the vessel, and the entire system was allowed to equil ibrate for 20 minutes. i i i ) Calibration of the transducer was accomplished by inserting one or more machined, stainless steel discs of known thickness, between the anvil and the probe, and noting the displacement on the chart recorder. A normal range of displacements covered in any given experiment was 0.125" -0.325" [0.25" from the horizontal null posit ion, which corresponds to a sample thickness of 0.125"]. One-inch diameter discs of the following thicknesses were used: 0.050", 0.100", 0.125", 0.275", a l l to a tolerance of ± 0.001. Calibrations were performed both before and after each test series [see below]. b) Stress-strain determination i) After ca l ibrat ion, the collagen disc, contained in the plexiglass ring [Figure 3.2.2.2], was placed on the disc support, and held in place by the restraining cyl inder. 40 The probe of the transducer protruded downwards from a pivot at the mid-point of the support arm, and moved in the plane of the arm. It was necessary to res t r i c t movement of the probe to the vert ical during test-ing, and this was made possible by a bar - 5 mm below the parallel to the supporting arm - which connected the probe to the arm support. Al l four vertices of the parallelogram thus formed allow rotation about an axis perpendicular to i ts plane, and thus the probe remained paral lel to the fixed arm" support. The arm was about 24 cm in length - long enough to neglect horizon-tal displacement of the probe, since vert ical displacement of the probe was always less than 0.25" from the null posit ion. [The null position corres-ponded to a sample thickness of 0.125".] The probe i t s e l f was a part ia l ly hollow stainless steel cylinder of radius 1.032 cm [ i .e . diameter 13/16"] and cross-sectional area 3.343 cm 2. The lower face of the probe was the surface in contact with the collagen d i sc , and consisted of a porous s in-tered stainless steel disc that allowed re la t ive ly free passage of the PBS. S imi lar ly, the anvil had a porous top of the same material. A ro l l e r bearing at the juncture of the arm and the arm support served to reduce f r i c t i on due to arm movement, and a screw-adjusted counterweight was set to balance the probe. The main apparatus was covered by a transparent plexiglass box. b) The l inear transducer was a variable permeance, electromechanical instrument in which the a.c. current produced was roughly proportional to the probe displacement from a null position [the horizontal]. The maximum allowable displacement was 0.25 inches. The output of the transducer was amplified by a carr ier amplif ier with a maximum output of 10 V d.c. It was discovered that at high ampl i f i -cations noise was considerably reduced, as was non-l inearity of the output. 41 A near-maximum setting was thus used throughout the experiments. The output of the amplifier was recorded on a str ip chart recorder. i i ) PBS was added to bring the level of the l iquid inside the vessel to just above the samples. The vessel covers were put in place. i i i ) The arm was lowered, and a 20 g weight was placed on i t , above the probe. The chart recorder was started. iv) Additional weights were added only when the collagen thick-ness was relat ively stable [Chapter 4]. The time taken to 'equil ibrate' was between 8 and 30 hours for each weight, depending upon the temperature and the weight involved. Model parameters D(H) and k/n were calculated at several values of average hydration for three temperatures and two sizes of step-change in swelling pressure. TABLE 3.3.3.1 Experiments Performed Temp. °C ~ - ^ S t e p Number 1 2 3 4 5 6 Sample Number Sequence —^_ Weight (grams) 22.0 1 30* 40 50 60 70 80 2,3,5 29.5 1 30 40 50 60 70 80 6,7,12,14,15 29.5 2 40 60 80 8,9,10,11 35.0 1 30 40 50 60 70 80 19,20,21,22,24 35.0 2 40 60 80 16,18,25,26 * All samples were preloaded to 20 g. 42 CHAPTER 4 DATA AND ANALYSIS 4.1 General Due to the large scatter inherent in biological data, experiments were designed [Table 3.3.3.1] to provide some idea of the r e l i a b i l i t y of the results: a) Experiments at each condition [e.g.. 35°C, Sequence 1] were repeated f ive times. b) A completely randomized experimental design would have been ideal : this would have ensured a minimum of systematic errors aris ing from, for example, a malfunction in the constant temperature bath or some mistake in the preparation of a particular batch of collagen. This was, however, not practical for the following reasons: experiments could not be carried out to equilibrium because a creep component in the response of the collagen was noticed. It was, therefore, decided to carry out experiments for at least f ive half-times [Chapter 5.2], to ensure as complete a measurement of the viscoelast ic component of the response as possible. However, in order to do th i s , i t was necessary to f i r s t ascertain the half-time, and this was only possible after a number of identical runs had been performed [due to scatter, the results of only one run could not be applied to an entire ser ies]. Because i t was necessary to determine the half-time for each new condition, a compromise was reached: at least one of the f ive identical runs at each condition would be done using collagen from a new batch [and 43 hence at a different time from the other runs]. Note that runs were not carried out for exactly f ive half-times, but for at least f ive half-t imes* [this was inevitable, since half-times were calculated only after a l l runs were complete]. The response curves were re lat ive ly f l a t in this region [at times greater than five half-times] and therefore the half-times were not greatly affected by th i s . Results were adjusted by extrapolation to an 'equil ibrium' hydration [Chapter 5.2.3]. c) Although precautions were taken to prevent the development of packing gradients in the discs [Chapter 3.2] a s l i ght ly denser packing was noted at the bottom of each disc produced. To investigate the magnitude of the effect of this anomaly on the results, runs 2, 6 and 8 were performed with collagen discs upside down, and the curves obtained were compared with curves obtained from other runs performed under identical conditions [but with the discs normally oriented], [Figure 4.1 1]. No excessive scatter resulted from th i s , and hence the effect was neglected. d) The power supply was subject to some isolated and re la t i ve ly fast changes in voltage. This was easily dealt with, although i t rendered useless some of the data obtained. The voltage changes were comparable in magnitude to those under normal conditions and thus were easi ly detected. Recall that cal ibrations of the chart recorder were carried out both before and after each weight sequence. If a voltage fluctuation was detected during any step of the weight sequence [Table 3.3.3.1], that step [for example, step 3] was discarded. Steps prior to the disturbance [steps 1 and 2 in our example] were referredto the f i r s t ca l ibrat ion, and steps after the disturbance [steps 4, 5 and 6] were refered to the end ca l ibrat ion. In * The half-times of most sequence runs at steps 5 and 6 were found to be large, and since data had not been taken for 5 t^, these runs were, d is -carded. 2 ( 45 the absence of a disturbance, beginning and end calibrations differed only s l ight ly. 4.2 Analysis The data obtained from the chart recorder were in the form of a series of curves [Figure A2.1.1.1]. These were reduced by means of a d ig i t -izer to a form suitable for computer analysis [Appendix 1]. Fitt ing the data to the model was done by computer [Appendix 2 ]. a) Chart recorder readings were converted to hydrations, and H H-HQ , a v was calculated for each point. A plot of In - q — v e r s u s time was generated i ~ o for each weight sequence [Figure 5.2.3.5]." The data for each weight step was f i t ted via a weighted, linear least-squares method [LSF; UBC-program "LQF"] Weighting of the LSF was held to be necessary because, although H, HQ and hL were known quite accurately, the error became particularly significant at values of H close to H . o The theory of the weighted linear LSF requires that points be weighted according to the inverse of the variance of each point (Carnahan et al_. (1969)). Since this was not known and also not measurable, i t was decided to use the inverse square of the absolute error of each point, as the best available approximation. This is a reasonable f i r s t approximation, since i t implies that the standard deviation of each point is proportional to the absolute error associated with that point. The weighted LSF package used returned values of both slope and intercept, and also the root-mean-square error associated with each. b) The value of the half-time, V>' for each weight step was G a l -'s culated, by linear interpolation, from the computer output. c) An average value for \ , of each weight step was calculated for each set of identical runs. 46 d) Output f i l e s containing values of time, weights for the LSF H-H and In „—u~ were truncated to f ive half-times and, after compensation for V H o equilibrium [Chapter 5.2.3], were plotted as functions of time for each weight step [Figures 5.1.1 to 5.1.10]. This was also done via a computer programme [Appendix 3.2]. e) Weighted LSFs were performed for each set of data produced in c) to determine D(H) for each sample at each weight step. Plots of D(H) as H.+H a function of H° = — ^ — w e r e prepared [Figure 5.1.11]. The value of dPs APs APS — ^ = H _ H was calculated for each weight step from Tables 5.1.2 to 5.1.6. f) The flow conductivity, k/n, for each weight step was also calcu-lated [Appendix 2.4.2]. A plot of k/n as a function of H° was also prepared [Figure 5.1.12]. 47 CHAPTER 5 RESULTS AND DISCUSSION 5.1 Results function of time were prepared for a l l experimental conditions tested: at 22, 29.5 and 35°C for sequence 1, and at 29.5 and 35°C for sequence 2. Of these, a representative cross-section is presented in Figures 5.1.1 to 5.1.10 for purposes of comparison. They include al l runs at 29.5°C and a l l runs with 40 g weights. [The time axis of each graph has been kept to 20 hours, regardless of the length of the run, to fac i l i ta te comparisons be-tween the graphs]. The goodness of f i t of the least squares f i t [LSF] performed for each run is indicated by the root-mean-square error associated with both the slope and intercept values l i s ted in Table 5.1.1. [Only data between tj and 5 t 5 was least squares f i t ted . The reasons for this are explained in Chapter 5.2]. It is clear from both the graphs and the errors l i s ted in Table 5.1.1 that the exponential model f i t s reasonably well in the region investigated at times between tj and 5 t1 . Values of D(H) and k/n were also calculated and plotted as func-H.+H tions of average hydration [H° - - ^ ^ ^ o r e a c n w e i 9 n t step [Figures 5.1.11 and 5.1.12, and Tables 5.1.2 to 5.1.6]. The plots show clearly that both D(H) and k/n are functions of hydration. The graphs also indicate that D(.H) and k/n at 35°C tend to be lower than at 22 and 29.5°C for any given H°. The implications of this are discussed below. Time (hours) FIGURE 5.1.1 Response of sample tested in sequence 1, 29.5°C, 30 g weight. o sample #6 A sample #12 + sampl e #14 x sample #15 0.0 4 .0 8 .0 1 2 . 0 ]6.0 20. Time (hours) FIGURE 5.1.2 Response of sample tested in sequence 1, 29.5 C, 40°g weight. \ Time (hours) ^ o FIGURE 5.1.3 Response of sample tested in sequence 1, 29.5°C, 50 g weight. o 1 I I 1 1 1 1 1 1 o 0 + sample #7 sample #12 o \ . + o re + \ . + CD \ ^ + CD \ + + + O \ * + + 0 zc 1 33, ^ ° . "~ 0 0 _ 1 CD \ . + + U CD \ . + + O + °CD \ . + + + — <s < D ? ° * * \ C D — 0 PO 1 1 1 1 1 1 1 1 1 T 1 1 1 1 1 I I I I r 0.0 4.0 8.0 12.0 16.0 20.0 Time (hours) cn FIGURE 5.1.4 Response of sample tested in sequence 1, 29.5°C, 60 g weight. 4 . 0 8 . 0 1 2 . 0 1 6 . 0 2 0 . 0 Time (hours) FIGURE 5.1.6 Response of sample tested in sequence 1, 35 C, 40°g weight. co o o © sample #8 A sample #9 + sample #10 i T - 1 1 n I i i i i I ' 0 . 0 4 . 0 8 . 0 1 2 . 0 1 6 . 0 2 0 . 0 Time (hours) FIGURE 5.1.7 Response of sample tested in sequence 2, 29.5°C, 40 g weight. o sample #8 A sample #9 + sample #10 x sample #11 0 . 0 1 1 1 8 . 0 .12.0 Time (hours) 1 T 4 . 0  . .  1 6 . 0 FIGURE 5.1.8 Response of sample tested in sequence 2, 29.5°C, 60 g weight. 20 CD O ©, sample #16 + sampl e #25 x sample #26 0 . 0 8 . 0 T 1 2 . 0 • 1 6 . 0 T Time (hours) FIGURE 5.1.10 Response of sample tested in sequence 2, 35°C, 40 g weight 20 . 0 cn 58 TABLE 5.1.1 Least Squares Fit For Hydration-Time Data Temp Weight Slope °C 9 hr i 22 30 - .389 ± .015 40 - .284 ± .009 50 - .179 ± .003 60 - .169 ± .003 29.5 30 - .443 ± .019 40 - .336 ± .006 50 - .170 ± .005 60 - .144 ± .008 35 30 - .352 ± .013 40 - .177 ± .008 50 - .171 ± .010 60 - .115 ± .003 Sequence Intercept No .188 ± .040 .201 ± .032 .180 ± .017 .191 ± .017 .451 ± .040 .439 ± .017 .427 ± .028 .597 ± .040 .489 ± .035 .428 ± .040 .745 ± .054 .488 ± .020 29.5 40 60 80 .450 ± .343 ± .135 ± .018 .014 .003 .470 ± .041 .446 ± .038 .070 ± .026 35 40 60 80 ,514 ± .062 .130 ± .010 ,079 ± .003 .772 ± .113 .687 ± .061 .361 ± .027 i 1—I 1 1— i — i I r x sequence 1, 22°C A sequence 1, 29.5°C A s e q u e n c e 1, 35°C v s e q u e n c e 2, 29.5°C T s e q u e n c e 2, 35°C x ^ V T X x A A x A v YA V A V X A X V A7 X X A X X X X A 7 * ' v v 1A • ' I I I I I L 1 1.5 2 3 4 5 6 8 10 Average Hydration, H° (g HfO/g collagen) FIGURE 5.1.11 Relationship of D(H) to average hydration, H°. CO I 0) c >> T J d -E O +-> o C o C_) 10 r10 8 x seq. 1, 22°C |- A seq. 1, 29.5°C A seq. 1, 35°C v s e q . 2, 29.°C T s e q . 2, 35°C J i 151-10 1.5h 10 121 T i—r • • V A A X & AA A A * A 1 X y A A * A V X A X V A T V x T V T V • • J 1 I I L 1.5 2 3 4 5 6 8 Average Hydration, H° Cg H2Q/g; collagen) 10 FIGURE 5,1.12 Relationship of k/n to average hydration, H' 61 TABLE 5.1.2 Model Parameters For 22°C, Sequence 1 Sampl e DW V 2 x l 0 3 30g 40g 50g 60g No. g cm2 H i H o H i Ho H. H H. H 1 0 1 0 2 .4353 2.326 5.04 4.51 4.54 3.92 3.97 3.47 3.50 3.12 3 .4760 2.781 4.61 4.19 4.22 3.68 3.72 3.27 3.31 2.96 5 .3994 2.355 4.56 3.96 4.00 3.43 3.46 3.05 3.07 2.76 Weight Run D(H)xl0 8 H° dP k/nxlO 1 1 g No. cm2/s g H20/g collagen cmVdyne-s 30 2 10.19 4.78 5538 6.19 3 12.18 4.40 6988 5.50 5 10.32 4.26 4892 6.49 40 2 7.435 4.23 4734 4.82 - 3 8.889 3.95 5435 4.76 5 7.527 3.72 5149 4.07 50 2 4.699 3.72 5870 2.23 3 5.618 3.50 6522 2.29 5 4.757 3.26 7159 1.68 60 2 4.419 3.31 7724 1.46 .3 5.283 3.14 8386 1.55 5 4.474 2.92 9468 1.11 62 TABLE.5.1.3 Model Parameters For 29.5°C, Sequence 1 DW V 2 x l 0 3 30g 40g 50g No. 9 cm2 H i H 0 H. l H 0 H. V H 0 6 .3994 1.958 4.76 4.23 4.16 3.78 3.76 3.50 7 .4184 2.149 4.65 4.04 * 12 .3793 1.766 4.46 3.79 3.75 3.34 14 .4590 2.586 4,01 3.65 3.64 3.26 2.24 2.80 15 .4083 2.046 4.24 3.62 3.60 3.15 3.07 2.68 60g H. H 3.13 2.90 2.95 2.72 Weight 30 x 40n 50 60^ Run D l l T x l O 8 dP. k / n x l O 1 1 No. cm2/s g H 20/g collagen dH cmVdyne-s - av 6 9.771 4.50 5538 5.66 7 10.72 4.35 4811 6.97 12 8.813 4.13 4381 6.05 14 12.90 3.82 8153 4.50 15 10.21 3.93 4734 6.25 6 7.415 3.97 7724 2.80 7 8.139 12 6.688 3.55 7159 2.51 14 9.794 3.45 7724 3.34 15 7.749 3.38 6522 3.08 6 3.739 3.63 11288 9.05xl0_ 1 7 4.104 12 3.372 14 4.938 3.02 6670 1.78 15 3.907 2.88 7526 1.20 6 3.181 7 3.492 3.02 12761 6.56xl0_ 1 12 2.869 2.84 12761 5.17xl0_ 1 14 4.202 15 3.324 * Blanks are l e f t where runs were discarded due to voltage supply fluctuations or other errors. [Chapter 4.1] 63 TABLE 5.1.4 Model Parameters for 35°C, Sequence 1 iample DW V 2 x l 0 3 3 0 9 4 0 9 50g 60g No. g cm2 R._ H H • H 0 1 0 H i H 0 H. H 1 0 19 .4041 2.004 5.16 4.57 4.49 3.83 3.77 3 .35 3.36 3.03 20 .3940 1.954 5.18 4.53 4.53 3.89 3.94 3 .44 3.47 3.14 21 .3838 1.904 5.34 4.83 4.15 3 .59 22 .3921 1.945 5.33 4.68 4.56 3.95 3.92 3.47 3.43 3.10 24 .4200 2.083 5.30 4.75 4.61 3.90 3.85 3 .03 ieight Run D(H)xl08 H° dP s k/nxl0" g No. cm2/s g H20/g collagen dH cm iVdyne-s 30 ia 7.952 4.87 4975 5.46 20 7.754 4.86 4515 5.85 21 7.555 5.09 5755 4.64 22 7.718 5.01 4515 5.97 24 8.266 5.03 5336 5.42 40 19 4.000 4.16 4447 2.72 20 3.900 4.21 4586 2.59 21 3.800 22 3.882 4.26 4811 2.48 24 4.158 4.26 4134 3.10 50 19 3.865 3.56 6988 1.49 20 3.768 3.69 5870 1.78 21 3.672 3.87 5241 2.01 22 3.751 3.70 6522 1.59 24 4.017 3.44 3579 2.95 60 19 2.593 3.20 8894 7.28xl0- 1 20 2.528 3.31 8894 7.27X10"1 21 2.464 22 2.517 3.27 8894 7.17X10"1 24 2.695 64 TABLE .5.1.5 Model Parameters For 29.5°C, Sequence 2 Sampl e No. DU 9 V 2 x l 0 3 cmz 8 .4061 2.024 9 .3847 1.817 10 .4325 2.296 11 .3832- 1.802 4.49 5.12 4.55 4.48 40g H o 3.34 4.04 3.33 3.41 60g 80g H 0 H i H o 3.13 2.71 2.69 2.39 3.78 3.42 3.27 2.97 3.04 2.59 2.06 1.89 3.21 2.87 2.78 2.37 Weight Run g No. 40 60 80 8 9 10 11 8 9 10 11 8 9 10 11 DlrTTxlO8 cm2/s 10.25 9.202 11.63 9.126 7.811 7.012 8.860 6.954 3.065 2.751 3.477 2.729 H° g H20/g collagen 3.92 4.58 3.94 3.95 2.92 3.60 2.82 3.04 2.54 3.12 1.98 2.58 dP^ dH 5104 5435 4811 5486 13976 16306 13044 17265 19567 19567 34529 14317 k/nxlO" cmVdyne-s 5.81 5.51 7.02 4.84 1.31 1.17 1.55 9.70X10"1 3 . 3 4 X 1 0 " 1 3.45X10"1 1.84x10"! 4.11x10"! 65 TABLE .5.1.6 Model Parameters For 35°C, Sequence 2 Sam pi e DW V 2 x l 0 3 40g 60g 80g No. g cm2 H i Hrt H. H 0 1 o H i H o 16 .4262 2.230 5.37 3.91 3.61 2.75 18 .4054 2.017 3.86 3.14 3.13 2.59 25 .4126 2.090 5.53 4.45 4.17 3.48 3.38 2.84 26 .4020 1.984 4.87 3.57 Weight Run D(.H)xlO H° k/nxlO 1 1 g No. cm2/s g H20/g collagen dH cm^/dyne-s 40 16 12.91 4.64 4021 10.6 18 •- 11.68 25 12.10 4.99 5435 7.74 26 11.49 4.22 4515 7.78 60 16 3.264 3.18 6826 1.19 18 2.953 3.50 8153 0.964 25 3.059 3.83 8507 1.02 26 2.904 •5-' . 80 16 1.972 18 1.784 2.86 10870 0.379 25 1.849 3.11 10870 0.416 26 1.755 66 5.2 Discussion 5.2.1 Se-YiAsOLLvAAy ofi the. ModeZ to H^: The model is moderately sensitive to the value of H Q . Although i t was not possible - due to time constraints - to carry out runs to equilibrium, i t was fe l t that consistency in application of the model would s t i l l allow useful conclusions to be drawn from the data. This was accomp-lished as described in sections 5.2.2 to 5.2.4. 5.2.2 Slgyvi^Xjcanaz Ojj the. hoJL^-tme.'. . H-H By def in i t ion the half-time, t, , occurs at the point where T J — n — = * V H o 0.50. Because the runs were not carried out to equilibrium, H Q could not be determined exactly. This did not greatly affect the value of t } because in a l l cases tj occurred during the steep portion of the response curve. The half-time is d i rect ly related to the time constant, x , of the model. Recall that H H 8 - W t / 4 f 2 1 0 Bearing in mind the def init ion of t^, manipulation of equation 2.2-7 results in 4 V 2 K K -h = 1 _ 5.2.2-1 TT^DTHJ l n ( \ ) - In 0.5 0.4831 TT Insertion of equation 5.2.2-1 into 2.2-7 gives 67 H-H 0 -0.4831t/V £ - = — r e 5.2.2-2 H.-H i o The time constant, T , is defined by H-H 8 •t /x and, therefore, x = 2.07 ^ . 5.2.3 Compe.vi-cuU.on faon. EgvULibfuixm It can be seen from equation 5.2.2-2 that the hydration rapidly approaches i t s f inal value, H . This is shown below: time H-H 0 ! H " H 0 H r H o H i " H o K 'a 0.500 0.500 2 K 0.308 0.692 3 t. 0.190 0.810 4 V "2. 0.117 0.883 0.072 0.928 6 t. h 0.045 0.955 etc. In other words, by the time five half-times have elapsed, the response should be 92.8% complete. In fact, only data upto 5 tj was considered, for practical reasons noted below: 68 a) Considering that average half-times ranged from 0.75 to 4.5 hours [Table A.2.2.1], and were as great as 8 hours for individual runs, i t was not possible to carry out tests to equilibrium. An element of creep [see below] noted in the response of the samples complicated matters even further. b) Experimental time had to be kept to a minimum to avoid loss of data due to irregularit ies in the voltage supply [Chapter 4.1]. The true value of H was calculated from that measured at the end o of five half-times as follows: H. - (H ) , (H) = H. - ( 1 0 ° 9 2 g e a S U r e d ) 5.2.3-1 true H-H This was possible due to the linear relationship between In ( u _^ ) and time. i o The effect of this truncation of data and the subsequent application of equation 5.2.2-1 is shown in Figures 5.2.3.1 to 5.2.3.4, which represent sample #10 [sequence 2 at 29.5°C] with data shown for 5, 6 and 7 half-times, and for 5 half-times with equation 5.2.3-1 applied. The modification is in part vindicated by the results: the plots show progressive l inearization when carried on for longer times, as the model would predict. In some of the few runs carried out to beyond 7 tj , hydration continues to decrease with time beyond the predicted value, and this indicates that creep becomes significant as the hydration curve flattens out. Sample #10 is one of these H-H runs, and a plot of ln Cu _^ ) versus time, before compensation by equation i " o 5.2.3-1, is shown in Figure 5.2.3.5. The curves for 40, 60 and 80 g weights l i e close together, and this is not surprising - time scaling cuts off the creep component before i t becomes significant and causes separation of the curves. That creep should occur is also to be expected, since soft tissues are known to be non-linear, viscoelastic materials. [However, few invest i -0 0 4 . 0 8 . 0 1 2 . 0 1 6 . 0 2 0 . 0 Time (hours) FIGURE 5.2.3.1 Relationship of dimensionless hydration and time (cut off at 5 t, ) for sample #10. 0.0 4.0 8.0 12.0 16.0 20.0 Time (hours) FIGURE 5.2.3.2 Relationship of dimensionl ess hydration and time (cut off at 6 t1 ) for sample #10. 0 . 0 4 . 0 8 . 0 1 2 . 0 1 6 . 0 2 0 . 0 Time (hours) FIGURE 5.2.3.3 Relationship of dimensionless hydration and time (cut off at 7" tj,) for sample #10. i 1 1 r 0 . 0 4 . 0 8 . 0 1 2 . 0 1 6 . 0 2 0 . 0 ; Time (hours) FIGURE 5.2.3.4 Relationship of dimensionless hydration and time (cut off at 7 tj_) for sample #10, and compensated for H Q. 2 T 0 . 0 4 . 0 B .O 1 2 . 0 1 6 . 0 2 0 . 0 Time (hours) FIGURE 5.2.3.5 Relationship of dimensionless hydration and time (unsealed for time) for sample #10. 74 gators have attempted to formulate non-linear models to describe their behaviour]. The creep effect would be masked at shorter times by the re lat ive ly steep nature of the hydration curve in that region. No attempt is made in this paper to quantify the creep term, but an attempt was made to determine whether creep also occurs in runs performed for only 5 t, . This involved recalculation of t, by means of equation 5.2.2-1, which is rewritten as • (0.4831)(V*) S m 2 M H TT2 • D W The values of ^ 2 and DCH) are known for each sample [Tables 5.1.2 to 5.1.6] and were calculated by curve f i t t i n g the hydration-versus-time graphs. Results of this recalculation are presented in Table 5.2.3.1. In nearly every case the recalculated t, is higher than the original value by 8 to 32%. This is to be expected in the case of creep because the modified HQ is s t i l l higher than the H produced at the "end" of creep, and therefore t : wi l l tend to be underestimated. 5.2.4 kcc.aA.acy ofa the. ModeZ Consider now whether the approximation made to obtain equation 2.2-4 is ju s t i f i ed for time greater than t1 . The solution to the boundary value problem [Chapter 2] as given by Crank (1975) i s : H -H. 1 TT 2n+l e c o s 2*' 2 ' 2 " 3 n=0 TABLE 5.2.3.1 Comparison Between Original and Recalculated Values o f t , 4g Sequence Temp Weight tt t t , Recalculated No. °C g "2 '2 hr hr 22 30 .1.14 1.24 40 1.56 1.70 50 2.46 2.69 60 2.61 2.86 29.5 30 0.95 1.09 40 1.22 1.44 50 2.15 2.85 60 2.97 3.35 35 30 1.20 1.37 40 2.30 2.72 50 2.40 2.82 60 3.20 4.20 29.5 40 0.99 1.07 60 1.29 1.41 80 3.79 3.59 35 40 0.75 0.94 60 2.58 3.72 80 4.49 6.15 76 L e t M L l i ^ k . Then 4 V 2 H-H. 4 TTIJ) -kt ^ 3THJJ -9kt 5mjj -25kt n - = 1 - - Ccos^-r e - cos^-r e + -F COS-OTT e - ...) H^HT " 1 " TT ^ 2 * ' c 3 " u ° 2 ^ ' c ' 5 v u a2,|, 5.2.4-1 Not that for n>l, the exponential term causes rapid decay - the second term is only ^ — r = 0.03% of the f i r s t , for any given value of e " 1 The approximation made [Chapter 2] was H-H. -kt , 1_ _ i 1 rr._TjjL_ 2 2-4 H-H. TT C 0 S 2 ^ ' . c - c * Both 2.2-3 and 2.2-4 were integrated over $ from 0 to V » a n d the results are presented below [note J*cosax.dx = j sinax] : „ -kt , -9kt . -25kt Hav = H o + ( H i " H o ) ( e + i e + k e + S - 2 - 4 " 1 for the rigorous case, and ft -kt H = H + (H.-H ) \ e 5.2.4-2 av o i o TT for the approximation. The approximation is acceptably accurate f o r t > \ [Table 5.2.4.1]. 77 TABLE 5,2,4.1 Errors Due to Approximation to the Model Time (H-H0)/(Hi Approximation -Ho). Rigorous Deviation % K .5000 .5012 0.23 1/2 t p .6366 .6469 1.62 1/4 t .7183 .7503 4.45 1/8 t .7631 .8234 7.91 1/16 t. .7685 .8741 11.14 Linear least squares f i t s were therefore done only for data points at t > t, V 5.2.5 vaUcLUy oj VW The diffusion coeff ic ient, D(.H), was defined by Bert as = 4~ Sn(H) • 2.1-13 3t 3ijj I v • 3^ ' An average diffusion coeff ic ient, D(H), was then defined by assuming D(H) to be a weak function of hydration over the hydration range in question: ft ' f = TJITO • 2.1-14 This assumption is just i f ied for most of the data, i f one assumes that the trend of D(H) values shown in Figure 5.1.11 also holds good for D(H). For example only for data in sequenced at 35°C, and for step 1 at 29.5°C, does D(H) change by more than ^30% over the hydration range [H. to HQ] in question. Bearing in mind the large scatter inherent in biological 78 data, the assumption of weak dependency is acceptable for any given weight step [D(H) does not vary more than <30% for most weight steps]. The assumption breaks down for those cases;, mentioned above, in which D(H) may have changed by ^70% or more during the course of the experiment. 5.2.6 Thz Relcvtiomhlp oj VIH\ and k/n to Hydnxition Both D(H) and k/n tend to be moderately strong functions of hydra-t ion in the hydration range investigated [Figures 5.1.11 and 5.1.12]. In both cases, data points for 22 and 29.5°C are nearly inseparable, whereas data for 35°C tends to give lower values of D(H) and k/n for any given hydration. This effect is more pronounced at low hydrations. The dependency of DCH) and k/n on hydration is to be expected be-cause as the hydration decreases the area available for f lu id transport is reduced due to compaction of the collagen f ibres. This wil l cause a de-crease in flow conductivity. ; .'• ,' The shift due to high temperature is more d i f f i c u l t to explain. Two possible explanations for this are: a) The breakdown of the assumption of weak dependency for sequence 2 data at 35°C [section 5.2.5] may cause underestimation of D(H) and k/n. It is l i ke l y that the bulk of f lu id transport occurs quite quickly [ i .e . while the value of D(H) is s t i l l re lat ively.high]. Any averaging process based on i n i t i a l and f inal values of D(H) is therefore l i ke l y to under-estimate D(H) or k/n-b) 35°C is quite close to the denaturation temperature of soluble collagens. It is quite conceivable that some unravelling of the collagen t r i p l e helix occurs during the experiments [Chapter 1.4]. This denatura-tion does not involve the breakage of peptide bonds, but only of weaker hydrogen bonds and bonds involving Van der Waal's forces - i . e . the individual 79 chains may separate but wil l not chemically degenerate. The physical un-ravel l ing of collagen molecules wil l cause a decrease in the area ava i l -able for f lu id transport, and thus lower D(.H) and k/n. This effect wi l l be independent of hydration. The second of the two explanations i s , in fact , the more l i ke l y . If the f i r s t effect predominated, one would expect the shift to be most pronounced for step 1 than for subsequent steps [hydration changes most during the i n i t i a l weight steps]. This is not the case. If, however, collagen was indeed degenerating at 35 C, one would expect the effect to be more pronounced for steps 2 and 3, because collagen molecules would then have had more time to unravel. A close look at figures 5.1.11 and 5.1.12 shows that this is indeed the case. Values of k/n obtained in this study range from 3.6x10" 1 2 to 2x10 " 1 1 cmVdyne-s at H°=3.0. These figures may be compared with values, obtained by Bert, of 0 .9x l0~ 1 2 , 3 x l 0 " 1 3 and 5 x l 0 " 1 3 cmVdyne-s for human skin, steer corneal stroma and rabbit corneal stroma, respectively. Bert also found k/n for human spinal discs to be ^8xl0~ 1 2 cmVdyne-s, for a subject of age 50 years at death. Note that the samples tested by Bert were a l l natural t issues, and hence structured and constituted d i f ferent ly from the collagen samples tested in this study. 80 CONCLUSIONS 1) The f lu id transport-based model considered in this study, describes collagen behaviour adequately for small changes in hydration, and within certain l imits [see below].' 2) Both D(H) and k/n are moderately strong functions of hydration in the hydration range investigated. 3) The behaviour of collagen under compression at 22 and 29.5°C is essentially the same. Some breakdown of collagen is the l ike ly cause of changes in collagen behaviour at 35°C. 4) A creep component in the response of collagen was noticed. This l imits appl icabi l i ty of the model to conditions under which the hydration changes relat ively rapidly - that i s , at times less than 5 ^ . 81 RECOMMENDATIONS FOR FURTHER WORK The model is promising, and further investigation of the be-haviour of collagen in isolation and in combination with proteoglycans and elastin is called for. The following recommendations are made: 1) Attempts should be made to investigate the effects of smaller hydration changes on D(H) and k/n- ' This would cal l for a reduction in the range of hydration studied [increasing chart recorder sensit iv ity would necessarily decrease the range] but will probably reduce scatter. 2) The behaviour of samples tested at 35-40°C should show whether the reduction of D(H) and k / n at 35°C i s , in fact, due to the denaturation of tropocollagen. 3) Securing a constant voltage supply would increase the accuracy of data. 82 NOMENCLATURE Only those symbols used in the main text of the thesis and Appendices are defined here. Symbols used in the equations or figures of other authors quoted are defined in the particular section in which they occur. A area (cm2) dm differential mass of dry membrane (g) dm differential mass of water in dm (g) w ^ ' D(H) diffusion coefficient (cm2/s) D(H) average diffusion coefficient (cm2/s) DW dry weight of membrane (g) f convective flux (g/cm2-s) fj diffusive flux (g/cm2-s) f flux in the x-direction (g/cm2-s) X H hydration at a point (g H20/g collagen) H +H. H° average hydration, ° ? 1 (g H20/g collagen) H-H. H dimensionless hydration, TT— r r -V H i H average hydration [integrated] (g H20/g collagen) av H.j init ia l hydration (g H20/g collagen) HQ final hydration (g H20/g collagen) k/n flow conductivity (cmVdyne-s) P s swelling pressure (dynes/cm2) t, half-time (hours, seconds) T sample thickness (cm) x space variable NOMENCLATURE (CONTINUED) density of collagen (g/cm3) ratio of water to collagen densities, y/6 C(eH -eH )/(H.-H o))xlOO* error associated with measured hydration Cg H20/g collagen) error associated with initial hydration (g H20/g collagen) error associated with final hydration (g H20/g collagen) CCeH+eH ) / (H -H o))xl00% £ T + eB density of water (g/cm3) thickness of dry material from 0 to x, 7 7 (cm) o M value of i|> at surface of sample (cm) density of water (g/cm3) time constant (seconds) 84 REFERENCES 1. Alexander, H. and Cook, T.H., J . Invest. Derm., 69, 310 (1977). 2. Aubert, X. quoted by Wilkins, E. and Pinder, K.L., Physiol. Chem. and Phys. II (1979). 3. Bert, J . , Ph.D. Dissertation, UCLA, Berkeley (1970). 4. Carnahan, B., Luther, H.A. and Wilkes, J.O., Applied Numerical Methods, John Wiley and Sons, New York (.1969). 5. Chapman, J.A., quoted by Fietzek, P.P. and Kiihn, K., in Ha l l , D.A. (ed.), The Methodology of Connective Tissue Research, Academic Press, New York (1976). 6. Chapman, J.A. and Hardcastle, R.A., quoted by Fietzek, P.P. and Kiihn, K., in Ha l l , D.A. (ed.), The Methodology of Connective Tissue Research, Academic Press, New York (1976). 7. Crank, J . , The Mathematics of Diffusion, Clarendon Press, London (1975), 8. Danielson, D.A., J . Biomechanics, 6_, 539 (1973). 9. Diamant, J . , Kel ler, A., Baer, E., L i t t , M. and Arridge, R.G.C., Proc. R. Soc. Lond. B., 180, 293 (1972). 10. Dick, J .C . , J . Physiol., U 2 , 102 (1951). 11. Dulbecco, R. and Vogt, M., J . Exper. Med., 99, 167 (1954). 12. Einbinder, J . and Schubert, M., J . B io l . Chem., 188, 335 (1951). 13. Elden, H.R., Biochem. Biophys. 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J . , 56, 558 (1954). 27. Hayes, W.C. and Bodine, A . J . , J . Biomech., 11, 407 (1978). 28. Holmes, J.H., Robinson, D.W. and Ashmore, C.R., J . Anim. Sc i . , 3_5, 1011 (1972). 29. Jackson, D.S., Biochem. J . , 65, 277 (1957). 30. Jamison, C.E., Marangoni, R.D. and Glaser, A.A., Trans. ASME, 90, 239 (.1968). 31. Kennedi, R.M., Gibson, T., Evans, J.H. and Barbenel , J .C. , Phys. Med. B io l . , 20, 699 (1975). 32. Lowther, D.A., in Hal l , D.A. and Jackson, D.S. (eds.), International Review of Connective Tissue Research , Volume 1, Academic Press, New York, Volume 1, Academic Press, New York, (1963). 33. Mooney, M., J . Appl. Phys., 11, 583 (1940). 34. Nomura, S., Hi ltner, A., Lando, J.B. and Baer, E., Biopolymers, 16_, 231 (1977). 35. Parsons, J.R. and Black, J . , J . Biomech., 1£, 21 (1977). 36. Prockop, D.J., Kivirikko, K.I., Tuderman, L., and Guzman, N.A., N. Engl . J . Med., 301,, 13 (1979). 37. Ramachandran, G.N. and Kartha, G., Nature, 17_6, 539 (1955). 38. Rich, A. and Crick, F.H.C., Nature, 17_6, 915 (1955). 39. Ridge, M.D. and Wright, V., Br i t . J . Derm., 77, 639 (1965). 40. Robins, S.P., Shimokomaki, M. and Bailey, A . J . , Biochem. J . , 131, 771 (1973). 86 41. Sakata, K., M.A.Sc. Thesis, .The University of Brit ish Columbia, (1969). 42. Schubert, M. and Hamerman, D., A Primer on Connective Tissue Biochemistry, Lea and Felsiger, New York (1968). 43. Schwartz, N.J., Mackay, R.S. and Sackman, J .L . , Bul l . Math. Biophys., 28, 585 (1966). 44. Scott, J .E . , Chem. in Gr. Br i ta in, 15_, 13 (.1979). 45. Van Duzee, B., J . Invest. Derm., 7l_» 140 (1978). 46. Veis, A., The Macromolecular Chemistry of Gelatin, Academic Press, New York (1964). 47. Veronda, D.R. and Westmann, R.A., J . Biomech., _3, 111 (1970). 48. Vi idik, A., in Hal l , D.A. and Jackson, D.S. (eds.), International Review of Connective Tissue Research, Volume 6, Academic Press, New York (1973). 49. Weissman, R.C. and Coeks, G.G., Reprint (1980). 50. Wilkins, E. and Pinder, K.L., Physiol. Chem. and Phys., 11, .23 (1979). 87 APPENDIX 1 EQUIPMENT 1.1 Linear Displacement Transducer The l inear displacement transducer used [Crescent Technology Corporation, Model ZD25] was a variable permeance transducer which produced an a.c. current proportional to the probe displacement from the null position. 1.2 Carrier Amplifier The amplifier used [Crescent Technology Corporation, Model 85-N-4] was a transistorized carr ier amplif ier, with a maximum output of 10V d.c. A maximum gain [setting 100] was used throughout the experiments. 1.3 Strip Chart Recorder The s tr ip chart recorder used [Watanabe Servocorder, Model SR652] was operated with an input sens i t iv i ty of 5 volts/chart width and a chart speed of 30 mm/min. 1.4 Recirculating Constant Temperature Bath The constant temperature bath [Colora, Model K] had an effective range of -30°C to +150°C, with a tolerance of ±0.02°C. 1.5 Centri fuge The centrifuge used [International Equipment Company, Universal 88 Model UV] was outfitted with a swing tube head {8 tubes] and tube holders for tubes of 1" O.D. Rotational speeds of 5000 rpm could be reached with this head. 1.6 Blender An ordinary kitchen blender [Osterizer, Model "Galaxie"] was used with 1 cup and 4 cup jars. 1.7 Digitizer Numerical data was obtained from the skip charts by means of a d ig i t izer [Talos] which was accurate to ±0.001 inches. 89 APPENDIX 2 SAMPLE CALCULATIONS* 2.1 Calculation of Hydration 2.1.1 VeXeAmZncution oft Sample. TkLcknzAA The thickness of collagen samples was determined by l inear inter -polation between the calibration: points immediately above and below the data point in question [Fig. A2.1.1.1]. , 2.1.2 VeXeAnu-ncution o{, HydfitxtLon The average hydration of the sample at any given time was determined by equation 2.2-8 which is reproduced below: H Ap T 1 w 2.2-8 av DW " 6 where A is the x-sectional area of the sample, cm2 DW* is the dry weight of the sample T is the thickness of the sample, cm * Dry weight was determined by drying at 40PC for 36 hours. 91 2.1.3 Elastic Rz£>povu>2. jon. Sequence. 2 CUAVQA An "e las t i c " component become signif icant in sequence 2 response curves. This may have represented a real elast ic component or merely have been a response to the manner in which weights were applied to the sample, or can be partly due to quick expression of surface water. Because the size of this component showed no consistent pattern, and was always re lat ive ly small, i t was simply ignored. That i s , the i n i t i a l hydration point, H Q , was considered to occur at the end of the elast ic response. The elast ic response was not noticeable for sequence 1 runs. 2.2 Calculation of the Half-Time H-H The half-time, by def in i t ion , occurs at ln(,„ ) [Chapter 5.2.1]. i ~ o Once thickness and hydration calculations were completed, t t for each weight step could be calculated. Half-times calculated for individual steps were averaged for each step in each set of indentical runs [Table A2.2.1], and this figure was used in further calculations. A typical plot H-H of l n - f n — n — ) for a sample, before scaling to 5 t 5 , is presented in Figure V o * 5.2.3.5. 2.3 The Least Squares Fit The computerized least squares f i t package, LQF, available at the University's computer centre, was used for f i t t i n g data. Calculation of weights was done as follows: i) The chart reading and i ts associated error (±0.1%) were con-verted into a hydration and error according to equation 2.2-8. H-HQ i i ) Error terms were combined to give the error in r j — r r as H i " H o shown below. 92 TABLE A2.2.1 Average Half-Times (error figures are root mean square errors). Sequence No. Temp. °C Weight Average Half-Time g hr. 1 22 30 1.14 ± .30 40 1.56:+ .26 50 2.46 ± .25 60 2.61 ± .09 30 30 0.95 ± .36 40 1.22 ± .22 50 2.15 ± .37 60 2.97 ± .50 35 30 1.20 ± .38 40 2.30 ± .39 50 2.40 ± .97 60 3.20 ± .09 2 30 40 0.99 ± .22 60 1.29 ± .47 80 3.79 ± 2.16 35 40 0.75 ± .29 60 2.58 ± 2.42 80 4.49 ± 1.68 93 The percentage errors eH + £H e T H - H o °- x 100% A2.4-2 £ H. + eH and eR = ^ - H ° x 1 0 0 % A2.4-3 i " o were then added to give Hence, we have H ± eH - H o ± H - HQ H - H 0 — = 1 7 — u ± e„ Cu _ u ) A2.4-5 H i ± £ H . - H ± e u H i - H o " t % V H i - H o l O HQ Or, substituting f i c t i t i ous numbers H = 4.5, HQ = 4.0, H.. = 5.0 and e M ± 0.005, 4.5 ± .005 - 4.0 ± .005 _ 0.5 ± 0 . 0 1 _ n r . n n q R 5.0 ± .005 - 4.0 ± .005 " 1.0 ± 0.01 " u ' ° " U " U 1 3 When logs are taken, i t is somewhat more d i f f i c u l t to calculate the absolute error. The method used was to calculate ln(0.5 + 0.015) and ln(0.5 - 0.015), 94 and calculate the larger deviation from lnt0.5). The inverse square of this value was then used as the weight for the point. ln(0.515) = - .664 deviation = .029 ln(0.5) = - .693 deviation = .031 ln(0.485) = - .724 weight = L-fifiY = 1040 2.4 Calculation of Model Parameters 2.4.1 The. V l l l u u - l o n C o z ^ X j c L z Y i t The diffusion coef f ic ient , D(H), for each weight step, was calculated from lumped data for i d e n t i c a l runs, by using the relationship expressed in equation 2.2-7. This can be rewritten as: H-H dOnyr^-) DIHJTT2 1 ° " I n ^ - ^ r r ^ A2.4.1-1 dt IT 4<j,' : H-H dCln^J-) DUiT = ^ ( l n § 7 - I T 2 - * A2.4.1-1 H-H H-H where d(ln,, _° ) is simply the slope of the graph of 1n( H _ H ) plotted as a i ~ o i o dt function of time. The values of D(H) calculated here considered to apply H.+H _ at H° = \ .. Values of D(H) are shown in tables 5,1.2 to 5.1.6. 2.4.2 T h z Flow C o n d u c t i v i t y The flow conductivity at each value of H° was calculated by means 95 of equation 2.1-12, rewritten below: D ( H ) ^ n dP s/dH A2.4.2-1 dP Values of -rrr- were approximated by segmented slopes dn dP AP ' _ _ i «b s A2.4.2-1 dH H o-H. where A P s = 2935 dynes/cm2 for sequence 1 = 5870 dynes/cm2 for sequence 2 Calculated values of - are presented in tables 5.1.2 to 5.1.6, n APPENDIX 3 COMPUTER PROGRAMS APPENDIX 3 .1 : Program f o r c a l c u l a t i o n and p l o t t i n g of d1 mens 1 on 1 e s s h y d r a t i o n c u r v e s f o r I n d i v i d u a l samples . REAL TH(150 ) ,PC I (150 ) ,PCE (150 ) .DT I (150 ) ,DPC (150 ) . 1DTH I (150 ) ,DTHE (150 ) ,PP (2 ) /0 .0 ,0 .0 / ,PXX (150 ) ,PYY (150 ) 1 ,TTH(150) ,H (150) ,LHAVE(150) ,T IME(150) ,PX (150) ,PY (150) 1,A,TMAX,DW,DOT,EBOT,R/-5.0/,0TH(6) DIMENSION B C D ( 2 0 ) , Y F ( 1 5 0 ) . W T ( 1 5 0 ) , E 1 ( 2 ) , E 2 ( 2 ) , X ( 1 5 0 ) , Y ( 1 5 0 ) 1 , DELH(150) ,DY(150) ,ET0P(150) ,EPCT(150) ,HPLUAV(150) ,HMINAV(150) COMMON MM,BCD INTEGER 0/1/ ,SYM(6)/1,2,3.4,5,6/ ,W,W1,W2,W3.WW,RX(150)/150*0/ 1.DRIFT,00 READ(5,1,END=103)MM,NI 1 F0RMAT(3I5) R E A D ( 5 , 36 ) (OTH( I ) , I =1 ,6) 36 F0RMAT(6F4.2) READ(5,2)EPS 2 F0RMAT(E8.4) C C C THE FOLLOWING COMMANDS DREAD IN THE TITLE OF THE GRAPH OF LHAVE/TIME C TO BE PLOTTED, AND 2)PL0T THE AXES, AXIS LABELS,AND T ITLE . C C READ(5,403)BCD WRITE(8,403)BCD 403 FORMAT(20A4) CALL PLTAX CALL OUTLAB READ(5 ,6)N,TMAX,A,DW 6 F O R M A T ( 1 2 , 2 X , F 5 . 1 , 2 X , F 6 . 4 , 2 X , F 6 . 4 ) D020 1=1,N READ(5,10) T H ( I ) , P C I ( I ) . P C E ( I ) 10 F 0 R M A T ( F 4 . 3 , 2 X , F 4 . 1 , 2 X , F 4 . 1 ) 20 CONTINUE READ(5, 1 1)DOT 11 FORMAT(F4. 1 ) 101 L=0 D030 K=1,150 READ(5,21) DT I (K ) ,DPC(K) ,DY(K) 21 F0RMAT(G9.3 ,G9.3 ,2X ,F4 .2 ) I F ( ( D T I ( K ) - D T I ( 1 ) ) . L T . ( 5 * 0 T H ( 0 ) ) ) G O T O 77 I F (L .GT .O )G0T0 77 L=K-1 77 I F ( D T I ( K ) - 9 0 0 . ) 3 0 , 7 6 , 7 6 76 I F ( L .GT .O )G0T0 52 L = K-1 GOTO 52 APPENDIX 3.1: ( C o n t i n u e d ) 30 CONTINUE 52 READ(5,23)DRIFT 23 FORMAT(11) DOT=DTI( 1 ) d = 0 DO 34 KK= 1 ,L IF(DPC(KK) .GT.DPC(L))GOTO 34 DPC(L)=DPC(KK)-0.01 34 CONTINUE 50 1 = 1 d = d+1 31 IF (DR IFT.GT.O)PC I ( I )=PCE( I ) I F (DPC (J ) - P C I ( I ) ) 3 3 , 3 3 . 3 2 32 1=1+1 GOTO 31 33 DTHI (d)=TH( I -1) + ( (DPC (J ) -PC I ( I - 1 ) ) / ( P C I ( I ) - P C I ( I - 1 ) ) ) * . 025 DTHE(J )=TH( I - 1) + ( ( D P C ( J ) - P C E ( I - 1 ) ) / ( P C E ( I ) - P C E ( I - 1 ) ) ) * . 025 IF(DRIFT.GT.O)GOTO 24 TTH(d)=DTHI(d) GOTO 25 24 TTH( J ) =DTHE (d) 25 H (d )= (A*2 .54*TTH(d ) /DW) - .7409 DELH(d )= (DY (d ) /DPC(d ) ) *H (J ) I F ( J - L ) 5 0 . 5 1 , 5 1 51 M=L-1 H X = H ( 1 ) - ( H ( 1 ) - H ( L ) ) / . 9 2 8 EBOT=DELH(1)+DELH(L) A1=ABS(H(1)-HX) Z= 1 D099 d=1,M A2=ABS(H(J)-HX) LHAVE(d)=AL0G(A2/A1) 95 I F ( A 2 - D E L H ( d ) ) 9 1 , 9 1 , 9 6 91 DELH(d)=A2-.001 96 ETOP(d)=DELH(d)+DELH(L) EPCT (J )= ( ( ET0P (d ) /A2 )+ (EB0T /A1 ) ) * (A2 /A1 ) HPLUAV(d)=AL0G((A2/A1)+EPCT(d)) I F ( ( (A2 /A1 ) - E P C T ( d ) ) - 0 . )93,93,94 94 HMINAV( J)=ALOG( (A2/A1 )-EPCT(<J) ) GOTO 97 93 HMINAV(«J) = -100. 97 PYY(d)=2*LHAVE(J)+6.0 I F ( LHAVE ( d ) '. LT . R )RX ( d ) = 1 I F (RX (d ) .GT .0 )G0T0 98 PY(Z)=PYY(d) ^ 00 APPENDIX 3 .1 : ( C o n t i n u e d ) Z = Z+1 W1=Z 98 TIME(d)=DTI(d)-DOT WR ITE (7 ,55 )T IME (d ) ,TTH(d ) ,H (d ) . LHAVE (J ) 55 FORMAT(4X.F4. 1 , 8 X , F 5 . 3 , 9 X , F 4 . 2 , 8 X , F 6 . 3 ) P X X ( d ) = ( ( T I M E ( J ) - 0 . 0 ) / 2 . 0 ) I F (T IME (d ) .GT .20 .0 )G0T0 99 I F ( RX(J).GT.O)GOTO 99 PX(Z-1)=PXX(d) W2=Z-1 99 CONTINUE IF(W1-W2)350,350,351 350 W3=W1 GOTO 352 351 W3 = W2 352 CALL P L O T ( P X ( 1 ) , P Y ( 1 ) , 3 ) CALL SYMB0L(PX(1 ) ,PY(1 ) ,0 . 10,SYM(O),0. , - 1) DO 888 W=1,W3 IF(W.GT.1)GOTO 35 WW= 1 35 IF(PX(W)-PX(WW)-0.25)888,889,889 889 CALL SYMB0L(PX(W),PY(W), .10,SYM(O),0. . -1) WW = W 888 CONTINUE 401 NN = W3 DO 4 11=1,M X(11 )=T IME( I I ) 4 Y(11 )=LHAVE( I I ) CALL WEIGHT(Y,HPLUAV,HMINAV,M,WT) EXTERNAL AUX CALL LOF(X , Y,YF,WT,E 1 ,E2,PP, 1.0,M.MM,NI,ND,EPS,AUX) IF(ND.NE.1)G0 TO 103 WRITE(6,5) 5 FORMAT(' ESTIMATES OF ROOT MEAN SQUARE TOTAL ERROR ' , 1'IN THE PARAMETERS') WRITE(6,7) (E2( I I ) ,11=1.MM) 7 F0RMAT(8G15.3) WRITE(6,8) 8 FORMAT(' VALUES OF X VALUES OF Y FITTED VALUES OF Y ' , 1' WEIGHTS') DO 9 1=1,NN WRITE(6,22) X ( I ) , Y ( I ) ,YF ( I ) ,WT( I ) 22 F 0 R M A T ( 6 X , F 5 . 2 , 9 X , F 5 . 2 , 1 0 X , F 6 . 2 . 9 X , F 7 . 2 ) PX(I )=PX(I )*2. PY(I ) =PY( I ) *0 .8 -5 . <£> APPENDIX 3.1: ( C o n t i n u e d ) WR ITE (8 ,353 )PX ( I ) .PY ( I ) ,WT( I ) 353 F0RMAT(3F8.3) 9 CONTINUE T IME(L)=DTI (L) -DOT WRITE(7 ,58)T IME(L ) ,TTH(L ) .HX 58 F O R M A T ( 4 X , F 4 . 1 , 8 X , F 5 . 3 , 9 X , F 4 . 2 ) READ(5,5G)0 56 FORMAT(12) 113 I F ( 0 - 1 0 ) 1 0 1 , 1 0 2 . 1 0 2 102 CALL PLOTND 103 STOP END C C THE FOLLOWING IS AN AUXILIARY FUNCTION CALLED UPON BY THE LEAST C SQUARES F IT PACKAGE, LQF. C FUNCTION AUX(PP.D,X,L) DIMENSION PP(1 ) ,D (1 ) COMMON MM D( 1 ) = 1 .0 AUX=PP( 1 ) DO 10 d=2,MM D(d)=D(d-1)*X 10 AUX=AUX+PP(d)*D(d) RETURN END C C SUBROUTINE WEIGHT CALCULATES THE RELATIVE WEIGHTS OF THE POINTS FOR C THE LEAST SQUARES FIT PROGRAM, LQF. C SUBROUTINE WEIGHT(Y,YPLUS,YMINUS , NN , WT) DIMENSION Y(100).YPLUS(100),YMINUS(100),ERRPLU(100), 1ERRMIN(100),WT(100),ERROR(100) DO 10 1=1,NN 15 ERRPLU( I )=ABS(YPLUS( I ) -Y ( I ) ) ERRMIN( I )=ABS(YMINUS( I ) -Y( I ) ) IF (ERRPLU( I ) -ERRMIN( I ) )11.11,12 11 ERROR(I )=ERRMIN(I) GOTO 13 12 ERROR(I)=ERRPLU(I) 13 WT(I ) = 1 ./ (ERROR( I )*ERROR( I ) ) 10 CONTINUE RETURN END 5 o APPENDIX 3.1: ( C o n t i n u e d ) C SUBROUTINE PLTAX PLOTS THE AXES FOR THE GRAPHS OF LOG DIMENSIONLESS C HYDRATION VS. TIME, WITH AXIS LABELS AND T ITLE . C SUBROUTINE PLTAX DIMENSION BCD(20) COMMON BCD CALL P L C T R L ( ' S C A L ' , 0 . 8 ) CALL PLOT( 1 . 0 , 1 . 0 , 3 ) CALL A X C T R L ( ' S I D E ' , 1 ) CALL AXCTRL( 'XOR IG IN ' ,0 .00) CALL AXCTRL( ' SYMS IZE ' ,0 .15 ) CALL A X P L O T ( 9 0 . 0 , 6 . 0 , - 3 . 0 , 0 . 5 ) CALL SYMBOL(1 .0 ,9 .5 ,0 .20 ,BCD,0 .0 ,80 ) CALL A X C T R L ( ' S I D E ' , - 1) CALL AXCTRL( 'YOR IG IN ' ,0 .00 ) CALL A X P L 0 T ( 0 . 0 , 1 0 . 0 , 0 . 0 , 2 . 0 ) RETURN END C C SUBROUTINE OUTLAB PRINTS THE COLUMN HEADINGS FOR F ILE 0UTPUT2. C SUBROUTINE OUTLAB WRITE(7,200) WRITE(7,201) WRITE(7,202) 200 FORMAT( ' TIME SAMPLE HYDRATION LN (H ) ' ) 201 FORMAT( ' THICKNESS (G COLLAGEN/ (AVERAGE) ' ) 202 FORMAT( ' (HOURS) (INCHES) G WATER) ' ) RETURN END APPENDIX 3.2: Program f o r c a l c u l a t i o n and p l o t t i n g of d i m e n s i o n l e s s h y d r a t i o n c u r v e s f o r lumped d a t a . DIMENSION PX(250) ,PY(250) .BCD(20) ,WT(250) ,PPX(250) , 1PPY(250) ,PAR(G) ,YF(250) ,E1 (2 ) ,E2 (2 ) ,X (250) ,Y (250) ,WWT(250) REAL E P S / 1 0 . 0 E - 1 0 / , P P ( 2 ) / 0 . 0 . 0 . 0 / . H A L F , T H A L F COMMON BCD.MM INTEGER S Y M ( G ) / 1 , 2 , 3 , 4 , 5 , 6 / . W , R X ( 2 5 0 ) / 2 5 0 * 0 / , 0 / 1 / . N I / 1 / 1.RR.KK/2/ EXTERNAL AUX MM = 2 L=0 RR = 0 READ(8,53)BCD 53 FORMAT(20A4) CALL PLTAX READ(8,1)THALF . 1 F0RMAT(F4.2) HALF = THALF/2. 14 LL=L+1 DO 10 d=LL,250 READ(8. 51 )PX(d).PY(d),WWT(d) 51 F0RMAT(3F8.3) IF (PX(d) .GT.900)GOTO 11 X (d )=PX(d ) /2 . Y(d)=2*PY(d)+6. 10 CONTINUE 11 L=d-1 d=LL-RR DO 19 I=LL,L IF (X ( I ) .GT.HALF)GOTO 21 RR = RR+ 1 GOTO 19 21 CALL S Y M B 0 L ( X ( I ) , Y ( I ) . O . 1 0 . S Y M ( 0 ) . 0 . . - 1 ) PPX(d)=PX( I ) PPY(d)=PY( I ) WT(d ) =WWT(I) d = d+ 1 19 CONTINUE IF (0 .LT .50 )GOTO 12 15 CONTINUE dd=d-1 CALL LQF(PPX,PPY,YF.WT,E1,E2,PP.1.0,dd,MM,NI .ND,EPS,AUX) IF(ND.NE.1)STOP WRITE(6,4) 4 FORMATC ESTIMATES OF THE ROOT MEAN SQUARE TOTAL ERROR ' , 1'IN THE PARAMETERS') WRITE(6,62) (E2( I ) ,1=1.MM) O ro APPENDIX 3.2: ( C o n t i n u e d ) 62 F0RMAT(F6 .3 ,4X ,F6 .3 ) WRITE(6,60) 60 FORMAT('VALUES OF X VALUES OF Y FITTED VALUES OF Y ' , 1' WEIGHTS') DO 17 I=1,dd WRITE(6,61 ) P P X ( I ) , P P Y ( I ) , Y F ( I ) , W T ( I ) 61 F 0 R M A T ( 3 X , F 5 . 2 , 9 X , F 5 . 2 , 1 0 X , F 6 . 2 , 1 0 X , F 7 . 1 ) 17 CONTINUE PX(1)=0. PY( 1 )=2*PP( 1 )+6. PX(2 ) = ( ( 3 , +PP (1 ) ) /ABS (PP (2 ) ) ) / 2 . PY(2)=0. CALL L INE(PX,PY,KK,1) GOTO 13 12 READ(8,52)0 52 FORMAT(12) IF (0 .GT.5O)G0T0 15 GOTO 14 13 CALL PLOTND STOP END SUBROUTINE PLTAX DIMENSION BCD(20) COMMON BCD CALL P L C T R L ( ' S C A L ' , 0 . 8 ) CALL PLOT( 1 .0 ,1 .0 ,3 ) CALL A X C T R L ( ' S I D E ' , 1 ) CALL AXCTRL( 'XOR IG IN ' ,0 .0 ) CALL AXCTRL( ' SYMS IZE ' ,0 . 15) CALL AXPL0T( ' ; ' , 9 0 . 0 , 6 . 0 , - 3 . 0 , 0 . 5 ) CALL SYMBOL(0 .0 .9 .5 ,0 .20 ,BCD,0 .0 ,80 ) CALL A X C T R L ( ' S I D E ' , - 1 ) CALL AXCTRL( 'YOR IG IN ' ,0 .00 ) CALL AXPLOT( ' ; ' , 0 . 0 , 1 0 . 0 , 0 . 0 , 2 . 0 ) RETURN END FUNCTION AUX(PP,D,X,L) DIMENSION PP (1 ) ,D (1 ) COMMON MM D(1)=1.0 AUX=PP(1) DO 18 d=2,MM D(d)=D(d-1 )*X 18 AUX=AUX+PP(d)*D(d) RETURN APPENDIX 4 DATA FOR GRAPHS PRESENTED TABLE A4.1 Data for Figure 4.1.1 Sample Swelling Pressure Hydration No. 10 3 dynes/cm2 g H20/g collagen 8 5.87 4.49 11.74 3.13 17.61 2.69 23.48 2.39 9 5.87 5.12 11.74 3.78 17.61 3.27 23.48 2.97 10 5.87 4.55 11.74 3.04 17.61 2.06 23.48 1.89 11 5.87 4.48 11.74 3.21 17.61 2.78 23.48 2.37 TABLE A4.2 Data f o r F i g u r e 5.1.1 Time l n ( H d l ) I n ( H d l ) Weight (Hours) ( F i t t e d ) RUN 1 .00 -0.84 -0.89 233.6 6 1 .34 -0.98 -1.04 190.9 1 .67 -1.13 -1.19 150.7 2.00 -1 .30 -1 .34 116.0 2.34 -1.42 -1 .49 94. 1 2.66 -1 .52 -1 .63 79.7 3.00 -1 .70 -1 .78 57.0 3.33 -1 .88 -1 .93 40.9 3.67 -2.08 -2.08 28.3 4.01 -2.20 -2.23 22.2 4.34 -2.46 -2.37 13.0 RUN 1 .00 -0.87 -0.90 338.3 7 1 .34 -1 .02 -1 .04 272.4 1 .67 -1.16 -1.19 216.5 2.01 -1 .31 -1 .34 170.9 2.35 -1 .44 -1 .49 138.0 2.69 -1.62 -1 .64 101.1 3.02 -1 .81 -1 .79 72.0 3.34 -1 .99 -1 .93 51 .3 3.68 -2.16 -2.08 37.5 4.02 -2.30 -2.23 28.0 4.35 -2.46 -2.38 20.4 RUN 1 .00 -0.89 -0.89 304.4 12 1 .34 -1 .05 -1 .04 237.8 1 .68 -1 .21 -1.19 185.2 2.01 -1 .37 -1 .34 143.2 2.34 -1 .50 -1 .49 114.8 2.68 -1 .63 -1 .64 90.3 3.01 -1.81 -1 .78 65.2 3.34 -1 .93 -1 .93 52.6 3.68 -2.08 -2.08 39.5 4.01 -2.21 -2.23 30.6 4.35 -2.39 -2.38 21 .4 RUN 1 .00 -0.75 -0.89 162.4 1 4 1 .33 -0.90 -1 .04 131.9 1 .68 -1 .02 -1.19 109. 1 2.00 -1.16 -1 .34 87.2 2.34 -1 .22 -1 .49 79.3 2.67 -1 .45 -1 .64 54.6 * Hdl i s the dimensionless hydration, (H-H5)/(.H.-Ho) TABLE A4.2 (Continued) Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) RUN 3.01 -1 .59 -1 .78 42.5 14 3.34 -1 .74 -1 .93 32.5 3.67 -1 .89 -2.08 24.2 4.01 -2.05 -2.23 17.8 4.34 -2.26 -2.38 1 1 .7 RUN 1 .00 -1.10 -0.89 229.3 1 5 1 .33 -1 .30 -1 .04 167.0 1 .66 -1 .43 -1.19 133.2 2.00 -1 .58 -1 .34 103.0 2.33 -1 .71 -1 .48 81.5 2.66 -1 .86 -1 .63 62.4 3.00 -1 .97 -1 .78 50. 1 3.33 -2.10 -1 .93 39.0 3.66 -2.23 -2.07 30.2 4.00 -2.36 -2.22 23.4 4.33 -2.49 -2.37 17.7 108 TABLE A4.3 RUN 6 RUN 7 RUN 1 4 Data f o r F i g u r e 5.1.2 Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 1.31 -0.83 -0.88 109.6 1 .65 -0.94 -1 .00 91 .7 1 .99 -1.10 -1.11 71 .4 2.32 -1 .20 -1 .22 61 .1 2.65 -1 .34 -1 .33 48. 1 2.99 -1 .44 -1 .44 40.4 3.32 -1 .58 -1 .56 31.5 3.65 -1 .68 -1.67 26. 1 3.98 -1 .86 -1 .78 18.4 4.32 -2.00 -1 .89 13.9 4.65 -2.16 -2.00 10.0 4.99 -2.23 -2.12 8.6 5.32 -2.34 -2.23 6.9 5.65 -2.42 -2.34 5.7 1 .34 -0.93 -0.89 87.9 1 .67 -1.06 -1 .00 70.9 2.00 -1 .20 -1.11 56.7 2.33 -1.31 -1 .22 46.6 2.67 -1 .44 -1 .34 36.9 3.00 -1 .55 -1 .45 30.7 3.33 -1.61 -1 .56 27. 1 3.66 -1 .73 -1 .67 21.7 4.00 -1 .89 -1 .79 15.7 4.34 -1 .96 -1 .90 13.9 4.67 -2. 14 -2.01 9.6 5.00 -2.25 -2.12 7.4 5.34 -2.41 -2.23 5.2 5.68 -2.51 -2.35 4. 1 1 .34 -0.89 -0.89 1 56.3 1 .67 -1 .02 -1 .00 129.8 2.01 -1.14 -1.11 1 07.8 2.34 -1 .22 -1 .23 94.8 2.67 -1 .28 -1 .34 85.3 3.00 -1 .44 -1 .45 65.0 3.33 -1.52 -1 .56 56.4 3.68 -1 .59 -1 .68 49.7 4.01 -1 .69 -1 .79 41 .4 4.34 -1.81 -1 .90 33.2 4.67 -1 .93 -2.01 26.4 5.01 -2.06 -2.12 20.5 5.34 -2.23 -2.24 14.6 5.68 -2.46 -2.35 9.0 109 TABLE A4.3 (Co n t i n u e d ) Time I n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 1 .35 -0.89 -0.89 142.9 1 .68 -1 .00 -1 .00 119.1 2.01 -1.10 -1.12 1 02.2 2.34 -1 .23 -1 .23 82.9 2.68 -1 .32 -1 .34 70.9 3.01 -1 .42 -1.45 60.0 3.35 -1 .55 -1 .56 47.7 3.68 -1 .60 -1 .68 43.6 4.02 -1 .73 -1 .79 34. 1 4.35 -1 .87 -1 .90 26. 1 4.68 -1 .98 -2.01 21 .0 5.01 -2.1 1 -2. 13 16.3 5.35 -2.28 -2.24 11.4 5.68 -2.46 -2.35 7.7 110 TABLE A4.4 Data f o r F i g u r e 5.1.3 Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 2.34 -1 .02 -0.82 34.4 2.67 -1.11 -0.88 29.5 3.00 -1.19 -0.94 26.1 3.34 -1 .27 -0.99 22.6 3.67 -1 .41 -1 .05 17.6 4.00 -1 .49 -1.11 15.2 4.34 -1 .56 -1.16 13.2 4.66 -1 .64 -1 .22 11.3 5.00 -1 .69 -1 .28 10.2 5.34 -1 .71 -1 .33 9.8 5.67 -1 .82 -1 .39 8.0 6.00 -1 .83 -1 .45 7.7 6.34 -1 .81 -1 .50 8.0 6.67 -1 .78 -1 .56 8.6 7.00 -1 .79 -1 .61 8.4 7.34 -1 .80 -1 .67 8.2 7.67 -1 .85 -1 .73 7.4 8.01 -1 .87 -1 .79 7.2 8.34 -2.05 -1 .84 4.8 8.68 -2.26 -1 .90 3.0 9.01 -2.36 -1 .95 2.3 9.34 -2.40 -2.01 2.0 9.68 -2.39 -2.07 2.1 10.01 -2.50 -2.13 1 .6 10.34 -2.46 -2.18 1 .7 2.33 -0.78 -0.82 232. 1 2.66 -0.85 -0.88 212.0 3.00 -0.93 -0.94 186.3 3.33 -1 .00 -0.99 1 68.5 3.66 -1.05 -1 .05 1 56.8 3.99 -1.10 -1.10 1 43. 1 4.33 -1.13 -1.16 136.6 4.66 -1.18 -1 .22 126.7 5.00 -1 .25 -1 .27 1 12.8 5.33 -1 .29 -1 .33 1 04.8 5.67 -1 .36 -1 .39 94.4 6.00 -1 .40 -1 .44 87.5 6.33 -1 .45 -1 .50 79.7 6.67 -1 .52 -1 .56 71.1 7.00 -1 .56 -1 .62 65.7 7.34 -1 .64 -1 .67 57.4 TABLE A4.4 (Co n t i n u e d ) Time l n ( H d l ) I n ( H d l ) Weight (Hours) ( F i t t e d ) 7.67 -1 .70 -1 .73 50.9 8.01 -1 .79 -1 .79 43.5 8.34 -1 .89 -1 .84 35.9 8.67 -1 .98 -1 .90 30.4 9.00 -1 .92 -1 .95 34.0 9.34 -1 .97 -2.01 30.6 9.68 -2.07 -2.07 25.5 10.01 -2.18 -2.12 20.3 1 0.35 -2.38 -2.18 13.5 2.34 -0.82 -0.82 80.4 2.67 -0.87 -0.88 74.6 3.00 -0.93 -0.94 68.0 3.34 -0.97 -0.99 64.2 3.67 -1 .02 -1 .05 58.5 4.01 -1 .07 -1.11 54.3 4.34 -1.11 -1.16 50.4 4.68 -1.17 -1 .22 45.6 5.02 -1 .20 -1 .28 43.4 5.35 -1 .26 -1 .33 39.3 5.68 -1.31 -1 .39 35.8 6.01 -1 .38 -1 .45 31 .6 6.35 -1.41 -1 .50 29.9 6.68 -1 .48 -1 .56 25.9 7.02 -1 .53 -1 .62 23.9 7.35 -1 .62 -1 .67 20.0 7.69 -1 .66 -1 .73 18.6 8.02 -1.71 -1 .79 16.8 8.35 -1 .79 -1 .84 14.4 8.69 -1 .88 -1 .90 11.9 9.02 -1 .98 -1 .96 9.7 9.35 -2.08 -2.01 7.8 9.68 -2.17 -2.07 6.3 10.02 -2.27 -2.13 5.0 10.35 -2.45 -2. 18 3.2 TABLE A4.5 Data f o r F i g u r e 5.1.4 Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 2.99 -1.11 -1 .03 14.9 3.33 -1.19 -1 .08 13.0 3.66 • -1 .27 -1.13 11.1 4.00 -1 .37 -1.17 9.3 4.33 -1 .46 -1 .22 7.8 4.66 -1 .52 -1 .27 6.8 5.00 -1 .53 -1 .32 6.8 5.33 -1 .56 -1 .37 6.4 5.66 -1 .55 -1.41 6.5 6.00 -1 .52 -1 .46 6.9 6.33 -1 .60 -1.51 5.8 6.66 -1 .69 -1 .56 4.8 7.00 -1 .79 -1.61 3.8 7.33 -1.82 -1 .66 3.6 7.67 -1 .86 -1 .70 3.2 8.00 -1 .91 -1 .75 2.9 8.34 -1 .91 -1 .80 2.9 8.67 -2.06 -1 .85 2.0 9.01 -2.05 -1 .90 2.0 9.34 -2.05 -1 .95 2. 1 9.67 -2.13 -1 .99 1 .7 10.01 -2.02 -2.04 2.2 1 0.34 -1 .99 -2.09 2.4 10.67 -2.29 -2.14 1 .0 1 1 .00 -2.33 -2.18 0.9 1 1 .34 -2.25 -2.23 1 .2 1 1 .67 -2.32 -2.28 0.9 12.01 • -2.47 -2.33 0.6 12.34 -2.60 -2.38 0.3 1 2.67 -2.53 -2.43 0.4 12.99 -2.43 -2.47 0.7 1 3.33 -2.49 -2.52 0.5 1 3.67 -2.43 -2.57 0.6 1 3.99 -2.48 -2.62 0.5 1 4.34 -2.58 -2.67 0.3 3.01 -0.85 -1 .03 14.4 3.34 -0.90 -1 .08 13.2 3.67 -0.97 -1.13 11.6 4.00 -1 .04 -1.18 10.3 4.34 -1.12 -1 .22 8.9 4.67 -1.19 -1 .27 7.8 113 TABLE A4.5 (Continued) Time In(Hdl) In(Hdl) Weight (Hours) (Fitted) 5.00 -1.21 -1 .32 7.5 5.34 -1 .23 -1 .37 7.2 5.68 -1 .27 -1 .42 6.7 6.00 -1 .32 -1 .46 6.0 6.34 -1 .40 -1 .51 5.1 6.67 -1.45 -1 .56 4.6 7.01 -1 .49 -1 .61 4.2 7.35 -1.51 -1 .66 4.1 7.68 -1 .56 -1.71 3.7 8.01 -1 .60 -1 .75 3.4 8.35 -1 .59 -1 .80 3.4 8.68 -1.71 -1 .85 2.5 9.02 -1 .79 -1 .90 2.1 9.35 -1 .88 -1 .95 1 .7 9.68 -1 .94 -1 .99 1 .4 10.02 -1 .92 -2.04 1 .5 10.35 -2.04 -2.09 1 . 1 10.69 -2. 14 -2.14 0.8 11.02 -2.19 -2.19 0.6 1 1 .35 -2.25 -2.24 0.5 1 1 .68 -2.29 -2.28 0.4 1 2.02 -2.49 -2.33 0.1 12.35 -2.60 -2.38 0.0 12.69 -2.52 -2.43 0.1 1 3.02 -2.46 -2.48 0.2 13.35 -2.56 -2.52 0.0 13.68 -2.49 -2.57 0.1 14.01 -2.34 -2.62 0.4 14.34 -2.32 -2.67 0.4 114 TABLE A4.6 Data f o r F i g u r e 5.1.5 Time In(Hdl) In(Hdl) Weight (Hours) ( F i t t e d ) 1 .65 -0.74 -0.67 363.0 1 .99 -0.83 -0.77 320.2 2.33 -0.98 -0.86 256.4 2.66 -1 .09 -0.96 217.8 3.00 -1.17 -1 .05 191 .8 3.34 -1 .25 -1.15 167.9 3.67 -1 .33 -1 .24 147.9 4.00 -1.41 -1 .34 128.7 4.34 -1 .47 -1 .43 116.2 4.67 -1 .57 -1 .53 97.7 5.01 -1 .63 -1.62 88.4 5.34 -1 .71 -1 .72 76.8 5.68 -1 .78 -1.81 67.2 6.01 -1 .90 -1 .91 53.8 6.34 -1 .97 -2.00 47.2 6.67 -2. 12 -2.10 35. 1 7.01 -2.22 -2.19 28.8 7.34 -2.40 -2.29 20. 1 1 .67 -0.61 -0.68 380.8 2.00 -0.69 -0.77 339.0 2.34 -0.78 -0.86 302.7 2.68 -0.87 -0.96 266.7 3.02 -0.96 -1 .06 231 . 1 3.35 -1 .05 -1.15 201 .4 3.68 -1.12 -1 .25 180.2 4.02 -1.21 -1 .34 156.0 4.35 -1.31 -1 .44 132.6 4.69 -1 .39 -1 .53 116.6 5.02 -1 .50 -1 .63 96.9 5.35 -1 .60 -1 .72 81 .2 5.69 -1.77 -1 .82 60.3 6.03 -1 .89 -1 .91 48.5 6.36 -2.03 -2.01 37. 1 6.70 -2.20 -2.10 26.6 7.03 -2.30 -2.20 21.6 7.36 -2.53 -2.29 13.4 115 TABLE A4.6 (Continued) Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 1 .67 -0.69 -0.68 167.6 2.01 -0.81 -0.77 141.9 2.34 -0.91 -0.87 120.8 2.68 -1 .00 -0.96 103.8 3.02 -1.12 -1 .06 85.9 3.35 -1 .22 -1.15 72.2 3.68 -1 .33 -1 .25 60.2 4.02 -1 .44 -1 .34 49. 1 4.35 -1 .58 -1 .44 38.0 4.68 -1 .68 -1 .53 31.7 5.02 -1.81 -1 .63 24.6 5.36 -1.91 -1 .72 20. 1 5.69 -2.00 -1 .82 16.8 6.02 -2.13 -1 .91 12.8 6.35 -2.26 -2.01 9.7 6.69 -2.34 -2.10 8.0 7.03 -2.42 -2.20 6.7 7.36 -2.50 -2.29 5.6 116 TABLE A4.7 Data f o r F i g u r e 5.1.6 Time l n ( H d l ) In(Hdl) Weight (Hours) ( F i t t e d ) 2.33 -0.76 -0.84 288.5 2.66 -0.84 -0.90 259.0 2.99 -0.90 -0.96 235. 1 3.32 -0.98 -1 .02 209. 1 3.65 -1 .05 -1 .08 189.6 3.99 -1.11 -1.14 172.0 4.33 -1.18 -1.19 153.3 4.67 -1 .24 -1 .26 137.5 5.00 -1 .31 -1 .31 123. 1 5.34 -1 .38 -1 .37 110.4 5.66 -1.46 -1 .43 95.9 6.00 -1 .52 -1 .49 86.5 6.34 -1 .57 -1 .55 79.2 6.67 -1 .64 -1.61 69.7 7.00 -1 .70 -1 .67 61 .6 7.34 -1 .77 -1 .73 54.5 7.68 -1 .82 -1 .79 49.7 8.02 -1 .89 -1 .85 43.4 8.35 -1 .95 -1 .91 39. 1 8.68 -2.03 -1 .97 33.4 9.01 -2.10 -2.02 29.3 9.34 -2.20 -2.08 23.5 9.68 -2.23 -2.14 22.5 10.01 -2.34 -2.20 17.8 10.34 -2.40 -2.26 15.8 10.68 -2.46 -2.32 13.8 11.01 -2.48 '-2.38 13.3 2.34 -1 .06 -0.84 224.9 2.68 -1.13 -0.90 203.7 3.00 -1 .20 -0.96 1 79.8 3.34 -1 .26 -1 .02 164.0 3.67 -1.31 -1 .08 1 50.4 4.02 -1 .39 -1.14 133. 1 4.35 -1 .45 -1 .20 118.5 4.68 -1 .50 -1 .26 109.9 5.02 -1 .58 -1 .32 95. 1 5.35 -1.61 -1 .38 90.5 5.69 -1 .63 -1 .44 86.8 6.02 . -1.72 -1 .49 73.8 6.36 -1 .76 -1 .56 69.0 6.69 -1 .83 -1.61 60.8 117 TABLE A4.7 (Continued) RUN 20 RUN 21 RUN 24 Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 7.03 -1 .87 -1 .67 55.9 7.36 -1.93 -1 .73 50.8 7.69 -1 .96 -1 .79 47.9 8.03 -2.13 -1 .85 34.6 8.37 -2.16 -1.91 32.3 8.70 -2.29 -1 .97 24.7 9.04 -2.26 -2.03 26.6 9.37 -2.35 -2.09 21 .9 9.71 -2.44 -2.15 18.4 1 0.03 -2.45 -2.21 18.1 2.35 -0.89 -0.84 190.0 2.69 -0.97 -0.90 167.4 3.02 -1 .07 -0.96 144.6 3.35 -1.14 -1 .02 130.2 3.69 -1 .22 -1.08 112.9 4.02 -1 .29 -1.14 100.8 4.35 -1 .33 -1 .20 93.7 4.69 -1 .43 -1 .26 80. 1 5.03 -1 .48 -1 .32 72.4 5.35 -1 .55 -1 .38 64.3 5.68 -1 .60 -1 .44 59.0 6.01 -1 .67 -1 .49 52.0 6.36 -1 .77 -1 .55 43. 1 6.69 -1 .82 -1.61 39.3 7.02 -1 .85 -1 .67 37.0 7.35 -1 .92 -1 .73 32.6 7.68 -1 .97 -1 .79 29.2 8.02 -2.02 -1 .85 26.9 8.34 -2.08 -1.91 23.5 8.68 -2.11 -1 .97 22.4 9.01 -2.22 -2.03 17.8 9.35 -2.27 -2.09 16.1 9.67 -2.30 -2.14 15.0 1 0.02 -2.45 -2.20 10.9 10.34 -2.39 -2.26 12.4 10.68 -2.61 -2.32 7.6 2.34 -0.75 -0.84 357.0 2.67 -0.79 -0.90 336. 1 3.01 -0.84 -0.96 312.7 3.33 -0.88 -1 .02 294.6 118 TABLE A4.7 (Continued) Time l n ( H d l ) In(Hdl) Weight (Hours) ( F i t t e d ) 3.67 -0.94 -1 .08 272.3 4.01 -0.96 -1.14 261 .4 4.35 -1 .03 -1 .20 236.3 4.67 -1 .08 -1 .26 217.8 5.00 -1.14 -1 .31 198.3 5.34 -1.17 -1 .37 189.8 5.68 -1 .22 -1 .43 174.4 6.01 -1 .27 -1 .49 160.4 6.34 -1 .34 -1 .55 142.9 6.68 -1 .39 -1 .61 131.2 7.01 -1 .46 -1 .67 116.1 7.35 -1 .52 -1 .73 105.7 7.69 -1 .56 -1 .79 97.5 8.01 -1 .63 -1 .85 87.6 8.35 -1.71 -1.91 75.3 8.68 -1 .77 -1 .97 67.5 9.02 -1 .86 -2.03 56.7 9.35 -1 .93 -2.09 50.6 9.69 -1 .99 -2.15 44.6 10.02 -2.11 -2.20 35.8 10.35 -2.25 -2.26 27. 1 10.69 -2.36 -2.32 21 .7 1 1 .02 -2.49 -2.38 16.5 119 TABLE A4.8 RUN 8 RUN 9 RUN 10 RUN 1 1 Data f o r F i g u r e 5.1.7 Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 0.99 -0.87 -0.92 1040.9 1 .32 -1 .06 -1 .07 776.4 1 .65 -1 .23 -1.21 594.3 1 .99 -1 .40 -1 .37 452.5 2.32 -1 .56 -1 .52 344.3 2.67 -1 .69 -1 .67 273.0 3.00 -1 .86 -1 .82 198.6 3.33 -2.02 -1 .97 148. 1 3.66 -2.13 -2.12 120.5 3.99 -2.26 -2.27 95.2 4.32 -2.50 -2.42 58.4 1 .28 -1.18 -1 .05 552.4 1 .62 -1 .34 -1 .20 431.5 1 .95 -1 .48 -1 .35 342. 1 2.29 -1.63 • -1 .50 265.0 2.63 -1 .78 -1 .65 204.9 2.96 -1 .93 -1 .80 154.6 3.30 -2.06 -1 .95 122.2 3.63 -2.22 -2.10 90.4 3.97 -2.37 -2.26 68.2 4.31 -2.49 -2.41 53.4 1.31 -0.94 -1 .06 1341.5 1 .65 -1.13 -1.21 1019.5 1 .97 -1 .29 -1 .36 790.4 2.30 -1 .43 -1 .51 628.5 2.62 -1 .55 -1 .65 513.1 2.96 -1 .69 -1 .80 406. 1 3.29 -1 .83 -1 .95 316.9 3.62 -1 .95 -2.10 252.4 3.95 -2.12 -2.25 186.8 4.27 -2.31 -2.39 128.4 4.60 -2,46 -2.54 97.2 1.31 -1.17 -1 .06 495.3 1 .64 -1 .37 -1.21 353.2 1 .98 -1 .52 -1 .36 271 .5 2.32 -1 .67 -1.51 209.7 2.66 -1.81 -1 .67 162.9 2.99 -1 .95 -1.81 126.2 3.32 -2.10 -1 .96 95.4 3.65 -2.24 -2.1 1 71.9 3.99 -2.36 -2.27 56.6 4.33 -2.52 -2.42 41 .8 120 TABLE A4.9 RUN 8 RUN 9 RUN 10 Data f o r F i g u r e 5.1.8 Time l n ( H d l ) l n ( H d l ) (Hours) ( F i t t e d ) 1 .32 -1.01 -0.90 1 .65 -1.13 -1.01 2.00 -1 .25 -1.13 2.34 -1.41 -1 .25 2.67 -1 .56 -1 .36 3.00 -1 .67 -1 .47 3.32 -1 .88 -1 .59 3.67 -2.07 -1 .70 4.00 -2.21 -1 .82 4.34 -2.30 -1 .93 4.67 -2.34 -2.05 5.00 -2.35 -2.16 5.33 -2.40 -2.27 5.66 -2.47 -2.39 6.00 -2.51 -2.50 1 .33 -1 .02 -0.90 1 .66 -1.14 -1 .02 2.01 -1 .23 -1.13 2.33 -1 .32 -1 .25 2.66 -1 .44 -1 .36 3.00 -1 .54 -1 .48 3.33 -1 .64 -1 .59 3.67 -1 .75 -1.71 4.01 -1 .90 -1 .82 4.34 -2.05 -1 .93 4.68 -2.26 -2.05 5.01 -2.40 -2.16 1.31 -0.80 -0.90 1 .65 -0.89 -1.01 1 .98 -1 .02 -1.12 2.31 -1.13 -1 .24 2.66 -1 .27 -1 .36 2.99 -1 .39 -1 .47 3.31 -1 .52 -1 .58 3.65 -1 .62 -1 .70 3.99 -1 .76 -1.81 4.32 -1 .84 -1 .93 4.65 -1 .93 -2.04 4.98 -2.03 -2.15 5.32 -2.14 -2.27 5.66 -2.22 -2.39 5.98 -2.48 -2.50 Weight 58.2 47.0 38, 28, 21 .8 17.5 1 1 7 5 3 6 4 4.4 4.0 4, 3, 2, 2 53, 43, 36, 0 4 9 6 4 4 9 31 .8 25. 1 21 , 17, 13.9 10.1 7.5 4.6 3.3 1 44, 125, 1 02, 86, 67, 54, 43, 36. 1 27.6 23.8 19.6 16.1 12.7 10.8 6.1 121 TABLE A4.9 (Continued) Time In(Hdl) In(Hdl) Weight (Hours) ( F i t t e d ) 1 .30 -0.94 -0.89 38.6 1 .65 -1 .07 -1.01 31.0 1 .98 -1.21 -1.13 24. 1 2.31 -1 .32 -1 .24 19.8 2.65 -1 .40 -1 .35 17.1 2.97 -1.51 -1 .46 13.8 3.31 -1 .60 -1 .58 1 1 .4 3.64 -1 .66 -1 .69 10.1 3.97 -1 .82 -1.81 7.2 4.30 -1 .93 -1 .92 5.7 4.65 -2.03 -2.04 4.5 4.97 -2.16 -2.15 3.3 5.30 -2.25 -2.26 2.7 5.64 -2.50 -2.38 1 .4 5.97 -2.60 -2.49 1 .0 122 TABLE A4.10 Data f o r F i g u r e 5.1.9 Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 3.89 -1 .20 -0.59 3.9 7.79 -1 .70 -1.12 2.9 8.11 -1 .77 -1.16 2.4 8.45 -1 .71 -1 .21 2.8 8.78 -1 .67 -1 .25 3.1 9.1 1 -1 .66 -1 .30 3.2 9.45 -1 .65 -1 .34 3.2 9.78 -1 .67 -1 .39 3. 1 10.11 -1 .60 -1 .43 3.6 10.45 -1 .70 -1 .48 2.9 10.78 -1 .68 -1 .52 3.0 11.12 -1 .74 -1 .57 2.6 1 1 .45 -1 .77 -1.61 2.4 1 1 .78 -1.81 -1 .65 2.2 12.12 -1 .94 -1 .70 1 .5 12.44 -2.06 -1 .74 1 . 1 1 2.78 -2.20 -1 .79 0.7 13.12 -2.32 -1 .83 0.4 13.45 -2.45 -1 .88 0.2 1 3.79 -2.42 -1 .92 0.3 14.12 -2.59 -1 .97 0.0 1 4.45 -2.46 -2.01 0.2 14.79 -2.28 -2.06 0.5 15.12 -2.13 -2.10 0.9 1 5.45 -2.10 -2.15 1 .0 1 5.79 -2.17 -2.19 0.7 16.12 -2.21 -2.24 0.7 16.47 -2.22 -2.29 0.6 16.80 -2.34 -2.33 0.4 17.12 -2.51 -2.37 0.1 1 7.46 -2.50 -2.42 0.1 17.79 -2.56 -2.46 0.0 18.12 -2.61 -2.51 0.0 18.46 -2.55 -2.55 0.1 3.99 -0.54 -0.61 33.8 4.33 -0.57 -0.65 32.3 4.65 -0.61 -0.70 30.2 4.99 -0.68 -0.74 27.3 5.32 -0.73 -0.79 25. 1 5.66 -0.77 -0.83 23.7 5.99 -0.87 -0.88 20. 1 123 TABLE A4.10 (Continued) Time In(Hdl) ln(Hdl) Weight (Hours) (Fitted) 6.32 -0.91 -0.92 18.7 6.65 -1 .01 -0.96 16.0 6.98 -1 .00 -1.01 16.2 7.31 -1 .09 -1 .05 13.8 7.65 -1.14 -1.10 12.7 7.98 -1.19 -1.14 11.5 8.32 -1 .26 -1.19 10.1 8.65 -1 .27 -1 .23 10.0 8.98 -1 .42 -1 .28 7.4 9.32 -1 .33 -1 .32 8.9 9.65 -1 .51 -1 .37 6.1 9.98 -1 .58 -1.41 5.3 10.32 -1 .63 -1 .46 4.8 10.65 -1 .66 -1 .50 4.5 10.99 -1 .76 -1.55' 3.6 1 1 .32 -1 .76 -1 .59 3.6 1 1 .65 -1 .69 -1 .64 4.2 1 1 .98 -1 .80 -1 .68 3.3 12.31 -1 .86 -1 .73 2.8 1 2.66 -1 .88 -1 .77 2.7 12.99 -1 .83 -1 .82 3.1 1 3.33 -1 .90 -1 .86 2.6 1 3.65 -2.12 -1.91 1 .4 1 3.98 -2.30 -1 .95 0.8 14.31 -2.32 -2.00 0.8 1 4.65 -2.37 -2.04 0.7 1 4.98 -2.51 -2.09 0.4 15.31 -2.41 -2.13 0.6 15.65 -2.31 -2.17 0.8 15.98 -2.39 -2.22 0.6 16.32 -2.28 -2.26 0.9 1 6.64 -2.16 -2.31 1 .3 1 6.98 -2.38 -2.35 0.6 1 7.32 -2.31 -2.40 0.8 17.65 -2.33 -2.44 0.8 1 7.98 -2.58 -2.49 0.2 18.31 -2.46 -2.53 0.5 TABLE A4.10 (Co n t i n u e d ) Time l n ( H d l ) l n ( H d l ) Weight (Hours) * ( F i t t e d ) 3.98 -0.82 -0.61 1 .6 4.31 -0.87 -0.65 1 .4 4.66 -0.89 -0.70 1.3 4.99 -0.95 -0.74 1 . 1 5.32 -0.96 -0.79 1 . 1 5.65 -1 .02 -0.83 0.9 5.98 -1 .05 -0.87 0.8 6.32 -1 .04 -0.92 0.9 6.65 -1 .03 -0.96 0.9 6.98 -1 .03 -1 .01 0.9 7.32 -0.99 -1 .05 1.0 7.66 -0.96 -1.10 1 . 1 7.99 -1 .06 -1.14 0.8 8.32 -1.12 -1.19 0.7 8.66 -1 .22 -1 .23 0.5 8.99 -1 .23 -1 .28 0.5 9.32 -1 .32 -1 .32 0.3 9.65 -1 .35 -1 .37 0.3 10.00 -1 .44 -1.41 0.2 10.32 -1 .49 -1 .46 0.1 10.66 -1 .48 -1 .50 0.1 10.99 -1 .52 -1 .55 0.0 11.32 -1 .63 -1 .59 0.0 1 1 .65 -1 .67 -1 .64 0.0 12.00 -1 .74 -1 .68 0.0 12.33 -1 .85 -1 .73 0.0 12.65 -1 .85 -1 .77 0.0 1 2.99 -1 .87 -1 .82 0.0 13.28 -1 .87 -1 .86 0.0 1 3.67 -1 .68 -1.91 0.0 1 3.99 -1 .72 -1 .95 0.0 14.33 -1 .72 -2.00 0.0 14.65 -1 .74 . -2.04 0.0 14.98 -1 .78 -2.09 0.0 15.32 -1 .88 -2.13 0.0 1 5.66 -1 .96 -2.18 0.0 15.98 -2.07 -2.22 0.0 16.32 -2.09 -2.26 0.0 16.66 -2.32 -2.31 0.0 16.99 -2.29 -2.36 0.0 17.32 -2.52 -2.40 0.0 1 7.66 -2.39 -2.44 0.0 17.99 -2.58 -2.49 0.0 18.33 -2.57 -2.53 0.0 125 TABLE A4.10 (Cont inued) Time In(Hdl) ln(Hdl) Weight (Hours) (Fitted) 3.97 -0.68 -0.60 27.3 4.30 -0.73 -0.65 25.2 4.63 -0.75 -0.69 24.5 4.97 -0.77 -0.74 23.3 5.29 -0.79 -0.78 22.7 5.62 -0.82 -0.83 21 .3 5.94 -0.85 -0.87 20.4 6.28 -0.89 -0.91 19.1 6.61 -0.92 -0.96 17.8 6.94 -0.93 -1 .00 17.7 7.28 -0.99 -1 .05 15.8 7.60 -1 .03 -1 .09 14.4 7.94 -1 .06 -1.14 13.8 8.27 -1.10 -1.18 12.8 8.61 -1.11 -1 .23 12.4 8.92 -1 .22 -1 .27 10.0 9.25 -1 .22 -1.31 10.1 9.57 -1 .29 -1 .36 8.7 9.90 -1 .29 -1 .40 8.6 10.23 -1 .28 -1 .45 8.8 10.56 -1 .30 -1 .49 8.5 10.90 -1 .34 -1 .54 7.8 1 1 .22 -1.41 -1 .58 6.7 1 1 .56 -1 .48 -1 .62 5.7 1 1 .88 -1 .57 -1 .67 4.7 12.22 -1 .65 -1.71 3.8 12.54 -1 .69 -1.76 3.5 12.88 -1 .64 -1 .80 3.9 13.20 -1 .66 -1.85 3.8 13.53 -1 .70 -1 .89 3.4 1 3.88 -1 .74 -1 .94 3.1 1 4.20 -1 .77 -1.98 2.8 1 4.54 -1 .87 -2.03 2.2 1 4.87 -1 .91 -2.07 2.0 1 5.20 -1 .99 -2.11 1 .6 1 5.52 -2.14 -2.16 1 .0 15.86 -2.20 -2.20 0.8 16.18 -2.20 -2.25 0.8 16.53 -2 . 1 9 -2.29 0.8 16.85 -2.35 -2.34 0.5 17.18 -2.38 -2.38 0.4 17.51 -2.33 -2.43 0.5 17.84 -2.45 -2.47 0.3 18.17 -2.50 -2.51 0.2 18.50 -2.56 -2.56 0.1 126 TABLE A4.11 Data for Figure 5.1.10 Time ln(Hdl) In(Hdl) Weight (Hours) (Fitted) • RUN 1.01 -1 .44 -1 .29 594.4 16 1 .35 -1.63 -1 .46 430.5 1 .69 -1 .80 -1 .64 316.8 2.03 -1 .93 -1.81 250.3 2.36 -2.11 -1 .98 182.0 2.69 -2.23 -2.15 1 45.2 3.02 -2.35 -2.33 115.1 3.36 -2.46 -2.50 92.7 RUN 0.97 -0.93 -1 .27 585.5 25 1 .30 -1.16 -1 .44 411.2 1 .64 -1 .35 -1.61 308.4 1 .97 ' -1.51 -1 .79 234.7 2.31 -1 .69 -1 .96 173.6 2.65 -1 .92 -2.14 113.8 2.98 -2.17 -2.31 71.7 3.32 -2.41 -2.48 45.3 1.01 -1 .44 -1 .29 594.4 RUN 1 .35 -1 .63 -1 .46 430.5 26 1 .69 -1 .80 -1 .64 316.8 2.03 -1 .93 -1 .81 250.3 2.36 -2.11 -1 .98 182.0 2.69 -2.23 -2.15 1 45.2 3.02 -2.35 -2.33 115.1 3.36 -2.46 -2.50 92.7 127 TABLE A4.12 Data f o r F i g u r e 5.2.3.1 40 g 60 g 80 g Time l n ( H d l ) (Hours) 0.0 0.0 0.32 -0.42 0.65 -0.63 0.98 -0.85 1.31 -1 .07 1 .65 -1 .30 1 .97 -1 .52 2.30 -1.71 2.62 -1 .89 2.96 -2.10 3.29 -2.34 3.62 -2.59 3.95 -2.95 4.27 -3.54 4.60 -4.23 0.0 0.0 0.31 -0.34 0.65 -0.55 0.98 -0.73 1.31 -0.90 1 .65 -1.01 1 .98 -1.17 2.31 -1 .30 2.66 -1 .49 2.99 -1 .66 3.31 -1 .85 3.65 -1 .99 3.99 -2.23 4.32 -2.36 4.65 -2.55 4.98 -2.75 5.32 -3.02 5.66 -3.23 5.98 -4.34 0.0 0.0 0.31 -0.23 0.64 -0.34 0.98 -0.45 1 .32 -0.52 1 .65 -0.58 1.99 -0.66 2.31 -0.70 2.65 -0.73 In(Hdl) Weight ( F i t t e d ) -0.09 3620.27 -0.32 2314.99 -0.57 1761.84 -0.80 1304.14 -1 .05 951.92 -1 .29 664.67 -1 .52 467.39 -1 .77 334.31 -2.00 243.83 -2.24 164.89 -2.49 104.36 -2.73 65. 10 -2.96 30.91 -3.20 8.42 -3.44 1 .41 -0.11 349.24 -0.28 234.84 -0.46 176.91 -0.64 137.39 -0.82 106.68 -1 .00 89.40 - 1 . 1 8 69.05 -1 .36 54.88 -1 .55 39.12 -1 .73 28.52 -1.91 19.97 -2.09 1 4.84 -2.28 9.06 -2.45 6.72 -2.64 4.36 -2.82 2.64 -3.00 1 .21 -3.18 0.59 -3.36 0.00 -0.21 5.96 -0.26 4.18 -0.31 3.48 -0.37 2.86 -0.42 2.50 -0.48 2.22 -0.53 1 .86 -0.58 1 .71 -0.64 1 .60 128 TABLE A4.12 (Continued) Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 2.99 -0.79 -0.69 1 .37 3.32 -0.83 -0.74 1 .24 3.65 -0.89 -0.80 1 .06 3.98 -0.92 -0.85 0.98 4.32 -0.98 -0.90 0.82 4.66 -1 .01 -0.96 0.75 4.99 -1 .08 -1 .01 0.59 5.32 -1 .09 -1 .06 0.58 5.65 -1.16 -1.12 0.45 5.98 -1 .21 -1.17 0.37 6.32 -1.19 -1 .22 0.40 6.65 -1.18 -1 .28 0.42 6.98 - 1 . 1 8 -1 .33 0.41 7.32 -1.13 -1 .39 0.50 7.66 -1.10 -1.44 . 0.56 7.99 -1 .22 -1.49 • 0.35 8.32 -1 .29 -1 .55 0.25 8.66 -1 .42 -1 .60 0.08 8.99 -1 .43 -1 .65 0.07 9.32 -1.56 -1 .71 0.00 9.65 -1 .59 -1 .76 0.00 10.00 -1 .72 -1.81 0.00 1 0.32 -1 .81 -1 .87 0.00 10.66 -1 .79 -1 .92 0.00 10.99 -1 .85 -1 .97 0.00 1 1 .32 -2.02 -2.03 0.00 1 1 .65 -2.08 -2.08 0.00 12.00 -2.20 -2.13 0.00 12.33 -2.39 -2.19 0.00 1 2.65 -2.39 -2.24 0.00 12.99 -2.43 -2.29 0.00 1 3.28 -2.42 -2.34 0.00 1 3.67 -2.10 -2.40 0.00 1 3.99 -2.16 -2.45 0.00 14.33 -2.15 - -2.51 0.00 14.65 -2.20 -2.56 0.00 1 4.98 -2.26 -2.61 0.00 1 5.32 -2.44 -2.67 0.00 1 5.66 -2.60 -2.72 0.00 15.99 -2.83 -2. 77 0.00 16.32 -2.88 -2.83 0.00 1 6.66 -3.56 . -2.88 0.00 16.99 -3.46 -2.93 0.00 17.32 -4.74 -2.99 0.00 17.66 -3.86 -3.04 0.00 129 TABLE A4 . 13 Data f o r F i g u r e 5.2.3.2 40 g 60 g Time In(Hdl) (Hours) 0.0 0.0 0.32 -0.40 0.65 -0.61 0.98 -0.82 1.31 -1 .02 1 .65 -1 .23 1 .97 -1 .42 2.30 -1 .59 2.62 -1 .74 2.96 -1 .91 3.29 -2.10 3.62 -2.28 3.95 -2.52 4.27 -2.85 4.60 -3.13 4.94 -3.51 5.26 -3.83 5.58 -4.42 0.0 0.0 0.31 -0.33 0.65 -0.53 0.98 -0.70 1.31 -0.85 1 .65 -0.95 1 .98 -1.10 2.31 -1 .22 2.66 -1 .39 2.99 -1 .53 3.31 -1 .69 3.65 -1.81 3.99 -1 .99 4.32 -2.09 4.65 -2.23 4.98 -2.36 5.32 -2.54 5.66 -2.65 5.98 -3.11 6.31 -3.43 6.65 -4.04 6.99 -4.07 In(Hdl) Weight ( F i t t e d ) -0.11 3834.13 -0.32 2497.50 -0.53 1930.66 -0.75 1460.15 -0.97 1095.61 -1.18 795.05 -1 .39 585.12 -1.61 440.37 -1 .82 339.61 -2.04 248.93 -2.26 176.25 -2.47 126.22 -2.68 78.42 -2.89 40.30 -3.11 22.66 -3.33 9.80 -3.54 4.48 -3.75 0.81 -0.13 370.10 -0.28 252.85 -0.44 193.50 -0.60 152.88 -0.76 121.17 -0.92 103.22 -1 .08 81 .92 -1 .24 66.93 -1.41 50.01 -1 .57 38.39 -1 .73 28.75 -1 .89 22.79 -2.05 15.78 -2.21 12.79 -2.38 9.62 -2.54 7.11 -2.70 4.78 -2.86 3.58 -3.02 0.99 -3.18 0.25 -3.34 0.00 -3.50 0.00 TABLE A4.13 ( C o n t i n u e d ) Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 0.0 0.0 -0.21 6.10 0.31 -0.23 -0.26 4.31 0.64 -0.33 -0.31 3.61 0.98 -0.44 -0.36 2.98 1 .32 -0.51 -0.42 2.62 1 .65 -0.56 -0.47 2.34 1 .99 -0.65 -0.52 1 .97 2.31 -0.68 -0.57 1 .82 2.65 -0.71 -0.62 1.71 2.99 -0.77 -0.67 1 .48 3.32 -0.81 -0.72 1 .34 3.65 -0.87 -0.77 1.16 3.98 -0.90 -0.82 1 .07 4.32 -0.96 -0.87 0.92 4.66 -0.99 -0.92 0.84 4.99 -1.05 -0.97 0.68 5.32 -1 .06 -1 .02 0.66 5.65 -1.13 -1 .07 0.53 5.98 -1.17 -1.12 0.45 6.32 -1.16 -1.18 0.48 6.65 -1.15 -1 .23 0.50 6.98 -1.15 -1 .28 0.49 7.32 -1.10 -1 .33 0.59 7.66 -1 .07 -1 .38 0.65 7.99 -1.19 -1 .43 0.42 8.32 -1 .25 -1.48 0.32 8.66 -1 .37 -1 .53 0.15 8.99 -1 .38 -1 .58 0.14 9.32 -1 .50 -1 .63 0.00 9.65 -1 .53 -1 .68 0.00 10.00 -1 .65 -1 .74 0.00 10.32 - 1 .73 - 1 .79 0.00 1 0.66 -1.71 -1 .84 0.00 10.99 - 1 .76 -1 .89 0.00 1 1 .32 - 1 .92 -1 .94 0.00 1 1 .65 -1 .98 -1 .99 0.00 12.00 -2.08 -2.04 0.00 12.33 -2.24 -2.09 0.00 1 2.65 -2.25 -2.14 0.00 12.99 -2.28 -2.19 0.00 13.28 -2.27 -2.24 0.00 13.67 -1 .99 -2.30 0.00 131 TABLE A4.13 (Co n t i n u e d ) Time I n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 13.99 -2.04 -2.34 0.00 1 4.33 -2.04 -2.40 0.00 14.65 -2.08 -2.45 0.00 14.98 -2. 13 -2.50 0.00 1 5.32 -2.28 -2.55 0.00 1 5.66 -2.42 -2.60 0.00 15.99 -2.60 -2.65 0.00 1 6.32 -2.64 -2.70 0.00 16.66 -3.12 -2.75 0.00 16.99 -3.05 -2.80 0.00 1 7.32 -3.70 -2.85 0.00 17.66 -3.30 -2.90 0.00 17.99 -3.92 -2.95 0.00 18.33 -3.85 -3.01 0.00 18.66 -4. 06 -3.06 0.00 19.01 -4.02 -3.11 0.00 19.33 -3.78 -3.16 0.00 1 9.66 -4.25 -3.21 0.00 132 TABLE A4.14 Data f o r F i g u r e 5.2.3.3 Time I n ( H d l ) (Hours) 40 g 60 g 0.0 0.0 0.32 -0.39 0.65 -0.58 0.98 -0.78 1.31 -0.96 1 .65 -1.16 1 .97 -1 .33 2.30 -1 .48 2.62 -1 .60 2.96 -1 .75 3.29 -1 .90 3.62 -2.04 3.95 -2.23 4.27 -2.45 4.60 -2.62 4.94 -2.83 5.26 -2.98 5.58 -3.18 5.92 -3.50 6.25 -3.86 6.57 -4.77 0.0 0.0 0.31 -0.31 0.65 -0.50 0.98 -0.66 1.31 -0.80 1 .65 -0.89 1 .98 -1 .02 2.31 -1.13 2.66 -1 .28 2.99 -1 .40 3.31 -1 .53 3.65 -1 .63 3.99 -1 .77 4.32 -1 .85 4.65 -1 .95 4.98 -2.05 5.32 -2.16 5.66 -2.24 5.98 -2.51 6.31 -2.66 l n ( H d l ) Weight ( F i t t e d ) -0. 13 4062.17 -0.31 2693.37 -0.51 2112.63 -0.69 1629.21 -0.89 1252.58 -1 .08 939.16 -1 .26 717.32 -1 .46 561.71 -1 .64 451.43 -1 .83 350.05 -2.03 266.34 -2.22 206.64 -2.40 146.72 -2.59 94.76 -2.78 67.77 -2.98 44.85 -3.16 33.05 -3.34 21 .58 -3.54 1 0.67 -3.73 4.45 -3.91 0.15 -0.15 396.79 -0.28 276.06 -0.42 214.97 -0.55 173.05 -0.69 140.16 -0.83 121.43 -0.97 99.05 -1.11 83. 1 3 -1 .26 64.91 -1 .39 52. 1 6 -1.53 41 .34 -1 .67 34.48 -1.81 26. 16 -1 .95 22.48 -2.09 18.45 -2.22 15.12 -2.37 1 1 .82 -2.51 1 0.03 -2.64 5.52 -2.78 3.82 133 TABLE A4.14 (Continued) " 8 0 g Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 6.65 -2.89 -2.92 2.10 6.99 -2.90 -3.06 .2.04 7.32 -3.13 -3.20 1 .04 7.65 -3.24 -3.33 0.69 7.98 -3.42 -3.47 0.32 8.31 -3.61 -3.61 0.00 8.65 -4.77 -3.75 0.00 0.0 0.0 -0.22 6.26 0.31 -0.22 -0.26 4.46 0.64 -0.33 -0.31 3.75 0.98 -0.43 -0.36 3.11 1 .32 -0.50 -0.41 2.75 1 .65 -0.55 -0.45 2.47 1 .99 -0.63 -0.50 2.10 2.31 -0.66 -0.55 1 .94 2.65 -0.69 -0.60 1 .84 2.99 -0.75 -0.65 1 .60 3.32 -0.79 -0.70 1 .46 3.65 -0.84 -0.74 1 .27 3.98 -0.87 -0.79 1.19 4.32 -0.93 -0.84 1 .02 4.66 -0.96 -0.89 0.94 4. 99 -1 .02 -0.94 0.78 5.32 -1 .03 -0.98 0.76 5.65 -1 .09 -1 .03 0.62 5.98 -1.13 -1 .08 0.54 6.32 -1.12 -1.13 0.57 6.65 -1.11 -1.17 0.59 6.98 -1.11 -1 .22 0.58 7. 32 -1 .06 -1 .27 0.68 7.66 -1 .03 -1 .32 0.75 7.99 -1.15 -1 .37 0.51 8.32 -1 .21 -1 .42 0.40 8.66 -1 .32 -1.46 0.23 8.99 -1 .33 -1.51 0.22 9.32 -1 .44 -1 .56 0.08 9.65 -1 .47 -1 .61 0.03 10.00 -1 .58 -1 .66 0.00 10.32 -1 .65 -1.71 0.00 10.66 -1 .64 -1 .75 0.00 10.99 -1 .68 -1 .80 0.00 134 TABLE A4.14 (Continued) Time l n ( H d l ) In(Hdl) Weight (Hours) ( F i t t e d ) 1 1 .32 -1 .82 -1.85 0.00 1 1 .65 -1 .87 -1 .90 0.00 12.00 -1 .96 -1 .95 0.00 12.33 -2.10 -1 .99 0.00 12.65 -2.11 -2.04 0.00 12.99 -2.13 -2.09 0.00 13.28 -2.12 -2.13 0.00 1 3.67 -1 .88 -2.19 0.00 13.99 -1 .93 -2.23 0.00 1 4.33 -1 .92 -2.28 0.00 1 4.65 -1 .96 -2.33 0.00 1 4.98 -2.00 -2.38 0.00 15.32 -2.14 -2.43 0.00 1 5.66 -2.25 -2.47 0.00 15.99 -2.40 -2.52 0.00 1 6.32 -2.43 -2.57 0.00 16.66 -2.80 -2.62 0.00 16.99 -2.75 -2.67 0.00 17.32 -3.17 -2.71 0.00 17.66 -2.92 -2.76 0.00 17.99 -3.29 -2.81 0.00 18.33 -3.25 -2.86 0.00 18.66 -3.36 -2.91 0.00 19.01 -3.34 -2.96 0.00 19.33 -3.21 -3.00 0.00 19.66 -3.45 -3.05 0.00 19.99 -3.39 -3.10 0.00 135 TABLE A4.15 Data f o r F i g u r e 5.2.3.4 Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 0.0 0.0 -0.14 4208.88 0.32 -0.38 -0.31 2813. 1 1 0.65 -0.57 -0.49 2220.67 0.98 -0.76 -0.67 1727.03 1.31 -0.94 -0.86 1341.52 1 .65 -1.13 -1 .04 1019.51 1 .97 -1 .29 -1 .22 790.41 2.30 -1 .43 -1 .40 628.53 2.62 -1 .55 -1 .58 513.08 2.96 -1 .69 -1 .76 406.11 3.29 -1.83 -1 .95 316.87 3.62 -1 .95 -2.13 252.44 3.95 -2.12 -2.31 186.78 4.27 -2.31 -2.49 1 28.45 4.60 -2.46 -2.67 97.24 0.0 0.0 -0.15 407.13 0.31 -0.31 -0.28 283.57 0.65 -0.50 -0.42 221.07 0.98 -0.65 -0.55 178. 18 1.31 -0.80 -0.69 144.52 1 .65 -0.89 -0.83 125.34 1 .98 -1 .02 -0.97 102.42 2.31 -1.13 -1.11 86. 10 2.66 -1 .27 -1 .25 67.42 2.99 -1 .39 -1 .39 54.32 3.31 -1 .52 -1 .52 43.20 3.65 -1.62 -1 .66 36. 1 4 3.99 -1.76 -1 .80 27.56 4.32 -1 .84 -1 .94 23.76 4.65 -1 .93 -2.08 19.58 4.98 -2.03 -2.21 16.12 5.32 -2.14 -2.35 12.70 5.66 -2.22 -2.49 1 0.83 5.98 -2.48 -2.63 6.10 0.0 0.0 -0.22 7.16 0.31 -0.21 -0.26 5.20 0.64 -0.31 -0.30 4.42 0.98 -0.41 -0.35 3.73 1 .32 -0.47 -0.39 3.33 1 .65 -0.52 -0.43 3.02 TABLE A4.15 (Cont inued) Time In(Hdl ) In(Hdl ) Weight (Hours) ( F i t t e d ) 1 .99 -0 .59 -0.48 2.61 2.31 -0 .63 -0.52 2.44 2.65 -0 .65 -0.56 • 2.32 2.99 -0.71 -0.60 2.05 3.32 -0 .74 -0.65 1 .89 3.65 -0 .79 -0 .69 1 .69 3.98 -0 .82 -0.73 1 .59 4.32 -0 .87 -0 .77 1 .40 4.66 -0 .89 -0.82 1 .32 4.99 -0 .95 -0 .86 1.13 5.32 -0 .96 -0 .90 1.11 5.65 -1 .02 -0.94 0.94 5.98 -1 .05 -0 .99 0.85 6.32 -1 .04 -1 .03 0.88 ' 6.65 -1 .03 -1 .07 0.91 6.98 -1 .03 -1.11 0.90 7.32 -0 .99 -1.16 1.01 7.66 -0 .97 -1 .20 1 .09 7.99 -1 .06 -1 .24 0.82 8.32 -1.12 -1 .28 0.69 8.66 -1 .22 -1 .33 0.48 8.99 -1 .23 -1 .37 0.47 9.32 -1 .32 -1.41 0.31 9.65 -1 .35 -1 .45 0.28 10.00 -1 .44 -1 .50 0. 15 1 0.32 -1 .49 -1 .54 0.08 1 0.66 -1 .48 -1 .58 0.09 1 0.99 -1 .52 -1 .62 0.04 1 1 .32 -1 .63 -1 .67 0.00 1 1 .65 -1 .67 -1.71 0.00 12.00 -1 .74 -1 .75 0.00 12.33 -1 .85 -1 .79 0.00 12.65 -1 .85 -1 .84 0.00 12.99 -1 .87 -1 .88 0.00 1 3.28 -1 .87 -1 .92 0.00 1 3.67 -1 .68 -1 .97 0.00 13.99 -1 .72 -2.01 0.00 14.33 -1.71 -2 .05 0.00 14.65 -1 .74 -2 .09 0.00 14.98 -1 .78 -2.13 0.00 1 5.32 -1 .88 -2.18 0.00 15.66 -1 .96 -2.22 0.00 137 TABLE A4.15 ( C o n t i n u e d ) Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 15.99 -2.07 -2.26 0.00 16.32 -2.09 -2.30 0.00 16.66 -2.32 -2.35 0.00 16.99 -2.29 -2.39 0.00 17.32 -2.52 -2.43 0.00 17.66 -2.39 -2.47 0.00 17.99 -2.58 -2.52 0.00 18.33 -2.57 -2.56 0.00 138 TABLE A4.16 - Data f o r F i g u r e 5.2.3.5 Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 0.0 0.0 -0.36 5888.64 0.32 -0.30 -0.42 4314.39 0.65 -0.44 -0.48 3646.39 0.98 -0.58 -0.54 3085.27 1.31 -0.70 -0.60 2639.18 1 .65 -0.81 -0.67 2255.78 1 .97 -0.91 -0.73 1971.83 2.30 -0.99 -0.79 1760.54 2.62 -1 .05 -0.85 1602.98 2.96 -1.11 -0.91 1449.68 3.29 -1.18 -0.97 1313.99 3.62 -1 .23 -1 .03 1209.55 3.95 -1 .29 -1 .09 1094.71 4.27 -1 .36 -1.15 981.44 4.60 -1 .40 -1 .22 913.62 4.94 -1 .45 -1 .28 847.40 5.26 -1 .47 -1 .34 808.03 5.58 -1.51 -1 .40 763.60 5.92 -1 .55 -1 .46 710.30 6.25 -1 .59 -1 .52 667.59 6.57 -1 .64 -1 .58 611 .43 6.91 -1 .67 -1 .64 575.75 7.24 -1.71 -1.71 534.64 7.57 -1 .77 -1 .77 488.51 7.90 -1 .80 -1 .83 455.61 8.22 -1 .86 -1 .89 409.79 8.55 -1 .91 -1 .95 375.68 8.89 -1 .97 -2.01 339.33 9.20 -2.02 -2.07 310.71 9.54 -2.03 -2.13 302.98 9.87 -2.05 -2.19 289.42 10.20 -2.11 -2.26 262.44 10.53 -2.15 -2.32 244.82 1 0.85 -2.20 -2.38 220.50 11.18 -2.25 -2.44 200.68 11.51 -2.31 -2.50 179.19 1 1 .84 -2.35 -2.56 165.71 12.17 -2.41 -2.62 147.40 12.51 -2.47 -2.69 130.72 12.83 -2.54 . -2.74 114.22 13.16 -2.56 - 2 . 8 1 109.83 13.49 -2.60 -2.87 101.39 139 TABLE A4.16 (Continued) Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 1 3.80 -2.67 -2.93 89.49 14.14 -2.72 -2.99 80.95 14.47 -2.70 -3.05 84.35 1 4.80 -2.73 -3.11 79.58 15.13 -2.81 -3.17 67.26 1 5.45 -2.83 -3.23 63.75 15.78 -2.86 -3.29 59.97 16.11 -2.99 -3.36 46.69 16.44 -3.01 -3.42 44.09 16.77 -3.07 -3.48 39.24 17.09 -3.15 -3.54 33.45 17.43 - 3 . 1 9 -3.60 30.35 17.76 -3.26 -3.66 26.03 18.09 -3.2.7 -3.72 25.64 18.42 -3.37 -3.79 20.68 18.74 -3.43 -3.85 18.00 19.08 -3.53 - 3 . 9 1 1 4.66 19.41 -3.56 -3.97 13.56 1 9.73 -3.69 -4.03 10.15 0.0 0.0 -0.35 553.88 0.31 -0.25 -0.39 415.92 0.65 -0.39 -0.44 346.41 0.98 -0.50 -0.49 298.34 1.31 -0.60 -0.54 260.09 1 .65 -0.66 -0.59 237.94 1 .98 -0.75 -0.64 210.93 2.31 -0.81 -0.69 191.21 2.66 -0.90 -0.74 167.85 2.99 -0.97 -0.79 150.77 3.31 -1.03 -0.83 135.54 3.65 -1 .08 -0.88 125.38 3.99 -1.14 -0.93 112.33 4.32 -1.18 -0.98 106.20 4.65 -1 .22 -1 .03 99. 1 4 4.98 -1 .26 -1 .08 92.96 5.32 -1 .30 -1.13 86.40 5.66 -1 .32 -1.18 82.58 5.98 -1 .40 -1 .22 71 .73 6.31 -1 .44 -1 .27 66.81 6.65 -1 .49 -1 .32 60.91 6.99 -1 .50 -1 .37 60.68 140 TABLE A4.16 (Continued) Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 7.32 -1 .54 -1 .42 56.21 7.65 -1 .56 -1 .47 54.34 7.98 -1 .58 -1 .52 51 .86 8.31 -1 .60 -1.57 49.64 8.65 -1 .68 -1 .62 42.82 8.98 -1 .72 -1 .66 40.00 9.31 -1 .74 -1.71 38.69 9.64 -1.81 -1 .76 33.38 9.97 -1.83 - 1 . 8 1 32.33 10.30 -1 .86 -1 .86 30.30 10.64 -1.91 -1 .91 27.51 10.98 -1 .93 -1 .96 26.70 11.31 -1 .93 -2.01 26.21 1 1 .64 -1 .97 -2.06 24.65 1 1 .97 -1 .99 -2.10 23.56 12.31 -2.01 -2.15 22.50 12.64 -2.03 -2.20 21 .75 12.97 -2.04 -2.25 21.16 1 3.30 -2.10 -2.30 18.77 13.64 -2.12 -2.35 17.93 13.97 -2.13 -2.40 17.79 14.31 -2.14 -2.45 17.10 14.64 -2.17 -2.50 16.31 14.97 -2.21 -2.54 15.03 15.30 -2.21 -2.59 14.76 15.63 -2.31 -2.64 12.14 15.97 -2.33 -2.69 1 1 .56 16.31 -2.36 -2.74 10.88 16.63 -2.40 -2.79 9.92 16.97 -2.40 -2.84 9.80 17.30 -2.44 -2.89 8.98 17.63 -2.48 -2.94 8.19 17.96 -2.61 -2.98 6.10 18.30 -2.64 -3.03 5.68 18.63 -2.66 -3.08 5.51 18.97 -2.72 -3.13 4.72 19.30 -2.85 -3.18 3.38 1 9.63 -2.92 -3.23 2.82 19.96 -2.98 -3.28 2.41 141 TABLE A4 . 1 6 (Co n t i n u e d ) Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 0.0 0.0 -0.22 6.30 0.31 -0.22 -0.26 4.50 0.64 -0.33 -0.31 3.80 0.98 -0.43 -0.36 3.16 1 .32 -0.49 -0.41 2.79 1 .65 -0.55 -0.45 2.51 1 .99 -0.62 -0.50 2.14 2.31 -0.66 -0.55 1 .98 2.65 -0.68 -0.59 1 .87 2.99 -0.75 -0.64 1 .63 3.32 -0.78 -0.69 " 1 .49 3.65 -0.84 -0.74 1.31 3.98 -0.86 -0.78 1 .22 4.32 -0.92 -0.83 1 .05 4.66 -0.95 -0.88 0.98 4.99 -1.01 -0.92 0.81 5.32 -1 .02 -0.97 0.79 5.65 -1 .08 -1.02 0.65 5.98 -1.12 -1 .07 0.57 6.32 -1.11 -1.11 0.60 6.65 -1.10 -1.16 0.62 6.98 -1.10 -1.21 0.61 7.32 -1 .05 -1 .26 0.71 7.66 -1 .02 -1 .30 0.78 7.99 -1.14 -1 .35 0.54 8.32 -1 .20 -1 .40 0.43 8.66 -1.31 -1 .44 0.26 8.99 -1 .32 -1 .49 0.25 9.32 -1 .42 -1 .54 0.11 9.65 -1 .45 -1 .59 0.07 10.00 -1 .56 -1 .63 0.00 1 0.32 -1 .63 -1 .68 0.00 10.66 -1.61 -1 .73 0.00 10.99 -1 .66 -1 .77 0.00 1 1 .32 -1 .79 -1.82 0.00 1 1 .65 -1 .84 -1 .87 0.00 12.00 -1 .93 -1 .92 0.00 12.33 -2.06 -1 .96 0.00 12.65 -2.07 -2.01 0.00 12.99 -2.09 -2.06 0.00 13.28 -2.09 -2.10 0.00 13.67 -1 .85 -2.15 0.00 142 TABLE A4.16 (Continued) Time l n ( H d l ) l n ( H d l ) Weight (Hours) ( F i t t e d ) 13.99 -1 .90 -2.20 0.00 1 4.33 -1 .89 -2.25 0.00 14.65 -1.93 -2.29 0.00 1 4.98 -1 .97 -2.34 0.00 1 5.32 -2.10 -2.39 0.00 15.66 -2.20 -2.44 0.00 15.99 -2.35 -2.48 0.00 1 6.32 -2.38 -2.53 0.00 16.66 -2.72 -2.58 0.00 16.99 -2.67 -2.62 0.00 17.32 -3.05 -2.67 0.00 17.66 -2.83 -2.72 0.00 17.99 -3.16 -2.77 0.00 18.33 " -3.13 -2.81 0.00 18.66 -3.22 -2.86 0.00 19.01 -3.20 -2.91 0.00 19.33 -3.09 -2.96 0.00 19.66 -3.29 -3.00 0.00 19.99 -3.24 -3.05 0.00 APPENDIX 5 RAW DATA 144 Sample format for Table A5.1 [following pages]: 2 1 10.0E-10 Run #1, TEMPERATURE=22°C • 7 76.0 3.343 0.4375 .150 3.0 1.8 !. 175 15.5 11.4 MM; NI 1 Parameters — \* — EPS J # calibration points; maximum time .300 98.5 99.8' Init ial time —20.0 19.982 91.507 30.10 20.319 88.557 20.10 Time (hours); chart reading {%) 27.679 83.879 20.10 999. 999. for LSF Init ial or final — 0 calibration 2 27.482 84.123 30.10 T i t le A; DW - T; Init ial and final calibration readings, Digitizer ar t i fac t ; Reading error {% scale) End of f i l e etc. 2 1 10 .OE-10 RUN #1, TEMPERATURE=22 C 7 7 6 . 0 3.343 0.4375 .150 3.0 1.8 .175 15.5 11.4 .200 4 1.5 37.7 .225 60 .7 5 7 . 7 .250 77.3 7 4 . 0 .275 88.7 87.4 .300 98 .5 97 .8 2 0 . 0 0 2 19 .982 91 . 507 30 . 10 20 .319 88 . 557 20 . 10 20 .657 87 .641 20 . 10 20 .985 87 . 253 20 . 10 21 .314 86 .845 20 . 10 21 .655 86 .417 20 . 10 21 .990 86 . 173 20 . 10 22 . 331 85 .857 20 . 10 22 .665 85 .652 20, . 10 22 .999 85 . 387 20, , 10 23 . 331 85 .284 20, , 10 23 .662 85 .039 20. , 10 23 .994 84 .885 20. , 10 24 . 336 84 .773 20. 10 24 .675 84 .589 20. 10 25 .007 84 .405 20. 10 25, . 340 84 .282 20. 10 25 .672 84, . 169 20. 10 26. .012 84 .067 20. 10 26. .341 83 , .995 20. 10 26. .678 83 , .974 20. 10 27. .008 84 , 033 20. 10 27 . 346 83 . 931 20. 10 27. 679 83. 879 20. 10 J99. 999. 27 . 482 84 . 123 30. 10 27 . 821 81 . 407 20. 10 28 . 143 80. 612 20. 10 28 . 481 79. 971 20. 10 28 . 818 79. 349 20. 10 29 . 152 78 . 799 20. 10 29 . 486 78 . 270 20. 10 29. 826 77. 811 20. 10 30. 155 77 . 434 20. 10 30. 493 77 . 169 20. 10 30. 825 76. 893 20. 10 0 3 31 . 154 76 .668 20 . 10 31 .494 76 . 373 20 . 10 31 .833 76 .098 20 . 10 32 . 164 75 .914 20 . 10 32 .504 75 .700 20 . 10 32 .837 75 .485 20 . 10 33 . 165 75 .362 20 . 10 33 .503 75 . 199 20 . 10 33 .841 74 .822 20 . 10 34 .171 74 .820 20 . 10 34 .510 74 .718 20 . 10 34 .843 74 .494 20 . 10 35 . 184 74 . 351 20 . 10 35 .509 74 . 502 20 . 10 999 999 35 .497 74 .578 30. . 10 35 .826 72 . 203 20. . 10 36 . 162 71 . 121 20. 10 36 .500 70 . 121 20. 10 36 .833 69 . 294 20. 10 37 . 172 68 .538 20. 10 37 .505 67 .874 20. 10 37 .835 67 . 230 20. 10 38 . 173 6.6, . 382 20. 10 38 .512 65. .830 20. 10 38 . ,835 65, , 277 20. 10 39. 161 64. ,683 20. 10 39 . 495 64 . 029 20. 10 39. 835 63. 721 20. 10 40. 168 63. 331 20. 10 40. 505 •62 . 942 20. 10 40. 833 62. 409 20. 10 41 . 171 62. 071 20. 10 41 . 502 61 . 589 20. 10 41 . 832 61 . 189 20. 10 42. 174 60. 790 20. 10 42. 512 60. 390 20. 10 42. 840 59. 868 20. 10 43. 175 59. 488 20. 10 43. 507 59. 129 20. 10 43. 843 58 . 811 20. 10 44. 176 58. 421 20. 10 44 . 510 58. 062 20. 10 44 . 843 57. 703 20. 10 45. 180 57. 486 20. 10 45. 507 57. 178 20. 10 45. 842 56. 982 20. 10 46 . 177 56. 714 20. 10 0 4 46 .511 56 .721 20. 10 46 .850 56 .647 20. 10 47 . 175 56 .318 20. 10 47 .509 56 .214 20. 10 47 .841 56 .017 20. 10 48 . 177 55 .780 20. 10 48 .510 55 .502 20. 10 48 .844 55 . 255 20. 10 49 . 177 54 .967 20. 10 49 . 508 54 . 567 20. 10 49 .842 54 . 300 20. 10 50 . 180 54 .043 20. 10 50 .511 53 .816 20. 10 50 .835 53 .578 20. 10 51 . 166 53 .789 20. 10 51 . 507 53 .857 20 . 10 999 999 59 .985 49 . 701 30. 10 60 . 329 47 .354 20 . 10 60 .658 45 .864 20 . 10 60, .993 44 .882 20 . 10 61 , 334 43 .981 20. 10 61 , .666 43 . 233 20. 10 61 , .997 42 . 424 20. 10 62, , 329 41 .809 20. 10 62 , 667 41 .223 20. 10 62 , .998 40 . 557 20. 10 63, . 335 40 .022 20. 10 63 , 674 39 . 599 20. 10 64 , 004 39 , . 1 16 20. 10 64 . 333 38 .592 20. 10 64. ,668 38 , . 292 20. 10 65 , 002 37 .839 20. 10 65. , 335 37 , .559 20. 10 65. ,672 37 , .207 20 . 10 66. ,010 36 , .926 20. 10 66 . , 343 36, .657 20. 10 66. ,678 36, .336 20 . 10 67 . ,009 36 , 066 20 . 10 67. ,341 35, . 746 20. 10 67 . ,676 35 , . 445 20. 10 68 . ,01 1 35 , 175 20. 10 68 . ,344 34 , 844 20 . 10 68 . 676 34 , 656 20. 10 69 . ,01 1 34 , . 376 20. 10 69 . , 346 34 . 167 20. 10 69 . 682 33 . 856 20. 10 70. 006 33 . 730 20. 10 70. ,335 33. 410 20. 10 2 1 29. 669 78. 833 20. 10 70. ,672 33. 191 20. 10 1.141. 562.462.614.477. 14 30. 004 78 . 515 20. 10 71 . 007 32 . 768 20. 10 10.0E-•10 30. 341 78. 349 20. 10 71 . 337 32. 539 20. 10 RUN #2, TEMPERATURE = 22 C 30. 668 78. 133 20. 10 71 , 679 32. 279 20. 10 8 79.3 3 . 343 0.4353 31 . 007 77 . 948 20. 10 72. ,007 32 . 142 20. 10 . 125 2. 1 3. 6 31 . 337 77 . 670 20. 10 72 . , 349 31 . 708 20. 10 . 150 20.2 21 . 7 31 . 674 77 . 526 20. 10 72 . 678 31 . 520 20. 10 . 175 38 .9 41 . 9 32 . 006 77 . 238 20. 10 73. .008 31 . 292 20. 10 .200 56.3 57. 4 32 . 339 77 . 073 20. 10 73 . , 350 31 . 194 20. 10 .225 69.2 70. 8 32 . 676 76 . 816 20. 10 73 , .681 30. .873 20. 10 .250 80.5 82 . 1 33 . 016 76 . 559 20. 10 74, .022 30. .735 20. 10 .275 89.7 90. 5 33 . 340 76 . 475 20. 10 74. .351 30. ,567 20. 10 .300 97. 1 96. 9 33 . 672 76. 300 20. 10 74 .690 30. .419 20. 10 19.0 999. 999. 75 .009 30. .212 20. 10 18. 977 96. 094 30. 10 0 75 .359 30. . 103 20. 10 19 . 312 93 . 502 20. 10 3 75 .684 30 .088 20. 10 19. 652 92. ,547 20. 10 33 . 978 76. ,702 30. 10 76 .014 29 .921 20. 10 19 . .986 91 . 917 20. 10 34 .304 74 . 686 20. 10 399 999 20. .318 91 , 471 20. 10 34 . 635 73. ,666 20. 10 20. .653 90. .994 20. 10 34 .954 73. .032 20. 10 20. .988 90. ,680 20. 10 35 .281 72. .409 20. 10 21 . 321 90. .406 20. 10 35 .609 71 , .937 20. 10 21 . ,653 90. . 194 20. 10 35 .936 7 1 .446 20. 10 21 . 988 89 . 879 20. 10 36 .268 7 1 .087 20. 10 22. ,326 89 . 636 20. 10 36 .587 70 . 738 20. 10 22. .663 89. .495 20. 10 36 .912 70 .419 20. 10 22. .996 89. .293 20. 10 37 .237 70 . 152 20. 10 23. .332 89, .070 20. 10 37 . 560 69 . 782 20. 10 23. .664 88. .919 20. 10 37 .883 69 . 454 20. 10 23, .999 88 .767 20. 10 38 .214 69 .267 20. 10 24 , . 329 88 .605 20. 10 38 .538 69 . 142 20. 10 24 .662 88 . 373 20. 10 38 .863 68 .813 20. 10 24 .999 88 .241 20. 10 39 . 186 68 .668 20. 10 25 . 334 88. . 151 20. 10 39 . 509 68 .492 20. 10 999 999 39 .839 68 . 326 20. 10 0 40 . 170 68 . 190 20. 10 2 40 .494 68 .024 20. 10 25 . 332 88 .206 30. 10 40 .818 67 .817 20. . 10 25 .647 85 .425 20. 10 41 . 138' 67 .702 20, , 10 25 .982 84 .212 20. 10 41 .461 67 .608 20, , 10 26 .319 83 . 294 20. 10 41 .786 67 .401 20, , 10 26 .652 82 . 599 20. 10 42 . 109 67 . 204 20, , 10 26 .987 82 .068 20. 10 42 .439 66 .916 20 . 10 27 .324 81 .587 20. 10 42 . 763 66 . 720 20. . 10 27 .661 80 .862 20. 10 43 .080 66 .503 20 . 10 27 .994 80 . 392 20. 10 43 .409 66 .317 20 . 10 28 .331 80 .013 20. 10 43 .733 66 .212 20 . 10 28 .667 79 .654 20. 10 44 .051 66 . 127 20 . 10 28 .999 79 .346 20. 10 44 . 380 66 .083 20 . 10 29 . 333 79 .039 20. 10 44 .704 66 .009 20 . 10 4 5 45. .025 65, .772 20. 10 45 , .353 65 , .616 20. 10 45 . 663 65 .419 20. 10 999 . 999 , 45 . 650 65, .345 30. 10 45. .987 63 , .869 20. 10 46. , 322 63 . ,002 20. 10 46 , 652 62, .420 20. 10 46 . ,991 61 , .930 20. 10 47 . ,326 61 . 622 20. 10 47 , 659 61 , . 223 20. 10 47 . ,994 60, , 834 20. 10 48. ,331 60, .639 20. 10 48 .663 60, .311 20. 10 48 .998 59, .993 20. 10 49, . 330 59 . 788 20. 10 49 .668 59 .439 20. 10 50 .004 59 .264 20. 10 50 .338 59 . 140 20. 10 50 .669 58 .751 20. 10 51 .002 58 .677 20. 10 51 . 337 58 .482 20. 10 51 .669 58, .367 20. 10 52 .001 58, . 223 20. 10 52 . 334 58 . 108 20. 10 52 .675 57 .841 20. 10 53 .003 57 .707 20. 10 53 . 337 57 . 593 20. 10 53 .664 57 . 509 20. 10 54 .000 57 .425 20. 10 54 .338 57 .219 20. 10 54 .668 57 . 166 20. 10 55 .002 57 .021 20. 10 55 . 335 56 . 785 20. 10 55 .673 56 .681 20. 10 56 .005 56 .496 20. 10 56 .339 56 .402 20. 10 56 .677 56 . 267 20. 10 57 .007 56 . 142 20. 10 57 . 345 56 .079 20. 10 57 .686 55 .913 20. 10 58 .013 55 . 779 20. 10 999 999 57 .990 55 .685 30. 10 58 .318 54 . 444 20. 10 58 .653 53 .884 20. 10 58. 992 53 . 365 20. 10 59. 324 52. 938 20. 10 59. 657 52. 592 20. 10 59. 993 52. 347 20. 10 60. 327 52. 052 20. 10 60. 665 51 . 787 20. 10 60. ,993 51 . 482 20. 10 61 . 331 51 . 309 20. 10 61 . ,664 51 . ,085 20. 10 61 . 998 50. ,820 20. 10 62. 328 50. ,617 20. 10 62 . ,664 50. ,403 20. 10 62 . 993 50. ,291 20. 10 63 . ,330 50. . 158 20. 10 63 , 670 50. ,015 20. 10 63 , 995 49 . 832 20. 10 64 , 329 49. .659 20. 10 64 , 662 49, .445 20. 10 64, .994 49, . 323 20. 10 65 , .330 49, . 109 20. 10 65, .661 48 .926 20. 10 66 .000 48, .722 20. 10 66 .336 48, .498 20. 10 66 .666 48 .426 20. 10 67 .007 48 . 355 20. 10 67 .336 48 . 192 20. 10 67 .681 48 .161 20. 10 68 .009 48 .008 20. 10 68 .340 47 . 784 20. 10 68 .678 47 . 723 20. 10 69 .01 1 47 .631 20. 10 69 .340 47 .610 20. 10 69 .671 47 . 549 20. 10 70 .006 47 .569 20. 10 70 .341 47 .427 20. 10 70 .675 47 .345 20. 10 71 .012 47 .294 20. 10 71 .343 47 .171 20. 10 71 .680 47 .059 20. 10 7 1 .987 47 .006 30. 10 72 .325 46 .934 20. 10 72 .652 46 . 761 20. 10 72 .995 46 .648 20. 10 73 . 322 46 . 557 20. 10 73 .660 46 .444 20. , 10 73 .996 46 . 372 20. , 10 74 .327 46 . 240 20. . 10 74 .662 46 . 239 20. , 10 75 .002 46 . 157 20. , 10 75 .337 46 . 147 20, . 10 0 6 75. ,504 46 . 162 20. 10 999 , 999. 75, ,495 46 . , 149 30. 10 75 , 824 45 . , 124 20. 10 76, , 150 44 . 669 20. 10 76 , .488 44 . , 152 20. 10 76, .829 43 , 929 20. 10 77, . 161 43. ,697 20. 10 77 , 493 43 . , 364 20. 10 77 , 828 43 . 253 20. 10 78 , . 168 42 . ,919 20. 10 78 . 495 42 . 739 20. 10 78 , .829 42 . ,649 20. 10 79, . 166 42 . , 335 20. 10 79 , . 507 42 , 285 20. 10 79 . 836 42 , 094 20. 10 80, ,171 41 , 923 20. 10 80, .498 41 . ,825 20. 10 80, .836 4 1 . ,653 20. 10 81 , . 167 41 , .666 20. i b 81 , .497 41 . ,516 20. 10 81 , .835 41 . , 263 20. 10 82 , . 165 4 1 . . 306 20. 10 82 . 501 4 1. 297 20. 10 82 , .834 4 1 ; , 198 20. 10 83 , . 157 4 1 , , 1 10 20. 10 83 .491 40, ,868 20. 10 83 , .826 40, , 798 20. 10 84, . 164 40, ,667 20. 10 95 . 499 37 , .024 20. 10 95, ,835 37 . 168 20. 10 96 , . 165 36 . 814 20. 10 96 , 501 36. .572 20. 10 96 , .838 36 . 583 20. 10 97 , . 178 36 , . 289 20. 10 97 , .514 36. .393 20. 10 97 , .857 36 . ,251 20. 10 999 , 999 . 0 99 2 1 1.141 .562.462.614.477. 14 10.0E-10 RUN #3: TEMPERATURE=22 C 7 94.0 3.343 0.4760 .150 3.0 12.0 .175 26.5 35.1 .200 49.2 55.2 .225 65.8 70.3 .250 79.0 84.1 .275 89.3 91.9 .300 97.4 98.6 16.0 0 2 16 .035 97 .399 30. 10 16 . 325 96 .070 20. 10 16 .666 95 .211 20. 10 16 .997 94 . 566 20. 10 17 .328 93 .982 20. , 10 17 .665 93 .418 20. 10 17 .997 92 .987 20. 10 18 . 332 92 .606 20. 10 18 .668 92 . 367 20. 10 19 .005 92 .007 20. 10 19 . 337 91 . 779 20. 10 19 .667 91 .571 20. 10 19 .990 91 .252 20. 10 20 . 336 91 .043 20. 10 20 .666 90 .775 20. 10 21 .001 90 .638 20. 10 21 .335 90 .471 20. 10 21 .666 90 . 365 20. 10 22 .000 90. . 330 20. 10 999 999 . 2 1 . .981 90. 261 30. 10 22 , 311 88. .054 20. 10 22, ,645 87 . 016 20. 10 22. .982 86. 150 20. 10 23. .319 85. 467 20. 10 23. ,650 84 . 897 20. 10 23. .985 84 . ,347 20. 10 24. .317 83. ,867 20. 10 24 . ,659 83 . 388 20. 10 24. .998 82. 909 20. 10 25 . 327 82 . 501 20. 10 25. .662 82. 205 20. 10 25. 997 81 . 858 20. 10 26. 329 81 . 511 20. 10 26. 666 81 . 265 20. 10 27 . 003 80. 949 20. 10 0 3 27 .336 80 .683 20. 10 27 .670 80 . 305 20. 10 28 .008 80 .070 20. 10 28 .341 79 .825 20. 10 28 .678 79 .569 20. 10 29 .009 79 .436 20. 10 29 .339 79 . 180 20. 10 29 .678 79 .097 20. 10 30 .01 1 78 .781 20. 10 30 . 340 78 .729 20. 10 999 999 30 .482 78 .904 30. 10 30 .818 77 .075 20. 10 31 . 153 76 . 101 20. 10 31 .486 75 .382 20. 10 31 .820 74 .714 20. 10 32 . 155 74 . 107 20. 10 32 .488 73 .633 20. 10 32 .822 73 .046 20. 10 33 . 158 72 .684 20. 10 33 .498 72 .392 20. 10 33 .835 71 . 999 20. 10 34, . 175 71 .646 20. 10 34 .501 71 .356 20. 10 34 , .838 70. .993 20. 10 35 , . 169 70, .692 20. 10 35 , .504 70. .390 20. 10 35, .839 70, , 130 20. 10 36 , . 169 69 , .777 20. 10 36 , .510 69. ,547 20. 10 36, .849 69 . 327 20. 10 37 , . 181 69. , 138 20. 10 37 . ,517 68. .887 20. 10 37. .846 68 . 739 20. 10 38. , 180 68. ,570 20. 10 38 , 515 68. . 258 20. 10 38 . ,852 68. , 120 20. 10 39 . 184 67 . 982 20. 10 39 . 514 67 . 782 20. 10 39 . ,847 67 . 583 20. 10 40. 180 67 . 414 20. 10 40. .514 67 . 418 20. 10 40. 847 67 . 341 20. 10 41 . 178 67. 264 20. 10 41 . ,513 67. . 156 20. 10 41 . 842 66. 947 20. 10 42. 177 66. 798 20. 10 42. 524 66 . 679 20. 10 0 5 999. 999 42. . 494 66 .802 30. 10 42 . 822 65 . 368 20. 10 43 , 154 64 .289 20. 10 43 , 483 63 .7 19 20. 10 43, .822 63 .006 20. 10 44 , 163 62 . 507 20. 10 44 . , 495 61 .937 20. 10 44 . , 828 61 . 326 20. 10 45 . , 163 60 .847 20. 10 45 . , 495 60 .419 20. 10 45 . 824 59 .910 20. 10 46, ,167 59 .624 20. 10 46, , 504 59 .237 20. 10 46, , 842 58 .890 20. 10 47 , 174 58 .676 20. 10 47 , 505 58 .44 1 20. 10 •47 . 839 58 .431 20. 10 48 . ,171 58 .318 20. 10 48 . 504 58 . 175 20. 10 48. . 840 57 .910 20. 10 49 . 173 57 . 746 20. 10 49 . 507 57 .542 20. 10 49 . 842 57 . 389 20. 10 50. . 175 57 .093 20. 10 50. . 507 56 .889 20. 10 50. .839 56 .675 20. 10 51 , 168 56 .421 20. 10 51 , 508 56 .114 20. 10 51 , 84 1 55 .961 20. 10 52 . , 174 55 . 778 20. 10 52. ,513 55 .716 20. 10 54 . 5 55 . 1 20. 10 999. 999 54 , 490 55 . 105 30. 10 54 . ,829 54 . 224 20. 10 55 . 159 53 . 578 20. 10 55. . 499 52 .972 20. 10 55. ,834 52 . 376 20. 10 56. . 164 52 .065 20. 10 56. .496 51 .602 20. 10 56. ,827 51 , . 159 20. 10 57. . 166 50 .868 20. 10 57 . 498 50 .476 20. 10 57 . 835 50 . 164 20. 10 58 . 175 49 .731 20. 10 0 6 58 . 508 49 .481 20. 10 58 . 840 49 . 262 20. 10 59 . 176 48 .890 20. 10 59. ,506 48 .833 20. 10 59. ,840 48 .604 20. 10 60. , 172 48 .496 20. 10 60. . 504 48 . 358 20. 10 60. ,837 48 .342 20. 10 61 . , 174 48 .112 20. 10 61 . 512 47 .933 20. 10 61 . 840 47 .917 20. 10 62 . , 172 47 .952 20. 10 62. , 504 47 .834 20. 10 62 . 829 47 . 564 20. 10 63 . 171 47 . 365 20. 10 63 . 501 47 .085 20. 10 63 . 842 46 .814 20. 10 64. , 173 46 .859 20. 10 64 . ,503 46 .813 20. 10 64 . 838 47 .010 20. 10 65. . 160 47 . 157 20. 10 65. .499 47 . 192 20. 10 65 . 845 47. .216 20. 10 66 . , 173 47 . 169 20. 10 66. 505 47. . 153 20. 10 66. .840 46 .995 20. 10 67. , 177 46 .857 20. 10 67. ,512 46. .851 20. 10 67. ,836 46 .520 20. 10 68. 176 46 . 503 20. 10 68. , 508 46 .467 20. 10 68 . ,846 46 .522 20. 10 69. . 176 46 .567 20. 10 69. ,504 46 . 551 20. 10 69. .842 46 . 525 20. 10 70. , 178 46 .610 20. 10 70. .513 46 .675 20. 10 70. ,846 46. . 751 20. 10 71 . 172 46 .755 20. 10 71 . 510 46, .770 20. 10 71 . ,841 46, .774 20. 10 72. .010 46, .827 20. 10 999. 999, 71 . 984 46. .979 30. 10 72. 323 46, . 106 20. 10 72. 661 45. .651 20. 10 72. 985 45, . 206 20. 10 73. .319 45, .056 20. 10 73. .656 44 . 855 20. 10 73. .995 44. ,746 20. 10 74, .327 44 . 637 20. 10 74, .660 44 . 467 20. 10 74, .991 44 . 368 20. 10 75, , 332 44 . 197 20. 10 75 , .667 44 . ,078 20. 10 75, ,995 43. ,969 20. 10 76, .329 43. .911 20. 10 76, .668 43. ,852 20. 10 77 , 005 43. ,712 20. 10 77 , .333 43. ,573 20. 10 77, .672 43 . ,453 20. 10 78, .008 43. , 385 20. 10 78 . 335 43. . 164 20. 10 78 . 669 43. , 126 20. 10 79, .008 43. .088 20. 10 79. .341 43. .060 20. 10 79 .672 42. ,931 20. 10 80 .003 42 . ,913 20. 10 80, . 333 42 . , 754 20. 10 80, .674 42 . , 746 20. 10 81 .006 42. , 596 20. 10 81 , . 337 42. .589 20. 10 81 . 667 42. ,470 20. 10 82 .007 42 . 441 20. 10 82 .335 42 . , 343 20. 10 82 .673 42 , 193 20. 10 83 .001 42 , 175 20. 10 83 .330 42 , .005 20. 10 83. .662 41 , .917 20. 10 84 , .003 41 , .858 20. 10 84. .335 41 , 820 20. 10 84 .672 41 . 680 20. 10 85. .002 41 , 398 20. 10 85 .337 41 . ,320 20. 10 85. .670 41 . , 241 20. 10 86. .002 41 . ,020 20. 10 86 .331 40. ,840 20. 10 86. .674 40, ,761 20. 10 87 .012 40. ,641 20. 10 87 ,341 40, .481 20. 10 87 .674 40. .311 20. 10 88 .013 39, .917 20. 10 88 .348 39, .767 20. 10 88 .687 39, .597 20. 10 89 .016 39 .447 20. 10 89 .345 39, ,419 20. 10 89 .683 39, . 188 20. 10 90 .021 39 .089 20. 10 90. . 357 38 . 908 20. 10 90. .686 38 . 799 20. 10 91 .014 38. 721 20. 10 91 . 346 38 . 551 20. 10 91 .688 38, ,533 20. 10 92 .007 38 . 384 20. 10 92 . 346 38. .274 20. 10 92 .673 38 , . 186 20. 10 93 .014 38. . 137 20. 10 93 . 346 37. .947 20. 10 93 .684 37 . 909 20. 10 94 .004 37 . 780 20. 10 999. 999. 0 99 2 1 28. 824 79. ,484 20. 10 44 . 181 72 1.141. 562.462.614.477. 14 29. , 153 79. .429 20. 10 44 . 511 72 10.0E- 10 29. ,490 79. .406 20. 10 999. 999 RUN #4 ; TEMPERATURE=22.0 C 29. 826 79, ,301 20. 10 0 7 97.00 3.8795 0.4150 30. 157 79, , 175 20. 10 99 . 150 2.4 1 . 5 30. ,495 79. ,253 20. 10 . 175 24. 1 22.6 30. .829 79, ,219 20. 10 .200 46.7 46 . 3 31 . , 167 79. . 155 20. 10 . 225 64.8 64.2 31 , 508 79, . 162 20. 10 .250 80. 2 79. 1 31 , .840 79, . 159 20. 10 . 275 90.8 90. 4 32 , . 175 79, . 145 20: 10 .300 98 .7 98.9 32 .503 78 .999 20. 10 18.0 999. 999 0 2 17 . 986 91 . ,317 30. 10 0 18. ,319 89 . 271 20. 10 3 18. ,654 88 . 353 20. 10 32 . 483 79. 125 30. 10 18. ,992 87 , .831 20. 10 32. 829 78. 369 20. 10 19. , 325 87 , .320 20. 10 33. 163 78. 131 20. 10 19, ,660 87 , .052 20. 10 33. 495 77. ,974 20. 10 19 , .996 86, .592 20. 10 33. 826 77 . ,797 20. 10 20, , 330 86 . 233 20. 10 34. 162 77. .559 20. 10 20, .662 86, .027 20. 10 34. 499 77 . ,311 20. 10 21 . ,001 85, .739 20. 10 34. 838 77. . 1 14 20. 10 21 . , 335 85, .563 20. 10 35. 168 76. ,876 20. 10 21 . ,667 85, .418 20. 10 35. 500 76. , 790 20. 10 22 . ,004 85, . 161 20. 10 35. 837 76. ,623 20. 10 22 . ,341 85, .005 20. 10 36. 167 76. .415 20. 10 22, .671 84 .829 20. 10 36. 496 76, .411 20. 10 23 , 004 84 , .745 20. 10 36. 827 76 , . 152 20. 10 23, . 342 84 , .589 20. 10 37. 163 76, .077 20. 10 23 , .676 84 .484 20. 10 37 . 501 75, .981 20. 10 999 , 999, 37. 826 75 .773 20. 10 38. 166 75 .668 20. 10 38. ,495 75 .409 20. 10 23, .482 84 .481 30. 10 38. ,831 75 . 334 20. 10 23, .821 82 .830 20. 10 39. , 175 75 .086 20. 10 24 , . 147 82 . 185 20. 10 39 , 501 74 .959 20. 10 24 .482 81 . 785 20. 10 39 , 837 74 .803 20. 10 24 .815 81 .436 20. 10 40. . 169 74 .717 20. 10 25 . 151 81 .219 20. 10 40, .501 74 .438 20. 10 25 .483 80 .941 20. 10 40, .842 74 . 323 20. 10 25 .818 80 .765 20. 10 41 , . 171 74 . 155 20. 10 26 . 157 80 .498 20. 10 41 , .510 73 .958 20. 10 26 .491 80 .291 20. 10 41 , .850 73 .731 20. 10 26 .823 80 . 145 20. 10 42 , 178 73 .594 20. 10 27 . 161 80 .020 20. 10 42 .514 73 .275 20. 10 27 . 487 79 .802 20. 10 42 .845 73 . 189 20. 10 27 .821 79 .809 20. 10 43 . 179 72 .758 20. 10 28 . 152 79 .673 20. 10 43 .515 72 .591 20. 10 28 . 491 79 .670 20. 10 43 .846 72 .271 20. , 10 cn O 2 1 1. 141 .562.462.614.477. 14 10.0E-10 RUN #5; TEMPERATURE=22 C 7 90.0 3.343 0.3994 . 150 1 . .9 3, .7 . 175 24 .0 26 , .3 . 200 48 . 1 47 , 1 . 225 66 .2 64 , 8 .250 80, .6 79 , 7 . 275 91 , .3 90, , 7 .300 98, .8 98 , .0 16.0 0 2 15 .990 80. . 130 30. 10 16 .319 76, . 195 20. 10 16 .656 74 , .426 20. 10 16 .994 73 , .095 20. 10 17 . 323 72 , .059 20. 10 17 .661 71 , .074 20. 10 17 .994 70, .333 20. 10 18 .328 69 , .622 20. 10 18 .654 69. .055 20. 10 18 .992 68 , .456 20. 10 19 . 325 67 . 858 20. 10 19 .666 67 . 360 20. 10 20 .002 66 , .802 20. 10 20 . 333 66. .438 20. 10 20 .666 66 . 053 20. 10 21 .000 65 . 739 20. 10 21 .334 65. .283 20. 10 21 .668 64 . 939 20. 10 22 .006 64. .778 20. 10 999 999. 21 .987 64 . 792 30. 10 22 .323 61 . 186 20. 10 22 .657 58 . 984 20. 10 22 .987 57. .393 20. 10 23 . 326 56 , .024 20. 10 23 .661 55, . 134 20. 10 23 .999 54 , 121 20. 10 24 . 330 53, .272 20. 10 24 .670 52 , .565 20. 10 25 .005 51 , .796 20. 10 25 . 339 51 , .181 20. 10 25 .669 50, .617 20. 10 26 .004 50. .062 20. 10 26 . 334 49, .467 20. 10 26 .671 49, . 106 20. 10 0 3 27. 007 48. ,663 20. 10 27 . 349 48 . ,351 20. 10 27 . 681 48. 112 20. 10 28. ,006 47 . 691 20. 10 28. 341 47. ,320 20. 10 28. ,677 47 . , 100 20. 10 29 . ,015 46. 912 20. 10 29 . ,347 46. ,744 20. 10 29. ,681 46 , 494 20. 10 30. ,018 46 , 265 20. 10 30. 350 45, ,985 20. 10 30. ,680 45 , 868 20. 10 999. 999 . 30, ,488 45, .871 30. 10 30. .829 43, .077 20. 10 31 . 164 41 , .647 20. 10 31 . 498 40, .624 20. 10 31 , .840 39, ,702 20. 10 32, ,171 38 . 883 20. 10 32. .502 38 . 165 20. 10 32. .846 37 , .558 20. 10 33 . , 178 36 , .932 20. 10 33 , 510 36, .469 20. 10 33, ,843 35, .843 20. 10 34, , 179 35 .450 20. 10 34 , 515 34 .997 20. 10 34 , 847 34 .676 20. 10 35, , 177 34 . 274 20. 10 35, .511 33 .810 20. 10 35 .843 33 .571 20. 10 36 . 181 33 .239 20. 10 36. .513 32 .847 20. 10 36. .849 32 .628 20. 10 37 . 178 32 .378 20. 10 37 . 514 32 .057 20. 10 37. .844 31 .716 20. 10 38 , . 180 31 .517 20. 10 38 .514 31 .318 20. 10 38 .842 30 .957 20. 10 39 . 176 30 .534 20. 10 39 .515 30 .345 20. 10 39. .842 30 .014 20. 10 40, . 178 29 .764 20. 10 40, .507 29 .454 20. 10 40, .840 29 .204 20. 10 41 , . 182 29 .096 20. 10 41 , .513 29 .060 20. 10 41 , .849 28 .871 20. 10 o 4 0 5 42. 179 28 . 418 20. 10 42. 512 28 . ,341 20. 10 999. 999. 42 . 493 28 , 257 30. 10 42. ,825 26, ,313 20. 10 43. , 164 25 , 315 20. 10 43. ,505 24 , 410 20. 10 43. ,839 23, .778 20. 10 44 . , 167 23, . 104 20. 10 44 . , 503 22 . 574 20. 10 44, ,843 22 .024 20. 10 45. , 181 21 .474 20. 10 45. ,510 21 .258 20. 10 45. .845 20 .809 20. 10 46. . 177 20 . 370 20. 10 46. . 506 20 . 104 20. 10 46 . 840 19 .817 20. 10 47 , 175 19 .541 20. 10 47 . 513 19 .469 20. 10 47 , .847 19 . 234 20. 10 48 , . 177 19 . 100 20. 10 48 . 510 18 .956 20. 10 48 , 843 18 .832 20. 10 49, , 175 18 . 434 20. 10 49 , 512 18 . 209 20. 10 49, . 849 17 .923 20. 10 50, , 181 17 .789 20. 10 50, ,513 17 . 747 20. 10 50, ,848 17 .634 20. 10 51 , 173 17 . 356 20. 10 51 , 513 17 . 152 20. 10 51 , 852 17 .040 20. 10 52 , 180 16 . 793 20. 10 52, ,519 16 .671 20. 10 52 , .853 16 . 537 20. 10 53, . 186 16 . 383 20. 10 53, .523 16 . 148 20. 10 53, .855 16 .034 20. 10 54 . 185 15 .880 20. 10 54 .514 15 .654 20. •10 999 999 54 .491 15 . 558 30. 10 54, .825 14 .079 20. 10 55 . 166 13 .239 20. 10 55 .497 12 .664 20. 10 • 55 .828 12 .181 20. 10 56. . 157 1 1 . .627 20. 10 56. ,495 1 1 . .245 20. 10 56 . 831 10. .974 20. 10 57. . 161 10. .563 20. 10 57 . 492 10. .374 20. 10 57. .830 10. .083 20. 10 58 . 164 9. .742 20. 10 58. ,496 9. 502 20. 10 58 . ,832 9 , . 273 20. 10 59. , 164 9. ,033 20. 10 59, ,500 8 . 824 20. 10 59. ,833 8. .483 20. 10 60, . 167 8 . 314 20. 10 60, ,495 8 . 136 20. 10 60. .829 8. .008 20. 10 61 . 161 7. .749 20. 10 61 .504 7, .792 20. 10 61 .836 7 . 583 20. 10 62 . 170 7 .496 20. 10 62 .505 7 . 256 20. 10 62 .837 7 . 169 20. 10 63. . 174 7 . 102 20. 10 63 . 509 7 .045 20. 10 63 . 832 6 .888 20. 10 64 , . 173 6 . 769 20. 10 64 , .515 6. .569 20. 10 64 . 838 6. .412 20. 10 65 . 175 6 . 386 20. 10 65. .507 6. . 278 20. 10 65 .843 6 .089 20. 10 66 . 176 5 .982 20. 10 66 .514 5 .853 20. 10 66 .841 5 .635 20. 10 67 .171 5 .609 20. 10 67 . 509 5 .593 20. 10 67 .844 5 .444 20. 10 68 . 173 5 .378 20. 10 68 .507 5 .423 20. 10 68 . 840 5 .204 20. 10 69, . 165 5 .220 20. 10 69. . 505 5 .243 20. 10 69. .835 5. .096 20. 10 70 . 177 5 .068 20. 10 70 . 506 4 .870 20. 10 70 . 838 4 . 732 20. 10 71 . 180 4 .715 20. 10 71 .510 4 .679 20. 10 71 .848 4 . 57 1 20. 10 72 . 182 4 .585 20. 10 72 .514 4 .620 20. 10 72 . 849 4 .634 20. 10 73. , 178 4 . 568 20. 10 73. .517 4. ,460 20. 10 73. .862 4 . 482 20. 10 74 . , 192 4 . ,243 20. 10 74 . 523 4 . 197 20. 10 74 . ,851 4 . ,212 20. 10 75. , 190 4. ,216 20. 10 75. , 530 4 . , 138 20. 10 75. ,857 4 . 204 20. 10 76 . , 187 4 . 158 20. 10 76. , 520 4 . 132 20. 10 76 . , 860 4 . 115 20. 10 77 . , 193 4 . , 180 20. 10 77 . ,515 4 . 186 20. 10 77. .856 4. ,200 20. 10 78. , 180 4 , . 175 20. 10 78, .517 4, . 169 20. 10 78 , .855 4 .213 20. 10 79, . 184 3. .964 20. 10 79, .512 3. .786 20. 10 79. .852 3. .779 20. 10 80. . 185 3 .682 20. 10 80. .516 3 .646 20. 10 80 .848 3 .579 20. 10 81 . 194 3 . 398 20. 10 81 .530 3 .463 20. 10 81 , .855 3. . 378 20. 10 82. . 191 3 . 392 20. 10 82 .519 3 .254 20. 10 82 .858 3 . 146 20. 10 83 . 191 3 .201 20. 10 83 . 522 3 .206 20. 10 83 .863 2 .914 20. 10 84 . 195 2 .644 20. 10 84 .534 2 .668 20. 10 84 .864 2 .653 20. 10 85 . 202 2 .677 20. 10 85 .533 2 .752 20. 10 85 .862 2 .747 20. 10 86 .204 2 .608 20. 10 86 .535 2 .714 20. 10 86 .867 2 .668 20. 10 87 . 199 2 .540 20. 10 87 .534 2 .646 20. 10 87 .867 2 .549 20. 10 88 . 201 2 .553 20. 10 88 . 524 2 .325 20. 10 88 .875 2 .438 20. 10 89 .210 2 . 158 20. 10 999 999 0 99 2 1 0.951.222.152.979.999.99 10.0E-10 RUN #6; TEMPERATURE=30 C 7 194.0 3.343 0.3994 125 2.0 2 . 5 150 17.9 24 . 4 175 41.8 48. 5 200 63 . 3 67 . 5 225 78.3 82. 4 250 90.8 93 . 8 275 98. 1 99 . 9 :o.o 19. 982 93 . 365 30. 10 20. 310 90. 331 20. 10 20. ,642 88. .850 20. 10 20. .984 88 . 027 20. 10 21 . ,317 87 . 339 20. 10 21 , .651 86 . ,671 .20. 10 21 , 980 86, ,066 20. 10 22 , .319 85. .661 20. 10 22 . 646 85 , 381 20. 10 22 . 979 84 . ,906 20. 10 23 , .316 84 . , 532 20. 10 23 .655 84 . 198 20. 10 23. .989 84 . 018 20. 10 24 . 319 83 . 697 20. 10 24. .651 83 . 537 20. 10 24 , .987 83 , 337 20. 10 25. .315 83. .057 20. 10 25 .651 82 . 967 20. 10 9999 ) 9999 2 33 . 501 80 .961 30. 10 33 .813 78 .089 20. 10 34 . 146 76 .858 20. 10 34 . 480 76 .075 20. 10 34 .813 75 . 475 20. 10 35 . 155 74 .954 20. 10 35 .489 74 . 343 20. 10 35 .821 74 .018 20. 10 36 . 147 73 .593 20. 10 36 .487 73 .327 20. 10 36 .821 73 .001 20. 10 37 . 149 72 .788 20. 10 37 .482 72 .453 20. 10 37 .817 72 . 238 20. 10 38 . 152 72 .024 20. 10 38 .489 71 .942 20. 10 38 .825 7 1 .829 20. 10 39. 147 71 . 750 20. 10 39 . 488 71 . 575 20. 10 39. 825 71 . 554 20. 10 40. 159 71 . 533 20. 10 40. 492 71 . 441 20. 10 40. 825 71 . 523 20. 10 9999. i 9999. 3 51 . 985 70. 380 30. 10 52 . 319 68. 296 20. 10 52. 656 67 . 433 20. 10 52 . 991 66. 956 20. 10 53 . 321 66. 683 20. 10 53 . 654 66. 217 20. 10 53. 990 65. ,771 20. 10 54 . , 321 65. .610 20. 10 54 . 652 65. .369 20. 10 54 . 986 65. . 197 20. 10 55. . 322 65. ,015 20. 10 55. .655 64. , 742 20. 10 55 . ,986 64 . 602 20. 10 5G. ,321 64. .482 20. 10 56. ,650 64. . 362 20. 10 56. ,986 64. ,292 20. 10 57 . 321 64 , 263 20. 10 57 . ,655 64 . 133 20. 10 57 . 987 64, , 1 15 20. 10 58 , .321 64 , . 136 20. 10 58 , .653 64. . 179 20. 10 58 .987 64 . 161 20. 10 59 .320 64. . 152 20. 10 59 .657 64 , .092 20. 10 59 .993 64 . 073 20. 10 60 . 323 63 .883 20. 10 60 .661 63, .700 20. 10 60 .993 63. .621 20. 10 61 . 329 63 . 592 20. 10 61 .661 63 .604 20. 10 61 . 998 63 .534 20. 10 62 . 329 63 . 556 20. 10 62 .666 63 .466 20. 10 63 .000 63 .518 20. 10 63 .337 63 .418 20. 10 63 .664 63 . 370 20. 10 63 .996 63 .341 20. 10 64 . 328 63 .221 20. 10 64 .659 63 .214 20. 10 64 .998 63 .112 20. 10 9999 9999 2 1 0.951 .222.152.979.999.99 10.0E-10 RUN 7; TEMPERATURE=22.0 C 7 145.0 3.343 0.4184 .125 2.0 0.0 .150 27.0 15.0 .175 47.7 40.7 .200 65.5 60.2 .225 79.1 75.4 .250 91.4 87.8 .275 98.7 95.4 17.0 16, .974 95 .983 30. 10 17, , 309 92 .717 20. 10 17 , .647 91 . 526 20. 10 17, .977 90. .500 20. 10 18 , .314 89 .655 20. 10 18, .640 88 .915 20. 10 18, .981 88 . 282 20. 10 19. . 321 87 . 801 20. 10 19, .660 87 . 220 20. 10 19. .989 86. .713 20. 10 20, .317 86 . 309 20. 10 20. .649 86. .004 20. 10 20. .989 85. . 768 20. 10 21 , .323 85 .554 20. 10 21 , .649 85, .364 20. 10 21 .983 85 . 191 20. 10 22, .317 84. .906 20. 10 22 . 651 84 , . 764 20. 10 399. 9999. 67 . 994 52 . 901 30. 10 68. .321 50. .455 20. 10 68 . ,660 49. .461 20. 10 68. ,993 48 . 967 20. 10 69. .324 48 . 494 20. 10 69. ,656 48 . 040 20. 10 69 . 988 47 . 790 20. 10 70. , 325 47 . 570 20. 10 70. .653 47 . 269 20. 10 70, ,987 47 . 090 20. 10 71 . 322 46 . 890 20. 10 71 . ,659 46, .670 20. 10 71 , 990 46 , .451 20. 10 72. , 326 46, .261 .20. 10 72. 658 46. . 133 20. 10 72. ,992 46 . 126 20. 10 73, ,320 46, .070 20. 10 73. 659 46. 084 20. 10 73 . 993 46 . 148 20. 10 74 . 321 45. 990 20. 10 74 . 658 45 . 841 20. 10 74 . 997 45. 692 20. 10 75. .326 45 . 646 20. 10 75 . 665 45 . 588 20. 10 75. .996 45. 531 20. 10 76 . 329 45. , 525 20. 10 76 . ,667. 45. . 355 20. 10 77 . ,001 45, , 359 20. 10 77 . ,335 45. ,363 20. 10 77 . 664 45 , 276 20. 10 78 . 000 45 , 391 20. 10 78, .331 45. .426 20. 10 78 .665 45, , 125 20. 10 78 .994 45, .089 20. 10 79 . 332 45. . 163 20. 10 79 .664 45, .096 20. 10 79 .999 44 .978 20. 10 80 . 329 44 .890 20. 10 80 .662 44 .935 20. 10 80 . 989 45 .011 20. 10 81 . 322 44 .964 20. 10 81 .667 45 .007 20. 10 81 .986 44 .973 20. 10 82 . 329 44 .904 20. 10 82 .661 44 .898 20. 10 82 .996 44 .820 20. 10 83 .331 44 . 742 20. 10 83 .662 44 . 777 20. 10 84 .002 44 .668 20. 10 84 .330 44 .653 20. 10 84 .667 44 .707 20. 10 85 .01 1 44 .577 20. 10 85 . 322 44 .463 20. 10 9999. 9999. 1 99 2 1 0 . 9 9 1 . 2 9 3 . 799 .999 .999 .99 1 0 . 0 e - 1 0 RUN #8; TEMPERATURE=29.5 C 7 8 1 . 7 3.343 0.4061 .125 2.0 2.1 .150 21.8 23 .5 . 175 46 .3 46. 1 .200 6 4 . 7 64 .5 .225 80.1 80.4 .250 91 .3 9 2 . 0 .275 98 .4 98.6 16.5 16 . 502 91 , ,291 20. 10 16, ,810 83. , 194 20. 10 17, . 154 78 , .823 20. 10 17 .494 75, ,856 20. 10 17 .824 73, .369 20. 10 18 . 154 71 , .563 20. 10 18 .491 70, .061 20. 10 18 .826 68, .823 20. 10 19 . 169 67 .940 20. 10 19 .503 66, .926 20. 10 19 .832 66. . 157 20. 10 20 . 163 65, .693 20. 10 20 .496 65, .229 20. 10 20, .827 64, .399 20. 10 21 , . 171 64 , .014 20. 10 21 , .499 63, .631 20. 10 21 , .835 63 , . 197 20. 10 22 . 170 62, .865 20. 10 22, .502 62 .563 20. 10 22 , .837 62, .352 20. 10 23. . 165 61 , .909 20. 10 23 , .497 61 , .475 20. 10 23, .832 61 , . 387 20. 10 24 . 170 60, .881 20. 10 24, . 502 60, .813 20. 10 24 .836 60, .796 20. 10 25 , . 166 60, .647 20. 10 25, .504 60, ,497 20. 10 25 , .837 60. , 338 20. 10 26, . 176 60, , 188 20. 10 26 . 509 59 , .988 20. 10 26, .839 59. .839 20. 10 27 . 168 59, ,640 20. 10 27 , .510 59. . 387 20. 10 27 , .844 58. .861 20. 10 28 . 175 58 , 601 20. 10 28 , 504 58 , 218 20. 10 0 2 28. ,847 58 , . 108 20. 10 29. , 179 58 , .051 20. 10 29. ,513 57, .708 20. 10 29. ,841 57, .610 20. 10 30. , 176 57 , .634 20. 10 30. ,512 57 , .372 20. 10 30. ,845 57, .294 20. 10 31 . , 176 57, . 156 20. 10 31 . ,511 57 , . 169 20. 10 31 . ,852 57, . 150 20. 10 32, , 186 57 .113 20. 10 32. ,514 56 .781 20. 10 32 . ,844 56 .633 20. 10 33, , 179 56 .585 20. 10 33, ,514 56 .567 20. 10 33, ,842 56 .500 20. 10 34, , 179 56 .503 20. 10 34, ,512 56 .415 20. 10 34 , .850 56 . 285 20. 10 35 , 185 56 .207 20. 10 35 ,512 56 .069 20. 10 35, .847 56 .072 20. 10 36 , . 180 56 .055 20. 10 36, ,518 55, .955 20. 10 36, ,851 55 .806 20. 10 37. , 183 55 .667 20. 10 37 , .516 55 .549 20. 10 37, .852 55 .490 20. 10 38 , . 189 55 .585 20. 10 38 .525 55 .425 20. 10 38 . 858 55 .296 20. 10 39, . 192 55, . 136 20. 10 39, .532 55, . 108 20. 10 39, .858 55 .021 20. 10 40, . 194 54 .963 20. 10 40, .524 54 .977 20. 10 40, .862 54 .877 20. 10 41 . . 193 54 .728 20. 10 41 , ,520 54, .753 20. 10 4 1 , .857 54 .603 20. 10 42, . 188 54 , .556 20. 10 42 , 524 54 .376 20. 10 42, .848 54 .482 20. 10 999. 999 43, .005 53 .615 20. 10 43 , .321 48 . 528 20. 10 43 , .659 46 . 124 20. 10 43 , .995 44 .941 20. 10 44 . 330 43. ,758 20. 10 44 . 657 42. ,923 20. 10 45. 001 42 . , 227 20. 10 45. 343 41 , . 399 20. 10 45. 671 40, , 787 20. 1.0 46. 004 40, .358 20. 10 46 . ,329 39 , 654 20. 10 46 . ,671 39 , 152 20. 10 47 . ,004 38, .814 20. 10 47 . , 340 38 ,639 20. 10 47 . .673 38 .565 20. 10 48 . 003 38 . 553 20. 10 48 , .336 38 .449 20. 10 48 . .670 38 . 345 20. 10 49, .006 38 .27 1 20. 10 49 . , 348 38 . 104 20. 10 49 . 679 38 .01 1 20. 10 50, ,012 37 , .825 20. 10 50. ,347 37, .599 20. 10 50. ,666 37, .588 20. 10 51 . ,005 37 . 280 20. 10 51 . , 338 37 . 186 20. 10 51 , 670 37 . 123 20. 10 52 , 014 36 .956 20. 10 52 , , 333 37 .007 20. 10 52, ,667 36 .953 20. 10 53 , .003 36 .900 20. 10 53 , . 332 36 .837 20. 10 53 , .667 36 .855 20. 10 54, .004 36 .943 20. 10 54, .335 36 .951 20. 10 54 . 670 36 . 867 20. 10 55 . 004 36 .865 20. 10 55, .340 36 .923 20. 10 55 , .668 36 .932 20. 10 56 , .009 36 .979 20. 10 56 , . 343 37 . 109 20. 10 56 .678 36 .995 20. 10 57 , .005 37 .044 20. 10 57, .338 37 .031 20. 10 57 , .674 36 .978 20. 10 58 .009 36 .914 20. 10 58, .341 36 .810 20. 10 58 .671 36 .849 20. 10 59 .012 36 .815 20. 10 59, . 343 36 .833 20. 10 59 .684 36 .626 20. 10 60 .008 36 . 737 20. 10 60 . 344 36 .714 20. 10 60 .675 36 .681 20. 10 3 61 . ,009 36, .689 20. 10 61 . 346 36, ,605 20. 10 61 . 677 36, .725 20. 10 62. 009 36, ,611 20. 10 62. 341 36. .629 20. 10 62. 678 36. .636 20. 10 63. 008 36. .573 20. 10 63. 345 36 . 560 20. 10 63. 678 36. ,548 20. 10 64 . 017 36 . ,453 20. 10 64 . 344 36 . ,462 20. 10 64 . 678 36 . 296 20. 10 65 . 009 36. .356 20. 10 65. ,342 36 , .201 20. 10 999. 999 , I 65 .510 35 .546 20. 10 65, .825 31 .776 20. 10 66, . 167 30 .222 20. 10 66, .503 29 .443 20. 10 66 . 846 28 .672 20. 10 67, . 175 28 .352 20. 10 67 , 501 27 .911 20. 10 67 , 841 27 .406 20. 10 68 . 170 26 .862 20. 10 68 . 516 26 .366 20. 10 69, .4 25 .8 0. 20 73 .299 24 . 165 30. 10 73, .620 23 .997 20. 10 73, .958 24 . 142 20. 10 74 . 293 24 .247 20. 10 74 .624 24 . 281 20. 10 74 .956 24 .295 20. 10 75 .292 24 .257 20. 10 75 .624 24 .433 20. 10 75 .960 24 . 182 20. 10 76 .291 .24 .216 20. 10 76 .629 24 .076 20. 10 76 .956 23 .999 20. 10 77 . 291 23 .920 20. 10 77 .626 23 .628 20. 10 77 .954 23 .408 20. 10 78 . 286 23 . 167 20. 10 78 . 631 22 .996 20. 10 78 .960 22 . 837 20. 10 79 . 296 22 .870 20. 10 79 .632 22 .679 20. 10 79 .965. 22 .825 20. 10 80 . 301 23 .052 20. 10 0 99 80, ,627 23. , 290 20. 10 80, ,959 23, ,344 20. 10 81 , .297 23 ,214 20. 10 81 , .628 23, , 157 20. 10 81 , .981 23 , 147 20. 10 82 .306 22, ,978 20. 10 82. .634 22, , 759 20. 10 82. .971 22, .771 20. 10 83 .295 22 .705 20. 10 83, .632 22 .657 20. 10 83 .966 22 .721 20. 10 84 .299 22 .643 20. 10 84 ,640 22 .482 20. 10 84 .969 22 .476 20. 10 85 .299 22 .479 20. 10 85 .632 22 .554 20. 10 85 .970 22 .505 20. 10 86 .303 22 .417 20. 10 86 .632 22 .034 20. 10 86 .971 21 .975 20. 10 87 . 299 21 .888 20. 10 87 .642 21 .971 20. 10 87 .969 21 .934 20. 10 88 .317 21 .833 20. 10 999 999 i 16 .480 93 . 176 30. 10 42 .988 54 .940 30. 10 65 .490 36 . 191 30. 10 2 1 0.991.293.799.999.999.99 10.0E-10 RUN 9, TEMPERATURE=29.5 C 7 105.0 3.343 0.3847 .125 2.0 4.8 .150 24.8 28.1 .175 35.5 41.0 .200 66.6 69.1 .225 80.5 82.8 .250 92.0 93. 1 .275 97.1 99.8 18.0 18 . ,026 95. ,204 20. 10 18 . ,310 90. , 224 20. 10 18. ,642 86 , 977 20. 10 18 . 980 84 , 990 20. 10 19. , 309 83 . 593 20. 10 19. ,650 82. ,602 20. 10 19. ,980 81 . 826 20. 10 20, ,316 81 . , 1 10 20. 10 20. ,657 80. . 505 20. 10 20, .990 79 , 840 20. 10 21 , . 324 79 , . 368 20. 10 21 , 655 78 , .856 20. 10 2 1 .999 78 , . 454 20. 10 22 , . 333 78 , 156 20. 10 22 .660 77 , .868 20. 10 22 , 992 77 , .651 20. 10 23 , . 330 77 , .361 20. 10 23 , .672 77 , .041 20. 10 23. .999 76 . 896 20. 10 24 , . 335 76 . 536 20. 10 24 , .666 76, .491 20. 10 25, .004 76, .111 20. 10 25, . 342 75, .852 20. 10 25 .668 75 . 564 20. 10 26 .000 75 . 347 20. 10 26 . 339 74 .946 20. 10 26 .669 74 . 709 20. 10 27 .004 74 .593 20. 10 27 .335 74 .467 20. 10 27 .673 74 .402 20. 10 28 .OOO 74 . 277 20. 10 28 . 333 73 . 988 20. 10 28 .663 73 .924 20. 10 28 .997 73 .676 20. 10 29 . 333 73 .539 20. 10 29 .669 73 .321 20. 10 30 .004 73 . 195 20. 10 30. , 340 73 . ,049 20. 10 45. 837 53. 962 20. 10 79 . 997 34 . 672 20. 10 30. .670 73. ,005 20. 10 57. O05 48. 445 20. 10 80. 325 34 . 488 20. 10 31 . ,001 72 . 848 20. 10 57. 319 48. 365 20. 10 80. 662 34 . 393 20. 10 31 . 339 72. ,854 20. 10 57. 654 48. 258 20. 10 80. 995 34 . 299 20. 10 31 . ,671 72. .789 20. 10 57. 995 48. 130 20. 10 81 . 328 34 . 184 20. 10 32 . ,003 72. ,603 20. 10 58. 322 48. 157 20. 10 81 . 660 34 . 172 20. 10 32. ,341 72 . 639 20. 10 58 . 666 47 . 957 20. 10 81 . 990 33 . 937 20. 10 32. .675 72. ,401 20. 10 58. ,996 47. .821 20. 10 82 . 329 34 . 075 20. 10 33. ,01 1 72. .417 20. 10 59 . 330 47 . 735 20. 10 82 . 665 33 . 818 20. 10 33 . 344 72. , 352 20. 10 59. .663 47 . 527 20. 10 82 . 991 33 . 736 20. 10 33 . ,674 72, .237 20. 10 60. .003 47 . 582 20. 10 83 . 334 33. 680 20. 10 34 . ,012 72. ,273 20. 10 60. . 335 47 . 445 20. 10 83 . 659 33. .649 20. 10 34. , 347 72. . 147 20. 10 60. ,671 47 , .288 20. 10 84 . 001 33. 543 20. 10 34 . ,676 72 , 083 20. 10 60. ,998 47 , 244 20. 10 84 . 331 33 . ,541 20. 10 35 . 012 7 1 , .906 20. 10 61 , .334 47, .086 20. 10 84 . 661 33 . 611 20. 10 35. .346 71 . 871 20. 10 61 , .667 47 , 143 20. 10 84 . ,993 33 . 507 20. , 10 35, .679 71 . 776 20. 10 62 . 000 47, ,098 20. 10 85. ,325 33 . 444 20. , 10 36. .01 1 71 , .589 20. 10 62 . 330 46, .881 20. 10 85 . 668 33 , 429 20. . 10 36 . 344 71 .575 20. 10 62 .671 46, .884 20. 10 86. ,001 33 , 477 20. , 10 36 .679 71 , .480 20. 10 63. .005 46 .951 20. 10 86 . 338 33, .413 20. , 10 37 .012 71 . 364 20. 10 63, . 337 46, .926 20. 10 86 . 663 33 . 240 20. . 10 37 . 350 71 . 187 20. 10 63. .671 46 .901 20. 10 86 . 994 33 . 126 20, , 10 37, .687 71 .213 20. 10 63 .997 46 .644 20. 10 87 . 326 33 .114 20, . 10 38 .012 71 .078 20. 10 64 .331 46 .772 20. 10 87 .667 33 .089 20, . 10 38 .350 70 .972 20. 10 64 .677 46 .683 20. 10 87 .994 33 .017 20, . 10 38 , .685 70 .795 20. 10 65 .001 46 . 538 20. 10 88 . 326 33 .066 20. . 10 39 .015 70 .649 20. 10 999 999 88 . 661 33 . 124 20. . 10 39 . 350 70 .584 20. 10 0 88 .997 33 .080 20 . 10 39, .681 70 .458 20. 10 3 89 . 329 33 . 139 20 . 10 40 .016 70 .373 20. 10 73 .012 43 .653 20. 10 89 . 651 33 .211 20 . 10 40 .347 70 . 186 20. 10 73 .314 40 .637 20. 10 89 .995 33 .084 20 . 10 999 999 73 .649 39 .403 20. 10 90 . 334 33 . 120 20 . 10 73 .998 38 .632 20. 10 90 .657 33 .111 20 . 10 74 . 329 38 .295 20. 10 90 . 994 32 .985 20 . 10 40 .500 69 . 340 30. 10 74 .661 37 . 754 20. 10 91 . 326 33 .044 20 . 10 40 .814 64 .257 20. 10 75 .002 37 .464 20. 10 91 .674 33 .007 20 . 10 41 . 161 62 . 104 20. 10 75 .334 37 .442 20. 10 92 .010 32 .862 20 . 10 41 .495 60 .799 20. 10 75 .670 37 .388 20. 10 95 .004 32 .862 20 . 10 41 .830 59 .820 20. 10 76 .002 37 . 192 20. 10 999 999 42 . 163 58 .973 20. 10 76 .332 36 .987 20. 10 0 42 . 505 58 . 399 20. 10 76 .667 36 .832 20. 10 99 42 .833 57 .920 20. 10 77 .002 36 .646 20. 10 17 .995 97 . 100 30 . 10 43 . 165 57 .267 20. 10 77 .338 36 . 378 20. 10 40 .487 70 .219 30 . 10 43 .503 . 56 .847 20. 10 77 .661 35 .992 20. 10 72 .980 44 .771 30 ,10 43 .834 56 . 407 20. 10 77 .999 35 .479 20. , 10 44 . 174 56 .007 20. 10 78 .336 35 .323 20. . 10 44 .512 55 .505 20. 10 78 .671 35 .219 20. , 10 44 .838 55 . 108 20. 10 78 .998 34 .963 20. , 10 45 . 176 54 .616 20. 10 79 .333 34 .859 20. . 10 45 .514 54 .327 20. 10 79 .661 34 .655 20. . 10 2 1 28. 169 67. 734 20. 10 43. 655 50. 378 20. 10 0.991 . ,293.799.999.999. 99 28. 506 67. 505 20. 10 44 . 002 49 . 653 20. 10 10.0E-•10 28. 824 67. 266 20. 10 44 . 333 49 . 1 12 20. 10 RUN #10; TEMPERATURE=29.5 C 29. 159 67. 200 20. 10 44 . 657 48. 591 20. 10 7 95.8 3 . 343 0.4325 29. 489 67 . 031 20. 10 44 . 995 48 . 202 20. 10 . 125 1 .7 0, .3 29 . 803 66 . 782 20. 10 45. 334 47 . 691 20. 10 . 150 27.2 24 , .7 30. 140 66. 594 20. 10 45 . 665 47 . 446 20. 10 . 175 48.8 47 , .7 30. 466 66. 670 20. 10 45 . 997 47 . 159 20. 10 .200 67.2 65, .6 30. 794 66. 563 20. 10 46. 329 46. 903 20. 10 .225 81.3 80. ,5 31 . , 129 66 . ,273 20. 10 46 . 670 46 . 626 20. 10 .250 91.5 91 , .2 31 . 453 66. 186 20. 10 47 . 005 46 . 462 20. 10 . 275 98.7 98. ,0 31 . 777 66 . 090 20. 10 47 . 325 45 . 982 20. 10 16.0 32. , 1 10 65. ,728 20. 10 47 . 659 45. 757 20. 10 15. ,999 97, . 108 20. 10 32. .441 65. 652 20. 10 47 . 996 45 . 480 20. 10 16 . ,316 91 , .441 20. 10 32 . ,773 65. 504 20. 10 48 . 333 45 . 469 20. 10 16 , 649 88 .422 20. , 10 33. .092 65. .316 20. 10 48 . 666 45 . 253 20. 10 16 . 977 85, .952 20. , 10 33. ,431 65. . 209 20. 10 48 . ,993 45 . , 161 20. 10 17 . 312 84, .012 20. , 10 33. ,756 65. .051 20. 10 49 . ,321 45. ,037 20. 10 17 .647 82, . 347 20. , 10 34. ,086 65. ,036 20. 10 49 , 657 44 . ,924 20. 10 17 . 967 81 , .039 20. , 10 34. ,420 64 . 837 20. 10 49. .991 44 , 566 20. 10 18. . 302 79 .781 20. , 10 34 . , 744 64. , 720 20. 10 50, . 322 44 , .412 20. 10 18 .620 78 .829 20. . 10 35, ,077 64 . 562 20. 10 50, .653 44 , 339 20. 10 18 , .957 77 .887 20. , 10 35. ,411 64. , 506 20. 10 50 .984 44 .033 20. 10 19, . 292 77 .037 20. . 10 35 . ,727 64 . ,318 20. 10 51 .316 43 .970 20. 10 19 , .623 76 .370 20. , 10 36, ,062 64, ,425 20. 10 51 .649 43 .847 20. 10 19 .946 75 .621 20. ,10 36, .399 64 . 318 20. 10 51 .982 43 .672 20. 10 20 . 271 74 .863 20. , 10 36, .730 64, . 190 20. 10 52 .320 43 .620 20. 10 20 .600 74 . 399 20. , 10 37, .060 64 , . 124 20. 10 52 .652 43 .588 20. 10 20 . 939 73 .936 20. , 10 37. .382 63. .987 20. 10 52 .982 43 .485 20. 10 21 , .259 73 .656 20. . 10 37 . 714 63 , .880 20. 10 53 .312 43 .412 20. 10 21 .579 73 . 335 20. , 10 38 . 037 63, .722 20. 10 53 .653 43 . 339 20. 10 21'. .923 72 . 943 20. . 10 38 , .363 63, .635 20. 10 53 .989 43 . 287 20. 10 22 .246 72 .622 20. . 10 38, .697 63. .569 20. 10 54 .319 43 . 245 20. , 10 22 , .570 72 . 190 20. , 10 39 , .029 63, .442 20. 10 54 .645 43 .071 20. 10 22, .904 71 .909 20. , 10 39 .354 63. .447 20. 10 54 .981 43 .008 20. , 10 23, . 240 71 .578 20. , 10 39, .687 63, . 248 20. 10 55 .311 42 .997 20. , 10 23 .570 71 . 196 20. , 10 40, .012 63 .284 20. 10 55 .657 42 .944 20, . 10 23 , .896 70 .916 20. , 10 40, .336 63, .086 20. 10 55 .984 42 .882 20 . 10 24 , . 224 70 .514 20. , 10 40, .665 63, .030 20. 10 56 .312 42 . 779 20 . 10 24, . 552 70 .204 20. , 10 40, .999 62, .943 20. 10 56 .649 42 . 757 20 . 10 24 .884 69 .862 20. . 10 999, 999, 56 .977 42 . 532 20 . 10 25 . 204 69 .583 20. , 10 0 57 .314 42 .479 20 . 10 25 . 538 69 .506 20, , 10 2 57 .657 42 .416 20 . 10 25 .867 69 .369 20. . 10 41 . 345 61 , .553 30. 10 57 .980 42 .324 20 . 10 26 . 196 69 .089 20, , 10 41 , .656 57 . 151 20. 10 58 .314 42 .312 20 . 10 26 . 528 68 .900 20, . 10 41 .993 55 .041 20. 10 58 .646 42 . 230 20 . 10 26 .853 68 .630 20, . 10 42 .320 53 .603 20. 10 58 .977 42 . 147 20 . 10 27 . 179 68 .401 20. . 10 42 .656 52 .461 20. 10 59 . 307 41 .911 20 . 10 27 . 509 68 . 142 20, . 10 42 .990 51 . 797 20. 10 59 .644 41 .859 20 . 10 27 .842 67 .973 20. . 10 43 .324 50 .981 20. 10 59 .973 41 .838 20 . 10 3 60 31 1 41 .734 20 10 60 64 1 41 539 20 10 60 971 41 447 20 10 61 303 4 1 374 20 10 61 64 1 41 219 20 10 61 973 41 188 20 10 62 300 41 014 20 10 62 640 40 951 20 10 62 971 40 827 20 10 63 305 40 714 20 10 63 640 40 417 20 10 63 970 40 375 20 10 64 301 40 191 20 10 64 641 40 190 20 10 999 999 64 840 19 723 30 10 65 149 17 971 20 10 65 480 17 291 20 10 65 821 16 672 20 10 66 161 16 317 20. 10 66 487 16 034 20. 10 66 829 15 654 20. 10 67 151 15 493 20. 10 67 487 15 378 20. 10 67 828 15 120 20. 10 68 164 14 964 20. 10 68 493 14 757 20. 10 68 821 14 652 20. 10 69 155 14 455 20. 10 69 501 14 360 20. 10 69 829 14 148 20. 10 70 163 14 124 20. 10 70 491 13 933 20. 10 70 820 13 813 20. 10 71 157 13 855 20. 10 71 487 13 887 20. 10 71 820 13 879 20. 10 72 163 14 017 20. 10 72 503 14 105 20. 10 72 830 13 777 20. 10 73 163 13 610 20. 10 73 496 13 332 20. 10 73 832 13 313 20. 10 74 160 13 071 20. 10 74 492 13 012 20. 10 74 836 12 805 20. 10 75 165 12 684 20. 10 75 496 12 706 20. 10 75 830 12 632 20. 10 76 164 12 420 20. 10 76 488 12 351 20. 10 76 838 12 235 20. 10 77 168 12 074 20. 10 77 495 12 070 20. 10 77 826 12 042 20. 10 78 1 19 12 050 20. 10 78 509 12 334 20. 10 78 830 12 275 20. 10 79 170 12 282 20. 10 79 492 12 238 20. 10 79 821 12 184 20. 10 80 162 12 038 20 10 80 497 1 1 928 20 10 80 825 1 1 797 20. 10 81 156 1 1 773 20 10 81 496 1 1 541 20 10 81 833 1 1 568 20 10 82 164 1 1 376 20 10 82 496 1 1 480 20 10 82 831 1 1 334 20 10 83 166 1 1 346 20 10 83 496 1 1 312 20 10 83 845 1 1 318 20 10 84 172 1 1 360 20 10 84 499 1 1 286 20 10 84 830 1 1 303 20 10 85 169 1 1 299 20 10 85 500 1 1 393 20 10 85 835 1 1 272 20 10 86 176 1 1 258 20 10 86 504 1 1 296 20 10 86 840 1 1 175 20 10 87 176 1 1 223 20 10 87 499 1 1 174 20 10 87 825 1 1 150 20 10 88 164 1 1 080 20 10 88 493 1 1 092 20 10 88 832 1 1 099 20 10 89 162 1 1 075 20 10 89 503 1 1 168 20 10 89 832 1 1 089 20 10 90 162 1 1 029 20 10 90 497 1 1 1 17 20 10 90 839 1 1 088 20 10 91 163 1 1 070 20 10 91 501 1 1 066 20 10 91 830 1 1 068 20 10 92 165 1 1 024 20 10 0 99 92 496 1 1 143 20. 10 92 824 1 1 170 20. 10 93 157 1 1 304 20. 10 93 486 1 1 295 20. 10 93 831 1 1 271 20. 10 94 166 1 1 278 20. 10 94 507 1 1 162 20. 10 94 833 1 1 093 20. 10 95 170 1 1 094 20. 10 95 486 1 1 005 20. 10 95 836 10 971 20. 10 999 999 15 980 98 799 30 10 4 1 319 63 032 30 10 64 823 20 135 30 10 2 1 0.991.293.799.999.999.99 10.0E-10 RUN 11; TEMPERATURE=29.5 C . 7 122.0 3.343 0.3832 . 125 1 .0 2 .0 . 150 24. .7 23 .9 . 175 49. .2 46 .6 .200 66 .8 66 .8 .225 81 . 2 81 .2 . 250 92 .3 91 .8 .275 99. . 1 99. . 1 22.5 22 . 497 85 .959 20. 10 22 , 803 77 .952 20. 10 23. . 140 73 .236 20. 10 23. .473 70 .260 20. 10 23, .808 68 . 167 20. 10 24 , . 141 66 .491 20. 10 24 , 474 65 . 263 20. 10 24 . 816 64 , . 254 20. 10 25 . 154 63, .420 20. 10 25. .485 62 .701 20. 10 25 , .815 62 , .033 20. 10 26 . 151 61 , .464 20. 10 26 . 487 61 , .048 20. 10 26 . 824 60 .600 20. 10 27. . 157 60 .307 20. 10 27, .491 59 .790 20. 10 27 , .821 59 .590 20. 10 28. . 159 59 .315 20. 10 28, , 490 58 .992 20. 10 28 , .822 58 .709 20. 10 29, . 165 58 .544 20. 10 29, .497 58 .424 20. 10 29 .831 58 .201 20. 10 30 . 165 58 .121 20. 10 30, .494 57 .850 20. 10 30, .821 57 .793 20. 10 31 , . 163 57 . 567 20. 10 31 , .491 57 .449 20. 10 31 , .833 57 , .254 20. 10 32, . 160 57, ,227 20. 10 32 , 494 56 , .985 20. 10 32. .822 57, .070 20. 10 33 . 159 56, . 998 20. 10 33. ,483 56, .780 20. 10 33 . 827 56 . 797 20. 10 34. , 160 56, .707 20. 10 34 . , 492 56, . 506 20. 10 0 2 34 . 813 56. 320 20. 10 35 . 160 56. 509 20. 10 35. 494 56. 357 20. 10 35. 814 56. 415 20. 10 36. 165 56. 145 20. 10 36. 490 55 . 977 20. 10 36. 835 55. 678 20. 10 37 . 150 55. 474 20. 10 37. 500 55. 093 20. 10 37. 837 54 . 818 20. 10 38. 162 55. , 199 20. 10 38. 494 55 . ,232 20. 10 38. 823 55. ,255 20. 10 39. 164 55. ,050 20. 10 39. .498 55. ,051 20. 10 39. .836 54. ,807 20. 10 40. . 167 54 , 474 20. 10 40. , 500 54 , .557 20. 10 40. .834 54, .304 20. 10 41 . , 174 54 , .201 20. 10 41 , .507 54 .040 20. 10 41 , .833 54 .075 20. 10 42 , . 174 53 .992 20. 10 42, .509 54 .074 20. 10 42 , .846 53 .972 20. 10 43, . 168 53 .917 20. 10 43 .502 53 .786 20. 10 43 .834 53 .707 20. 10 44 . 167 53 .668 20. 10 44 .503 53 .495 20. 10 44 .832 53 .519 20. 10 45 . 166 53 .510 20. 10 45 .507 53 .315 20. 10 45 .832 53 .381 20. 10 46 . 176 53 .378 20. 10 46 .502 53 . 301 20. 10 46 .835 53 . 242 20. 10 47 . 173 53 .201 20. 10 47 .506 53 .202 20. 10 999 999 47 .854 51 .496 20. 10 48 . 148 47 .438 20. 10 48 .486 45 .503 20. 10 48 .823 44 .403 20. , 10 49 .151 43 .226 20. , 10 49 . 499 42 .506 20. , 10 49 .836 41 .812 20. , 10 50 . 166 41 .345 20. , 10 50. 501 41 . 048 20. 10 50. 821 40. 647 20. 10 51 . 164 40. 347 20. 10 51 . 494 40. 165 20. 10 51 . 826 39 . 748 20. 10 52 . 156 39 . 494 20. 10 52 . 500 39. 285 20. 10 52. 828 39 . 052 20. 10 53. 158 38 . 901 20. 10 53 . 490 38 . 555 20. 10 53. 827 38 . 430 20. 10 54. 161 38. ,408 20. 10 54. 496 38. ,458 20. 10 54 . 829 37 . ,979 20. 10 55 . 160 37 , 735 20. 10 55. 493 37 , 785 20. 10 55 . 828 37 , .499 20. 10 56. 164 37 , . 344 20. 10 56 . 500 37 . 190 20. 10 56. .826 37 . 182 20. 10 57 . , 159 36 . 958 20. 10 57 . , 495 36 .731 20. 10 57 . ,833 36 .840 20. 10 58 , . 163 36 . 750 20. 10 58 , 495 36 .627 20. 10 58 .829 36 .575 20. 10 59 . 170 36 . 377 20. 10 59 . 499 36 .277 20. 10 59 . 835 36 . 295 20. 10 60 . 165 36 . 123 20. 10 60 . 503 36 . 150 20. 10 60 .835 36 . 150 20. 10 61 . 173 35 .953 20. 10 61 . 502 35 .965 20. 10 61 .837 35 .638 20. 10 62 . 168 35 .669 20. 10 62 .504 35 . 544 20. 10 62 .832 35 .698 20. 10 63 . 172 35 .552 20. . 10 63 . 502 35 .430 20. , 10 63 .836 35 . 389 20. , 10 64 . 174 35 .477 20. , 10 64 .510 35 . 393 20. , 10 64 .835 35 . 488 20, , 10 65 . 173 35 . 403 20, . 10 65 . 498 35 . 264 20, . 10 65 .840 35 . 147 20 . 10 66 . 178 35 . 185 20 . 10 66 .508 35 .094 20 . 10 66 .838 35 .034 20 . 10 G7 . 182 34 .916 20. 10 67 .518 34 .944 20. 10 67 .853 34 .800 20. 10 68 . 177 34 .803 20. 10 68 .514 34 .699 20. 10 68 .850 34 .687 20. 10 69 . 180 34 .830 20. 10 69 .512 34 .657 20. 10 69 .848 34 .502 20. 10 70 . 179 34 . 563 20. 10 70 . 508 34 .422 20. 10 70 .837 34 .322 20. 10 7 1 . 167 34 .332 20. 10 71 . 524 34 . 269 20. 10 999 999 I 71 . 508 33 .453 30. 10 71 .818 30 .482 20. 10 72 . 153 29 . 239 20. 10 72 .490 28 .260 20. 10 72 .813 27 .555 20. 10 73 . 144 27 .095 20. 10 73 . 476 26 .746 20. 10 73 .819 26 .012 20. 10 74 . 152 25. .521 20. 10 74 . 479 25, . 172 20. 10 74 , .805 24. .986 20. 10 75 . 138 24 , .668 20. 10 75 . 476 24. .493 20. 10 75. .804 24, .083 20. 10 76.. . 137 23. .938 20. 10 76 .474 23, .712 20. 10 76, . 796 23. .576 20. 10 77 , . 125 23, . 309 20. 10 77. .453 23. . 123 20. 10 77 . , 790 22. .846 20. 10 78. , 123 22 . , 579 20. 10 78. ,452 22. ,555 20. 10 78. 788 22 . , 156 20. 10 79 . 104 21 . 848 20. 10 79. 446 21 . 703 20. 10 79 . 773 21 . 466 20. 10 80. 114 21 . 382 20. 10 80. 428 20. 789 20. 10 80. 755 20. 807 20. 10 81 . 081 20. 448 20. 10 81 . 410 20. 425 20. 10 81 . 739 20. 493 20. 10 82 . 065 20. 398 20. 10 82 .407 20, .213 20. 10 82 .732 19. .884 20. 10 83. .067 19. .597 20. 10 83. .390 19. .268 20. 10 83. .724 18 . 961 20. 10 84. .045 18, .836 20. 10 84 . 390 19, .006 20. 10 84. .707 18, .952 20. 10 85, .042 18 .807 20. 10 85, .385 18 .672 20. 10 85, .711 18 . 587 20. 10 86 .045 18 .310 20. 10 86. .379 18 . 206 20. 10 86. . 705 18 .010 20. 10 87 .029 17 .681 20. 10 87 .367 17 .556 20. 10 87 .686 17 .543 20. 10 88 .034 17 .571 20. 10 88 .359 17 .283 20. 10 88 .684 17 . 230 20. 10 89 .017 17 .318 20. 10 89 . 351 17 . 122 20. 10 89 .680 17 .048 20. 10 90, .010 16 .964 20. 10 90 .346 16 .880 20. 10 90 .684 16 .592 20. 10 90 .996 16 .518 20. 10 91 . 346 16 .078 20. 10 91 . 667 16 . 157 20. 10 91 .994 15 .981 20. 10 92 . 324 16 .029 20. 10 92 .655 15 .639 20. 10 92 .978 15 .616 20. 10 93. .311 15 .512 20. 10 93. .645 15 . 356 20. 10 93 .964 15 .312 20. 10 94 . 294 15 .076 20. 10 94 .631 15 .012 20. 10 94 .964 15 .273 20. 10 95 . 295 15 . 199 20. 10 95 .635 15 .502 20. 10 95 .958 15 .427 20. 10 96 .289 15 .221 20. 10 96 .628 15 . 198 20. 10 96 .942 14 .94 1 20. 10 97 . 277 14 .968 20. 10 97 .610 14 .783 20. 10 97, .949 14 .810 20. 10 98 .269 14 .695 20. 10 98 .598 14 .581 20. 10 98. 927 14 . 547 20. 10 99 . 273 14 . 463 20. 10 99. 580 14 . 582 20. 10 99 . ,925 14 . 406 20. 10 100. . 249 14 . , 393 20. 10 100. .588 14. , 370 20. 10 100. ,921 14 . ,316 20. 10 101 , 261 14 . 273 20. 10 101 , 580 14 . 321 20. 10 101 , .913 14 . 409 20. 10 102 . 237 14 . 234 20. 10 102 , .572 14, .200 20. 10 102 .892 14 .024 20. 10 103 . 226 14 , .001 20. 10 103 . 555 13 .988 20. 10 103 .889 13, .934 20. 10 104 . 217 13 . 728 20. 10 104 , . 540 13 . 735 20. 10 104 .877 13 . 631 20. 10 105 . 209 13 .404 20. 10 105 . 536 13 .513 20. 10 106 . 200 13 . 761 20. 10 106 . 538 13 . 738 20. 10 106 . 863 13 . 593 20. 10 107 . 198 13 .692 20. 10 107 .519 13 .252 20. 10 107 .855 13 .046 20. 10 108 . 180 13 .083 20. 10 108 .517 12 .918 20. 10 999 999 o 99 2 1 0.951.222.152.97 10.0E-10 RUN 12; TEMPERATURE=29.5 C 7 1G8.0 3.343 0.3793 . 125 2.0 7 . 3 . 150 28 .0 31 . 2 . 175 49.8 52. 9 .200 67.2 70. 6 . 225 81.3 83 . 7 .250 91 .6 92 . 9 .275 98.4 99. 9 19.5 19. 477 84 , 227 30. 10 19. 817 78. 732 20. 10 20. . 144 76 . ,767 20. 10 20. ,479 75 , 369 20. 10 20. ,816 74 . ,327 20. 10 21 , 155 73. ,467 20. 10 21 . 488 72 . ,740 20. 10 21 . ,820 72. ,217 20. 10 22. , 155 71 . 734 20. 10 22 , 484 71 . , 191 20. 10 22 . 816 70, .891 20. 10 23, . 155 70, .550 20. 10 23 , .488 70, .291 20. 10 23, .825 69 , .990 20. 10 24 , .151 69 , .661 20. 10 24, .488 69, .361 20. 10 24 . 821 69, . 213 20. 10 25 . 151 69, .097 20. 10 9999 0 9999 2 31 . 178 67 .609 30. 10 31 .514 63 .349 20. 10 31 .846 61 .812 20. 10 32 . 175 60 .845 20. 10 32 .513 59 .998 20. 10 32 .849 59 . 355 20. 10 33 . 180 58 . 794 20. 10 33 .512 58 . 374 20. 10 33 .847 57 .945 20. 10 34 . 178 57 .658 20. 10 34 .512 57 .482 20. 10 34 .841 57 . 196 20. 10 35 . 1.82 56 .857 20. 10 35 .515 56 .742 20. 10 35 .844 56 .445 20. 10 36 . 179 56 .280 20. 10 36 .515 56 .084 20. 10 36 .857 55 .978 20. 10 37 . 183 55 .865 20. 10 37 .510 55 .609 20. 10 37 .850 55 .555 20. 10 38 . 180 55 .390 20. 10 38 .515 55 .255 20. 10 999 9999 68 .990 40 .857 30. 10 69 . 328 38 .456 20. 10 69 .663 37 .805 20. 10 69 .993 37 . 551 20. 10 70 . 330 37 . 265 20. 10 70 .663 36, .970 20. 10 70, .992 36, .848 20. 10 71 .321 36, . 279 20. 10 71 .664 35 , .942 20. 10 71 .995 35, .688 20. 10 72; . 327 35, .495 20. 10 72, .664 35, .230 20. 10 72 .994 35, .006 20. 10 73, . 326 34 , . 762 20. 10 73 .664 34 , .558 20. 10 73 , .993 34 , .508 20. 10 74 , .330 34 , .456 20. 10 74 , .666 34 . 364 20. 10 74 , .993 34 . 222 20. 10 75, .330 34. .039 20. 10 75, .663 33, .937 20. 10 75, .999 33. ,845 20. 10 76, .338 33. ,814 20. 10 76, ,667 33. ,722 20. 10 77, .003 33. ,651 20. 10 77. ,336 33. ,671 20. 10 77. ,672 33. ,447 20. 10 78. ,007 33 . 334 20. 10 78. ,338 33. , 192 20. 10 78. 672 33 . 121 20. 10 79. ,009 33. 140 20. 10 79. , 338 32. 998 20. 10 79 . ,676 32 . 886 20. 10 80. 007 32. 825 20. 10 80. 340 32 . 774 20. 10 80. 669 32. 734 20. 10 81 . 005 32 . 570 20. 10 81 . 341 32 . 489 20. 10 81 . 675 32. 549 20. 10 82. 006 32. 590 20. 10 82. 342 32. 519 20. 10 82 .669 32. ,570 20. 10 83 .004 32 . 692 20. 10 83 . 332 32, ,702 20. 10 83, .669 32 , 631 20. 10 84 .008 32. ,650 20. 10 84 . 339 32 . 599 20. 10 84 .669 32 , .508 20. 10 85 .006 32 , 507 20. 10 85 . 342 32 . 334 20. 10 85 .672 32 . 212 20. 10 86 .016 31 , .977 20. 10 86, .347 31 . 916 20. 10 86 . 684 31 . 722 20. 10 9999. 9999. 0 99 2 1 31 . 894 58. 821 20. 10 2 1 10.0E-•10 32. 215 58. 853 20. 10 0.951. 222 . 152.979.999. 99 RUN #13; TEMPERATURE=29.5 C 32. 523 58 . 839 20. 10 10.OE- 10 7 93.0 3.343 0.4230 32. 837 58 . 812 20. 10 RUN 14; TEMPERATURE=29.5 . 125. 2. 1 2 . 1 33. 165 58. 852 20. 10 7 117.0^ 3 . 343 0.4590 . 150 27 . 5 27. 5 33. 474 59. 000 20. 10 . 125 2 . 1 O.C 1 . 175 49.7 49. 7 33. 791 59. ,064 20. 10 . 150 27 . 7 4 .C 1 . 200 67 .0 67 . 0 34. , 118 59. , 125 20. 10 . 175 49.5 31 . 6 .225 79.7 79. 7 34, ,428 59, , 171 20. 10 .200 68. 1 51 . 8 . 250 89.5 89. 5 34. ,740 59 . , 124 20. 10 . 225 81.0 69 . 0 .275 97.9 97, 9 35. ,060 59. , 106 20. 10 .250 89 . 7 81 . 9 19.0 35. ,371 59, ,090 20. 10 . 275 98 . 9 90. 0 19. 908 84 . 153 20. 10 35. ,697 59, . 192 20. 10 21.0 20. 193 73. 823 20. 10 36. .009 59, , 146 20. 10 20. 990 92 . 175 30. 10 20. 514 69. 641 20. 10 36 . 327 59 . 189 20. 10 21 . 329 89 . 813 20. 10 20. 833 67. 404 20. 10 36. .645 59, , 201 20. 10 21 . 661 89. 155 20. 10 21 . 153 66. 072 20. 10 36, ,959 59 . 144 20. 10 21 . 988 88 . 499 20. 10 21 . 467 64. ,936 20. 10 37, .276 59 .218 20. 10 22 . 324 88 . 075 20. 10 21 . ,786 64. , 124 20. 10 37 . 593 59 .221 20. 10 22 . 666 87 . 751 20. 10 22. , 105 63 . ,515 20. 10 37 .906 59 .164 20. 10 22 . 993 87 . 431 20. 10 22 . 430 62. .711 20. 10 38 .227 59 . 176 20. 10 23 . 329 87 . 312 20. 10 22. ,733 62, ,321 20. 10 38 .541 59 .119 20. 10 23. 664 86. 919 20. 10 23 . ,051 61 , . 764 20. 10 38 .864 59 . 161 20. 10 23. 996 86 . 709 20. 10 23. 366 61 . 431 20. 10 39 . 178 59 . 154 20. 10 24 . 327 86 . 521 20. 10 23 . 687 61 . ,413 20. 10 39 .486 59 . 129 20. 10 24 . 663 86 . 351 20. 10 23. ,999 61 , 316 20. 10 39 .811 59 . 170 20. 10 24 , 996 86 . 203 20. 10 24 . ,320 61 , 480 20. 10 40 . 113 59 .066 20. 10 25, ,332 86 . 043 20. 10 24. .634 60. .843 20. 10 40 .439 59 .087 20. 10 25 , .666 85. 833 20. 10 24 .951 60, .428 20. 10 40 .750 59 . 101 20. 10 25, .992 85. 718 20. 10 25 .257 60 .017 20. 10 - 41 .064 59 .085 20. 10 26, .332 85. 638 20. 10 25 .576 59 .785 20. 10 41 .380 59 .057 20. 10 26. .667 85. 459 20. 10 25 .895 59 .604 20. 10 41 .703 58 .845 20. 10 9999, 9999 . 26 .217 59 .361 20. 10 42 .015 58 .920 20. 10 0 26 . 529 59 . 152 20. 10 999 999 2 26 .839 59 . 137 20. 10 0 27 . 306 85 . ,046 30. . 10 27 . 171 58 .972 20. 10 99 27 .649 82 . ,853 20. , 10 27 .482 58 .814 20. 10 19 .886 86 .277 30. , 10 27 .983 81 . ,852 20. . 10 27 .796 58 .991 20. 10 28 .316 81 . , 198 20. , 10 28 . 108 58 .802 20. 10 28 .645 80, ,7 17 20, . 10 28 .420 58 .898 20. 10 28 .977 80, ,215 20 . 10 28 . 744 58 .756 20. 10 29 .311 79 . 784 20 . 10 29 .054 58 .700 20. 10 29 .648 79, .524 20 . 10 29 .376 58 .650 20. 10 29 . 979 79. . 328 20, . 10 29 .678 58 .648 20. 10 30 . 309 78 .888 20, . 10 29 .999 58 .670 20. 10 30 .640 78 .691 20 . 10 30 . 320 58 .518 20. 10 30 .982 78 .532 20 . 10 30 .633 58 .533 20. 10 31 .316 78 .324 20 . 10 30 .949 58 .424 20. 10 31 .650 78 . 107 20 . 10 31 . 264 58 .580 20. 10 31 . 977 77 .911 20 . 10 31 .575 58 .829 20. 10 32 32 .315 . 648 77 77 .723 .515 20 20 . 10 . 10 32. .990 77 . 285 20. 10 2 1 42 .668 58 . ,648 20. 10 33 . 324 77 . 149 20. 10 0.951 . 222. 152.979.999.99 43 . 002 58 . 457 20. 10 33 .653 76 .973 20. 10 10.0E--10 43 . 333 58 , 2 16 20. 10 33 .991 76. . 754 20. 10 RUN #15; TEMPERATURE=29.5 C 43 . 663 58 . 015 20. 10 34 . 328 76 .698 20. 10 7 146.0 3.343 0.4083 44. .000 57. ,785 20. 10 34 . 663 76 , .541 20. 10 . 125 1 .9 2 . , 1 44 . 332 57 . 554 20. 10 9999 . 9999 , . 150 26.3 26. ,0 999. 999 . 0 . 175 49.2 49. ,0 0 3 .200 66. 1 67 . , 1 3 35. ,998 75. ,957 30. 10 .225 81 .3 81 . 0 50 .985 54 . 712 30. 10 36. ,325 73. ,290 20. 10 .250 92.3 91 . 9 51 .319 50. .988 20. 10 36. .660 72. ,379 20. 10 .275 99.4 99. . 1 51 .654 50, ,047 20. 10 36. .992 71 . 652 20. 10 26.5 51 .989 49 , . 299 20. 10 37 . 325 70. ,924 20. 10 26. 50 87. ,653 30.10 52 .320 48 . 621 20. 10 37. .660 70, .277 20. 10 26 . 83 81 . 507 20. 10 52 .659 48. . 1 17 20. 10 37. .992 69, .712 20. 10 27. 16 79. ,511 20.10 52 .989 47 . 521 20. 10 38. .331 69. .247 20. 10 27. 50 78. .014 20. 10 53 .323 47. .006 20. 10 38 .663 68, .906 20. 10 27. .83 76 . 936 20. 10 53 .658 46 . 654 20. 10 38, .997 68 .463 20. 10 28 . 16 76. .313 20.10 53 .988 46 , .250 20. 10 39 . 328 68 . 153 20. 10 28. .50 75. .715 20.10 54 . 323 46 . 010 .20. 10 39. .660 67 , .882 20. 10 28. 83 75. .256 20.10 54 .659 45 , .648 20. 10 39 , .993 67 . 531 20. 10 29 . 16 74 . 811 20.10 54 .993 45 . 377 20. 10 40. , 324 67 . 363 20. 10 29 . 50 74 . 499 20.10 55 . 329 45 . 126 20. 10 40, .658 67. , 103 20. 10 29 . 83 74 . 191 20.10 55 .665 44 . 804 20. 10 40. ,995 66 . , 730 20. 10 30. 16 73. .924 20. 10 56 .002 44 . 655 20. 10 4 1 . , 330 66 . 510 20. 10 30. 50 73. .691 20.10 56 .337 44 . 364 20. 10 41 . ,665 66. ,218 20. 10 30. 83 73. .478 20.10 56 .667 44 , . 1 13 20. 10 41 . ,994 66. .020 20. 10 31 . 16 73. .296 20.10 56 .993 43 . 801 20. 10 42. , 331 65. ,790 20. 10 31 . 50 73, .186 20.10 57 .331 43 , 673 20. 10 42 . ,667 65. .529 20. 10 31 . 83 73 .035 20. 10 57 .662 43 . 361 20. 10 43, .002 65. .360 20. 10 32. . 16 72, .802 20.10 58 .000 43 . 202 20. 10 43, ,335 65, .089 20. 10 999. 999 58 . 338 42 . 870 20. 10 43, .668 64 . 870 20. 10 0 58 .671 42 . 74 1 20. 10 44 . 005 64 , .609 20. 10 2 59 .004 42 . 572 20. 10 44. .335 64. .319 20. 10 36. 989 *71 . 538 30.10 59 .338 42 .341 20. 10 44 , .669 64 . 099 20. 10 37 . 321 66 .931 20.10 59 .670 42. .090 20. 10 44 , .999 64 . 247 20. 10 37 . ,658 65, .367 20.10 60 .001 4 1 , .840 20. 10 45. .339 64 . , 107 20. 10 37. ,997 64, .374 20.10 60 . 334 41 , .609 20. 10 45 . 675 63. .886 20. 10 38. 337 63 .471 20.10 60 .665 41 , .419 20. 10 46. 005 63. 647 20. 10 38. .669 62 .793 20.10 61 .002 41 , .230 20. 10 46 . 344 63. 284 20. 10 39. ,001 62 .297 20.10 61 . 337 40, .938 20. 10 46. 672 62. 923 20. 10 39. . 333 61 .710 20.10 61 .676 40, , 708 20. 10 47 . 010 62. ,723 20. 10 39. .668 61 .326 20.10 62 .001 40, .630 20. 10 47. .347 62. 533 20. 10 40. ,002 60 .963 20.10 62 .330 40, , 440 20. 10 47 . 674 62 . 163 20. 10 40. . 335 60 .529 20.10 62 .672 40, . 301 20. 10 48. .010 62. 156 20. 10 40. ,667 60 .379 20. 10 63 .001 40, ,071 20. 10 9999. 9999 . 41 . ,007 60 .006 20.10 63 . 331 39 , .891 20. 10 0 41 , 336 59 .663 20.10 63 .668 39, , 691 20. 10 99 41 . 42. 42, 669 ,002 . 337 59 59 58 .422 20.10 .181 20.10 .899 20.10 999 0 99 999 , 2 1 0.752.584 . 499.999.999.99 10.0E-10 RUN #16; TEMPERATURE=35 C 7 85.0 3.8795 0.4262 . 125 1 . . 8 1 .8 . 150 27 , 1 25 .8 . 175 49. .2 48 . 2 .200 67 , 2 67 .9 . 225 81 . ,6 82 .0 .250 92 . 2 92 . 7 . 275 99, .6 99 .6 18.5 18 . 478 96. ,452 30. 10 18. 818 83. , 253 20. 10 19 . , 154 78 . 889 20. 10 19 . ,490 76 . , 426 20. 10 19. .825 74 . 939 20. 10 20. . 165 73. .798 20. 10 20. .504 73. .063 20. 10 20. .836 72, .227 20. 10 21 . 164 71 , .726 20. 10 21 . 502 71 . 276 20. 10 21 . 835 70. .908 20. 10 22 . 167 70. .427 20. 10 22 . 499 70. .008 20. 10 22 . ,835 69 . 690 20. 10 23. , 167 69. .413 20. 10 23 , .500 69 . 126 20. 10 23 .834 68 .646 20. 10 24 . 173 68 .247 20. 10 24 .509 68 .041 20. 10 24 .839 67 .764 20. 10 25 . 170 67 .629 20. 10 25 . 509 67 .322 20. 10 25 .845 67 . 238 20. 10 26 . 178 67 . 144 20. 10 26 , .512 66 .806 20. 10 26 . 847 66 .468 20. 10 32 , .983 65 .734 20. 10 33 , . 309 65 .559 20. 10 33 . 649 65 .618 20. 10 33 .987 65 .432 20. 10 34. .318 65 . 185 20. 10 34, .650 64 .959 20. 10 34 . 988 64 .764 20. 10 35 , . 322 64 .426 20. 10 35. .657 64 . 169 20. 10 35 , .986 64 .014 20. 10 36 . 321 63 .839 20. 10 999 0 2 36 . 651 63. 623 20. 10 36. 987 63. 447 20. 10 37 . 325 63 . 282 20. 10 37 . 654 63 . 259 20. 10 37. 983 63 . 084 20. 10 38 . 315 62 . ,787 20. 10 38 . 650 62 . 571 20. 10 38. 990 . 62. ,507 20. 10 39. 321 62 . 281 20. 10 39 . 658 62 . , 167 20. 10 39 . 988 61 . 900 20. 10 40. ,334 61 . ,796 20. 10 40. ,660 61 . ,549 20. 10 40. ,997 61 . ,506 20. 10 41 . ,330 61 , 341 20. 10 41 . ,665 61 , .207 20. 10 42. ,006 61 , .001 20. 10 42. , 332 60, .785 20. 10 42. ,670 60, .691 20. 10 43. ,005 60 .566 20. 10 43. ,344 60 .391 20. 10 43. ,675 60 .226 20. 10 44. ,000 59 .878 20. 10 44 . 340 59, .774 20. 10 44. ,676 59 .578 20. 10 45. .008 59 .433 20. 10 45 . 341 59 .258 20. 10 45, .671 59 . 113 20. 10 46. I . .001 58 .887 22 . 00 45, .979 58 .825 30. 10 46, .320 49 .728 20. 10 46 ,657 47 .693 20. 10 46 .991 46 . 228 20. 10 47 .324 45 . 242 20. 10 47 .665 44 . 396 20. 10 48 .005 43 .693 20. 10 48 .328 42 .974 20. 10 48 .664 42 .364 20. 10 48 .993 41 .725 20. 10 49 .328 41 . 186 20. 10 49 .668 40 .625 20. , 10 49 .997 40 .444 20. , 10 50 .329 39 .804 20. . 10 50 .663 39 .489 20. , 10 50 .999 39 . 143 20. . 10 51 .328 38 .636 20. , 10 51 .664 38 .270 20. , 10 52 . 000 37. 985 20. 10 52 . 334 37 . 610 20. 10 52 . 669 37 . 325 20. 10 52. 998 37 . 103 20. 10 53 . 336 36 . 746 20. 10 53. 672 36. 390 20. 10 54 . 005 36 . 167 20. 10 54 . 337 35 . 700 20. 10 54 . 673 35 . 405 20. 10 55 . 007 35 . 040 20. 10 55 . 333 35 . 022 20. 10 55 . 666 34 . 738 20. 10 55. 998 34. 342 20. 10 56 . 334 33 . 793 20. 10 56 . ,675 33. 171 20. 10 57. .001 32 . 777 20. 10 57 . 339 32 . 258 20. 10 57 . ,679 31 . 717 20. 10 58 . ,000 31 . 273 20. 10 58 , 337 30. 734 20. 10 58. .660 30. 402 20. 10 58 , .996 29. 862 20. 10 59 . 344 29 . ,483 20. 10 59 .672 29. .088 20. 10 60 .001 28. ,643 20. 10 60 . 339 28 . , 144 20. 10 60 .666 27 . 800 20. 10 61 .009 27 . 503 20. 10 61 . 334 27 , . 160 20. 10 61 .671 26. .621 20. 10 62 .010 26 . 305 20. 10 62 . 343 25. . 776 20. 10 62 .679 25 .420 20. 10 63 .012 25 . 157 20. 10 63 . 342 24 .853 20. 10 63 .682 24 .425 20. 10 64 .015 24 . 120 20. . 10 64 . 345 23 .918 20. . 10 64 .676 23 .441 20. . 10 65 .017 23 . 125 20. . 10 65 . 351 22 .851 20. . 10 65 .685 22 . 536 20. . 10 66 .017 22 .313 20, 10 66 . 343 21 .868 20. . 10 66 .678 21 .482 20 . 10 67 .020 2 1 . 185 20. . 10 67 . 343 20 .883 20 . 10 67 .680 20 .670 20 . 10 68 .014 20 .283 20 . 10 68 . 347 19 .939 20 . 10 68 .677 19 .686 20. 10 2 1 52. 164 61 . 222 20. 10 69. .009 19 .300 20. 10 2.582. 584.. 499.999.999.99 52 . 502 61 . 153 20. 10 69 , . 354 19 .390 20. , 10 10.0E-•10 52. 835 61 . 064 20. 10 69 .685 19 .513 20. 10 RUN #18; TEMPERATURE=35 C 53 . 168 60. 935 20. 10 70. .023 19 .604 20. 10 7 114.5 3.343 0.4054 53 . 506 60. 815 20. 10 85, .0 14 .7 22. 00 . 125 2.0 9. ,8 53 . 836 60. 828 20. 10 999. . 150 24.8 31 . 8 54 . 170 60. 688 20. 10 0 . 175 46 .6 52 . ,2 54 . ,501 60. 599 20. 10 99 .200 64 .9 69 . 3 54. ,835 60. ,703 20. 10 .225 78 .8 81 .9 55 . , 165 60. ,685 20. 10 .250 89.7 92 . 4 55, , 505 60. .606 20. 10 .275 96 . 7 98 .8 55, .839 60. ,658 20. 10 40.5 56, , 172 60. . 580 20. 10 40. 499 79 . 168 30. 10 56. .507 60. 592 20. 10 40. 489 79, .270 30.10 56, 838 60. ,503 20. 10 40. 518 77 , .434 30.10 57 . , 174 60. ,404 20. 10 40. 822 72 .991 20.10 57 . 503 60. , 376 20. 10 41 . 163 70 .875 20.10 57 . ,845 60. , 337 20. 10 i 41 . 497 69 .509 20.10 58 . 175 60. , 279 20. 10 41 . 829 68 .620 20.10 58 . , 504 60. , 342 20. 10 42 . 164 67 .873 20.10 58 . 841 60. , 293 20. 10 42 . 502 67 .236 20.10 59, , 174 60. , 255 20. 10 42 . 828 66 .773 20.10 59. ,512 60. , 206 20. 10 43 . 168 66 .359 20.10 59 , 835 60, ,088 20. 10 43. 512 65 .935 20.10 60. .171 60. 029 20. 10 43 . ,844 65 .542 20.10 60. .507 60, ,01 1 20. 10 44. , 172 65 .231 20.10 60. . 84 1 59 . ,922 20. 10 44 . ,505 64 .848 20.10 61 . 175 59 . ,853 20. 10 44 . ,839 64 .607 20.10 61 , 504 59 . ,805 20. 10 45 . , 177 64 .264 20.10 61 . ,837 59 , 696 20. 10 45. ,509 64 .105 20.10 62 . 166 59 , 708 20. 10 45 . ,841 63 .712 20.10 62 . 504 59 . , 599 20. 10 46 . , 181 63 .460 20.10 62 , 831 59 , 551 20. 10 46. ,51 1 63 .392 20.10 63 , . 169 59 , 472 20. 10 46, ,842 63 .060 20.10 63 . 501 59 . 433 20. 10 47 , . 180 62 .900 20.10 63 , . 842 59. , 506 20. 10 47 , .514 62 .902 20.10 64 , . 179 59 . , 396 20. 10 47 , .852 62 .802 20.10 64 , . 502 59 . 491 20. 10 48, . 178 62 .653 20.10 64 , .837 59 . 179 20. 10 48 .517 62 .493 20.10 65 . 178 59 , . 180 20. 10 48 , .851 62 .363 20.10 65, .510 59 . 132 20. 10 49 , . 181 62 .244 20.10 65 .844 59 . 073 20. 10 49 , .515 62 .115 20.10 66 . 176 58 . 944 20. 10 49 .835 61 .905 20.10 66 . 513 58 . 824 20. 10 50, . 176 61 .755 20.10 999 , 999 . 50 .507 61 .686 20.10 1 50, .838 61 .679 20.10 3 51 . 170 61 .590 20.10 66 , .490 59. .022 30. 10 51 .500 61 .430 20.10 66 .513 57 , 911 30. 10 51 .832 61 .281 20.10 66 .830 54 . 524 20. 10 G7 . 164 53. 369 20. 10 G7 . 491 52 . 662 20. 10 G7 . 827 52 . 128 20. 10 68 . 159 51 . 615 20. 10 68 . 501 51 . 245 20. 10 68 . 840 50. 997 20. 10 69 . 172 50. 718 20. 10 69 . 500 50. 388 20. 10 69 . 833 50. 109 20. 10 70. 170 49. 810 20. 10 70. 503 49. 664 20. 10 70. 836 49. 466 20. 10 7 1 . 161 49 . 228 20. 10 71 . ,504 49. 072 20. 10 71 . ,838 48. 915 20. 10 72. , 165 48. ,789 20. 10 72. ,495 48. ,572 20. 10 72 . ,829 48. ,456 20. 10 73, , 166 48. ,442 20. 10 73 , .503 48 . 062 20. 10 73, .836 47 . 864 20. 10 74 . 173 47, ,514 20. 10 74, . 505 47 , 317 20. 10 74 , .834 47 , 160 20. 10 75 , . 162 46 . 861 20. 10 75 , .506 46 . 766 20. 10 75 , .834 46 . ,660 20. 10 76 , . 172 46 , . 473 20. 10 76 , .507 46 . 195 20. 10 76 , .834 46, , 130 20. 10 77, . 169 45, .851 20. 10 77 .504 45 . 735 20. 10 77 .841 45 . 579 20. 10 78 . 172 45 . 494 20. 10 78 .493 45 .235 20. 10 78 .843 45 .079 20. 10 79 . 177 44 .933 20. 10 79 .505 44 .735 20. 10 79 .834 44 . 568 20. 10 80 . 168 44 .310 20. 10 80 . 503 44 . 178 20. 10 80 .833 44 .002 20. 10 81 . 163 43 .825 20. 10 81 .493 43 . 668 20. 10 81 .831 43 .471 20. 10 82 .171 43 . 294 20. 10 82 . 499 43 . 189 20. 10 82 .837 43 . 104 20. 10 83 . 172 42 .906 20. 10 83 .507 42 .668 20. 10 83. 839 42. 654 20. 10 84. 172 42. 437 20. 10 84 . 507 42. 311 20. 10 84 . 839 42 . 256 20. 10 85 . 172 42. 008 20. 10 85 . 504 42. 025 20. 10 85. 843 41 . 716 20. 10 86 . 180 41 . 519 20. 10 86. 513 41 . 433 20. 10 86. 844 41 . ,226 20. 10 87 . 175 41 . ,151 20. 10 87. 509 40, ,994 20. 10 87 . ,841 40, .736 20. 10 88. , 175 40, .569 20. 10 88. ,511 40, .586 20. 10 88. ,841 40, .541 20. 10 89. , 176 40, .476 20. 10 89. .506 40, .422 20. 10 89, ,838 40 .275 20. 10 90, . 170 39 .875 20. 10 90. .502 39 .718 20. 10 90, .843 39 .592 20. 10 91 , . 172 39 .558 20. 10 91 , .507 39 .340 20. 10 91 , .841 39 .052 20. 10 92, . 167 39 .048 20. 10 92 .506 38 .952 20. 10 92 .835 38 .887 20. 10 93 . 168 38 .721 20. 10 93 .508 38 .513 20. 10 93 .842 38 .398 20. 10 94 . 174 38 .394 20. 10 94 .505 38 .329 20. 10 94 .841 38 .284 20. 10 95 . 171 38 . 250 20. 10 95 .510 38 .226 20. 10 95 .843 38 .151 20. 10 96 . 183 38 .076 20. 10 96 .505 38 .062 20. 10 1 14 .5 37 .2 20. , 10 999 999 1 99 2 1 1.202.302.403.209.999.99 10.0E-10 RUN 19; TEMPERATURE=35 7 76.5 3.343 0.4041 .150 5.7 5.7 .175 30.4 30.4 .200 51.3 52.8 .225 66.8 68.5 .250 80.1 81.2 .275 87.3 88.3 .300 97.7 98.7 23.5 999 0 2 23 . 486 89 . 777 30. 10 23. 827 86 . 410 20. 10 24. 169 85. 569 20. 10 24 . 486 84 . 823 20. 10 24 . 827 84 . 399 20. 10 25. 163 84 . 017 20. 10 25 . 497 83 . 604 20. 10 25 . 838 83 . 364 20. 10 26. . 166 83 . 125 20. 10 26. ,493 82 . 785 20. 10 26 . ,825 82 . 628 20. 10 27 . 166 82 . ,407 20. 10 27 . ,495 82 . , 138 20. 10 27 , .830 82 . 000 20. 10 28 . 166 81 . ,873 20. 10 28 . 502 81 . ,694 20. 10 28 . 829 81 , 659 20. 10 29, . 162 81 , .430 20. 10 29, .497 81 , 343 20. 10 29 .835 81 , .3 17 20. 10 30 . 168 81 .118 20. 10 30 .510 80 .928 20. 10 30 l . .839 80 . 751 20. 10 34 . 996 79 . 479 30. 10 35 . 326 76 . 123 20. 10 35 .658 74 . 799 20. 10 35 . 990 73 .628 20. 10 36 . 328 72 .629 20. 10 36 .660 71 .864 20. 10 36 .990 71 . 181 20. 10 37 .326 70 .609 20. 10 37 .656 70 .058 20. 10 37 .990 69 .608 20. 10 38 .315 69 . 109 20. 10 38 . 649 68. 730 20. 10 66 . 17 51 . , 157 20. 10 83 , .685 38 . , 260 20. 10 38. 987 68 . 381 20. 10 66 .50 50. .933 20. 10 84 . 016 38 . ,064 20. 10 39 . 322 68 . 002 20. 10 66, .87 50. 801 20. 10 84 , . 352 37 . 796 20. 10 39. 663 67. 673 20. 10 67 , . 17 50. ,627 20. 10 84 , 676 37 . 682 20. 10 39 . 997 67 . 365 20. 10 67 , .50 50. . 341 20. 10 85 , 013 37 . 618 20. 10 40. 334 67. 087 20. 10 67. .83 50. , 199 20. 10 85, .346 37 . 401 20. 10 40. 661 66. 750 20. 10 68 . 17 49. .985 20. 10 85, .684 37 , .245 20. 10 40. 997 66 . 493 20. 10 68 . 50 49. ,781 20. 10 86, .016 37 , . 141 20. 10 41 . 336 66 . 286 20. 10 68 .83 49. .668 20. 10 86 , . 354 36 , .812 20. 10 41 . 669 66 . 009 20. 10 69, . 17 49 . ,628 20: 10 86. .679 36 , . 708 20. 10 41 . 998 65. 763 20. 10 69, .50 49. ,393 20. 10 87 .004 36, .818 20. 10 42 . 333 65. 536 20. 10 69. .83 49. .311 20. 10 87 . 350 36, ,631 20. 10 42 . 673 65 . 380 20. 10 70, . 17 49. ,301 20. 10 87 .684 36. , 445 20. 10 43. 01 1 65. 163 20. 10 70 .50 49. , 199 20. 10 88 .01 1 36 , 341 20. 10 43. 348 65. 007 20. 10 70, .83 48. .903 20. 10 88 . 346 36 , . 257 20. 10 43. 673 64 . 793 20. 10 71 , . 17 48 . 720 20. 10 88 . 675 36 , . 193 20. 10 44 . 002 64 . 628 20. 10 71 .50 48 . ,546 20. 10 89 .009 36 .119 20. 10 44 . 337 64 . 381 20. 10 71 .83 48 , 373 20. 10. 89 . 348 35 .994 20. 10 44 . 675 64 . ,337 20. 10 72 . 17 48 , 230 20. 10 89 .676 35 .889 20. 10 45 . 008 64 . ,111 20. 10 72 .50 48 , 067 20. 10 90 .025 35 .672 20. 10 45 . 337 64 . ,007 20. 10 72 .83 47 , .904 20. 10 90 . 349 35 . 578 20. 10 45 . ,678 63. ,901 20. 10 73 . 17 47 . , 781 20. 10 90 .684 35 .361 20. 10 46 . 010 63 . 868 20. 10 73 .50 47 . , 740 20. 10 91 .018 35 . 308 20. 10 46 . , 343 63 , 652 20. 10 73 .83 47 . ,648 20. 10 91 . 354 35 . 172 20. 10 46. ,673 63 , . 549 20. 10 74, . 17 47 . 506 20. 10 91 .687 35 .210 20. 10 47 , 338 63 . 391 20. 10 74 , .50 47 . ,485 20. 10 92 .016 34 . 984 20. 10 47 . 679 63 . ,285 20. 10 74 .83 47 . 444 20. 10 92 .352 34 .961 20. 10 48 .016 63, . 160 20. 10 999. 92 .686 34 .938 20. 10 48 . 342 63 . 1 18 20. 10 0 93 .014 34 . 874 20. 10 48 .682 62 .921 20. 10 4 93 . 348 34 . 820 20. 10 999. 76 .995 47, , 144 30. 10 94 .020 34 .540 20. 10 0 77 , . 328 44 , 402 20. 10 94 . 349 34 . 456 20. 10 3 77 .666 43 , 432 20. 10 94 .687 34 . 504 20. 10 60 .535 60 .267 30. 10 77 .999 42 , 879 20. 10 95 .009 34 . 593 20. 10 60 .83 57 .527 20. 10 78 . 328 42 , 327 20. 10 95 . 348 34 . 356 20. 10 61 . 17 56 .68 1 20. 10 78 .666 41 , 805 20. 10 95 .682 34 . 343 20. 10 61 .50 56 .070 20. 10 79 .001 41 , 293 20. 10 96 .008 34 . 147 20. 10 61 .83 55 . 397 20. 10 79 .339 40. 923 20. 10 999 . 62 . 17 54 .674 20. 10 79 .672 40, ,696 20. 10 0 62 .50 54 .215 20. 10 80 .014 40. .438 20. 10 99 62 .83 53 .827 20. 10 80 .348 40, ,008 20. 10 63 . 17 53 .521 20. 10 . 80 .677 39 . 619 20. 10 63 .50 53 . 134 20. 10 81 .016 39 . ,422 20. 10 63 .83 52 .747 20. , 10 81 . 344 39, . 145 20. 10 64 . 17 52 .523 20. , 10 81 .677 39. ,050 20. 10 64 .50 52 .319 20, , 10 82 .015 38 . 935 20. 10 64 . 83 52 .024 20. , 10 82 .347 38, .770 20. 10 65 . 17 51 .780 20, , 10 82 .680 38 .533 20. 10 65 .50 51 .616 20. , 10 83 .082 38 .424 20. 10 65 .83 51 .402 20. . 10 83 .344 38, .375 20. 10 2 1 1.202.302.403.209.999.99 10.0E-10 RUN #20; TEMPERATURE=35 C 7 136.5 3.343 0.3940 .125 2.0 9.6 .150 24.4 30.9 .175 47.6 50.9 .200 63.9 68.5 .225 77.5 82.0 .250 89.6 92.2 .276 96.6 98.5 20.5 20. 476 96. 563 30. 10 20. 798 93. 566 20. 10 21 . 123 92 . 429 20. 10 21 . 452- 91 . 728 20. 10 21 . , 772 91 . 242 20. 10 22. .086 90. , 767 20. 10 22 . , 406 90. ,453 20. 10 22. ,727 90. . 160 20. 10 23. ,050 89. ,827 20. 10 23. , 366 89. 483 20. 10 23 . 691 89. ,302 20. 10 24. .015 89. 161 20. 10 24. ,328 88. 930 20. 10 24. .638 88. ,739 20. 10 24 . ,957 88. 568 20. 10 25. .288 88. .488 20. 10 25 . 605 88. .409 20. 10 25 .931 88 . 258 20. 10 26; .247 88. ,087 20. 10 26 . 569 87 . 957 20. 10 27 , . 7 87. .90 20. 10 32 I. . 5 87 . 0 20. 10 32 . 473 86. ,994 30. 10 32 , 804 82 . 650 20. 10 33, . 143 81 . 193 20. 10 33 , 477 80. . 103 20. 10 33 , .810 79. . 308 20. 10 34 , . 145 78. .777 20. 10 34 , .478 78, . 1 14 20. 10 34 .816 77 .541 20. 10 35 .151 77 , . 203 20. 10 35 .477 76 . 806 20. 10 35 .810 76 . 539 20. 10 36 . 147 76 . 303 20. 10 36 . 488 75 .995 20. 10 999 0 3 36 .825 75 .727 20. . 10 37 . 155 75 .563 20. . 10 37 .488' 75 .276 20. , 10 37 .827 75 . 182 20. . 10 38 . 163 75 . 108 20. , 10 38 .492 74 .832 20. . 10 38 .832 74 .727 20. , 10 39 . 165 74 .542 20. , 10 39 .504 74 .427 20. . 10 39 .836 74 .303 20. 10 40 . 167 74 . 230 20. 10 40 .500 73 .873 20. 10 40 .840 73 .808 20. 10 41 . 173 73 .572 20. 10 41 .509 73 .631 20. 10 41 .840 73 .477 20. 10 42 . 180 73 . 352 20. 10 42 .507 73 .340 20. 10 42 .847 73 .113 20. 10 44 ). .519 73 .071 20. 00 44 .479 73 . 280 30. 10 44. .816 69 .612 20. 10 45. . 145 68 .356 20. 10 45. .482 67 .526 20. 10 45 . 817 66 .951 20. 10 46 , . 151 66 .224 20. 10 46. .485 65 .811 20. 10 46. .822 65. .358 20. 10 47. , 162 65, .067 20. 10 47. ,490 64, .473 20. 10 47. ,826 64 , .091 20. 10 48. , 158 63. , 729 20. 10 48. 499 63 . ,459 20. 10 48. 837 63. , 168 20. 10 49. 174 63. .030 20. 10 49. 501 62. ,741 20. 10 49. 839 62 . 674 20. 10 50. 181 62. .606 20. 10 50. 515 62 . 469 20. 10 50. 849 62. 209 20. 10 51 . 179 62. 103 20. 10 51 . 510 62 . 017 20. 10 51 . 843 61 . 819 20. 10 52. 180 61 . 732 20. 10 52. 51 1 61 . 737 20. 10 52. 845 61 . 559 20. 10 53. 179 61 . 482 20. 10 999 0 4 53 . ,515 61 . ,568 20. 10 53. ,849 61 , .482 20. 10 54 . , 181 61 . 497 20. 10 54 . 517 61 . 370 20. 10 54 . 850 61 . 385 20. 10 55. , 183 61 , 421 20. 10 55. .517 61 , . 253 20. 10 55. ,853 61 , 227 20. 10 56 . 180 61 , . 182 20. 10 56 . ,511 61 , . 198 20. 10 56 . 846 61 . 131 20. 10 57 . 180 61 , . 1 16 20. 10 57 . I . 516 60. .998 20. 00 57 .478 61 .023 30. 10 57, .809 58 . 193 20. 10 58 , . 149 57 .427 20. 10 58 . 490 56 . 895 20. 10 58 , 831 56 .445 20. 10 59 , . 160 56 . 047 20. 10 59 , 488 55. .751 20. 10 59 , .8 17 55. .455 20. 10 60. . 160 55. . 208 20. 10 60, ,495 55. .023 20. 10 60. .830 54 . 817 20. 10 61 , . 165 54 . 500 20. 10 61 , .497 54 . 489 20. 10 61 . 834 54 . 232 20. 10 62 . 160 54 . 079 20. 10 62 . , 499 53. .914 20. 10 62. .830 53. ,872 20. 10 63. . 168 53 . , 778 20. 10 63. ,500 53. , 705 20. 10 63 . ,837 53 . 510 20. 10 64 . 167 53 , 407 20. 10 64 . ,500 53, .222 20. 10 64 . 833 53 . 241 20. 10 65. . 173 53 , .228 20. 10 65 . ,512 53, , 175 20. 10 65 . 836 53 . 043 20. 10 66 . , 172 53 . 244 20. 10 66. , 507 53 . 090 20. 10 66 . ,841 52 . 895 20. 10 67. . 169 52 , . 894 20. 10 67. ,503 52 . 729 20. 10 67 . 833 52 . ,627 20. 10 68 . 177 52 , 440 20. 10 68 . 513 52 , 306 20. 10 68. 846 52. 406 20. 10 86. .334 46. ,628 20. 10 101 , 808 40. 805 20. 10 69. 179 52 . 283 20. 10 86. .669 46. ,757 20. 10 102 . ,14 1 40. 859 20. 10 69 . 513 52. 098 20. 10 86 . 999 46. 722 20. 10 102, ,475 40. 811 20. 10 69. 851 51 . 831 20. 10 87 . 331 46. 667 20. 10 102. ,818 40. 824 20. 10 70. 186 51 . 758 20. 10 87 . ,672 46. ,531 20. 10 103. , 149 40. 654 20. 10 70. 524 51 . 644 20. 10 88 . ,017 46. ,631 20. 10 103. ,476 40. 688 20. 10 70. 858 51 . ,510 20. 10 88 . ,343 46. .442 20. 10 103. ,806 40. 661 20. 10 74. 0 51 . , 3 20. 00 88 . ,671 46. ,509 20. 10 104 , 149 40. 593 20. 10 999 . 89. .015 46 . , 394 20. 10 104 , 477 40. ,494 20. 10 0 89 . ,341 46, , 379 20. 10 104 , 812 40. 518 20. 10 99 89. ,687 46. , 305 20. 10 105, , 151 40. 409 20. 10 73 . 983 51 . ,358 30. 10 90. .013 46, . 188 20. 10 105 , 491 40. 544 20. 10 74 . 312 49. .477 20. 10 90. .347 46, ,256 20. 10 105, .815 40. ,466 20. 10 74 . 650 48. .941 20. 10 90. .681 46, .221 20. 10 106, . 147 40. ,489 20. 10 74 . 991 48 . ,497 20. 10 91 . 018 45, .912 20. 10 106 , .484 40. , 370 20. 10 75. 334 48. , 297 20. 10 91 , .353 45, .878 20. 10 106, .813 40. ,435 20. 10 75 . 666 48 . 046 20. 10 91 , .680 45, .873 20. 10 107, . 156 40. .468 20. 10 75 . ,996 47 , 773 20. 10 92. .012 45, .848 20. 10 107 .492 40. ,400 20. 10 76 . , 338 47 .675 20. 10 92 .343 45, .721 20. 10 107, .818 40. . 332 20. 10 76 . 667 47 .494 20. 10 92 .680 45 .494 20. 10 108, . 158 40. , 355 20. 10 77 . 003 47 . 365 20. 10 93 , 007 45 .479 20. 10 108 .497 40. . 378 20. 10 77 . 337 47 . 307 20. 10 93 .352 45 .456 20. 10 108 .826 40. , 361 20. 10 77. .676 47 . 178 20. 10 93 .682 45, .258 20. 10 109 . 170 40. .242 20. 10 78 . 015 46 .998 20. 10 94 , .017 45 . 285 20. 10 109 . 496 40. , 367 20. 10 78 , .338 47 .081 20. 10 94. .351 45, . 199 20. 10 109 .823 40. ,117 20. 10 78. .675 46 .952 20. 10 94 , .682 45 .062 20. 10 1 10 . 153 40. , 191 20. 10 79 .010 46 .894 20. 10 95 .01 1 45 . 1 19 20. 10 1 10, .492 40. ,235 20. 10 79 .349 46 .846 20. 10 95, . 344 45 ,074 20. 10 1 10 .838 40. . 288 20. 10 79 .678 46 .899 20. 10 95 .687 44 .878 20. 10 111 . 158 40. . 353 20. 10 80 .010 46 .647 20. 10 96 .020 44, .813 20. 10 111 . 486 40. , 244 20. 10 80 . 357 46 .448 20. 10 96 . 358 44 .718 20. 10 111 . 828 40. . 328 20. 10 80 .688 46 . 359 20, . 10 96 .687 44 .713 20. 10 112 . 183 40. .361 20. 10 81 .023 46 . 403 20. . 10 97 .028 44 .455 20. 10 112 . 482 40. . 203 20. 10 80 .992 46 .825 20, 10 97 .357 44 . 563 20. 10 112 .818 40. . 298 20. 10 81 .322 46 .596 20, 10 97 .692 44 .386 20. 10 113 . 173 40. . 289 20. 10 81 . 658 46 .542 20. 10 98 .029 44 . 382 20. 10 113 . 507 40, , 394 20. 10 81 , .661 46 .644 20. 10 98 , .513 44 .389 20. 00 113 . 838 40. .326 20. 10 81 , .995 46 .609 20. 10 999. 1 14 .171 40, .441 20. 10 82 . 322 46 . 553 20. 10 0 114 . 505 40. .394 20. 10 82 .660 46 .662 20. , 10 6 1 14 . 844 40. .417 20. 10 82 . 991 46 .607 20. . 10 98. ,478 44 .515 30. 10 115 . 174 40, .318 20. 10 83 .321 46 . 551 20. . 10 98 .807 42 .597 20. 10 1 15 .504 40, .312 20. 10 83 .669 46 . 529 20. . 10 99 . 147 42 . 294 20. 10 115 .831 40, . 305 20. 10 84 .001 46 .565 20. . 10 99 .478 41 .850 20. 10 1 16 . 175 40, . 389 20. 10 84 . 322 46 .488 20. . 10 99 .806 41 .650 20. 10 1 16 .505 40, , 34 1 20. 10 84 .664 46 .618 20. . 10 100 . 141 41 .491 20. 10 1 16 .847 40, . 364 20. 10 84 .994 46 .562 20. . 10 100 .473 41 .423 20. 10 117 . 179 40, , 164 20. 10 85 . 333 46 .640 20, . 10 100 .809 41 . 182 20. 10 117 . 507 39 , .761 20. 10 85 .669 46 .576 20, . 10 101 . 139 41 .002 20. 10 117 .850 39, ,672 20. 10 85 .996 46 .540 20. . 10 101 . ,478 40 .964 20. 10 118 . 179 39 , .492 20. 10 118, .516 39 , 434 20. 10 135.196 118 , 857 39. ,061 20. 10 135.520 119, . 190 38 . ,993 20. 10 135.851 1 19, 518 38 . ,894 20. 10 136. 183 1 19 , .848 38 . ,877 20. 10 136.513 120, . 184 38 . 555 20. 10 999. 120, .519 38 . ,690 20. 10 0 120, .853 38 . ,531 20. 10 50 121 . , 189 38 . ,513 20. 10 121 . ,532 38. ,445 20. 10 121 , 861 38 . 316 20. 10 122, . 188 38, , 147 20. 10 122, .522 38. .343 20. 10 122 , .850 38 . ,031 20. 10 123 , . 188 38. .003 20. 10 123 , .517 37 . 895 20. 10 123 .848 37 .827 20. 10 124 . 178 37 .861 20. 10 124 .520 37 .701 20. 10 124 . 872 37 .632 20. 10 125 . 185 37 .565 20. 10 125 .529 37 .537 20. 10 125 .865 37 .438 20. 10 126 .195 37 .350 20. 10 126 . 528 37 . 180 20. 10 126, .866 37 .092 20. 10 127, . 196 37 . 176 20. 10 127 , .527 37 . 302 20. 10 127 , .863 37 .111 20. 10 128 , . 198 37 .247 20. 10 128 , .525 37 .077 20. 10 128 , .862 36 . 796 20. 10 129, .222 36 .950 20. 10 129, .531 37 .046 20. 10 129, .864 36 .856 20. 10 130, . 220 36 . 766 20. 10 130 .531 36 .638 20. 10 130 .869 36 .489 20. 10 131 . 206 36 .461 20. 10 131 . 530 36 .668 20. 10 131 .855 36 .417 20. 10 132 . 174 36 .279 20. 10 132 .515 36 .353 20. 10 132 . 844 36 .285 20. 10 133 . 174 36 . 105 20. 10 133 .504 35 .865 20. 10 133 .845 35 .776 20. 10 134 . 175 35 .667 20. 10 134 .522 35 .710 20. 10 134 .847 35 . 368 20. 10 35.289 20.10 2 1 35.425 20.10 1.202.302.403.209.999.99 35.316 20.10 10.0E-10 34.994 20.10 RUN #21; 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, .677 81 . 446 20. 10 30 .009 81 . 146 20. 10 30. .352 81 , .121 20. 10 49. 005 66. 894 20. 10 74. 50 49. 336 66. 693 20. 10 74 . 83 49. 669 66. 299 20. 10 75. 17 50. 008 66. 068 20. 10 75. 50 50. 333 65. 814 20. 10 75. 83 50. 664 65. 644 20. 10 76. 17 50. 994 65 . 411 20. 10 76. 50 51 . 340 65 . 100 20. 10 76. 83 51 . 667 64. 959 20. 10 77 . 17 52 . 005 64 . 871 20. 10 77. 50 52 . 331 64 . 699 20. 10 77 . 83 52 . 663 64 . 559 20. 10 78. 17 52. 997 64 . ,460 20. 10 78. 50 53 . 326 64 . 309 20. 10 78. 83 53. .658 64 . ,260 20. 10 79. , 17 53. .996 64 , .039 20. 10 79. ,50 54 . , 334 63. .951 20. 10 79. ,83 54 . ,656 63, .890 20. 10 80. , 17 54 . 997 63 .650 20. 10 80. ,50 55 . 326 63 . 743 20. 10 80. .83 55. .662 63 .430 20. 10 81 , 17 56. .002 63 .464 20. 10 81 . 50 56. .677 63 . 206 20. 10 81 .83 57. .006 63 . 157 20. 10 82 . 17 57 . 340 63 . 1 18 20. 10 82 50 57 .672 62 .998 20. 10 999 . 57, .999 62 .888 20. 10 0 58. .334 62 .819 20. 10 4 58 .666 62 .811 20. 10 92, .464 I. 92, .801 93 . 138 93 .480 68 .50 61 .271 30. 10 93 .809 68 .83 61 . 321 30. 10 94 . 146 69 . 17 57 .964 20. 10 94. .477 69 .50 56 . 840 20. 10 94 .822 69 .83 56 .115 20. 10 95 . 158 70 . 17 55 . 390 20. 10 95 .491 70 .50 55 .082 20. 10 95 .827 70 . 83 54 .449 20. 10 96 . 152 71 . 17 54 .006 20. 10 96 . 484 71 .50 53 .647 20. 10 96 .826 71 .83 53 . 247 20. 10 97 . 159 72 . 17 52 .971 20. 10 97 .491 72 .50 52 .682 20. 10 97 .829 72 .83 52 . 404 20. 10 98 . 169 73 .17 52 . 107 20. 10 98 .500 73 .50 51 .869 20. 10 98 .831 73 .83 51 .541 20. 10 99 . 174 74 . 17 51 .465 20. 10 99 . 503 51 . 187 20. 10 99 . 825 35 . 281 20. 10 50. 879 20. 10 100. 164 34 . 979 20. 10 50. 631 20. 10 100. 502 34 . 829 20. 10 50. 455 20. 10 100. 835 34 . 741 20. 10 50. 239 20. 10 101 . 173 34 . 754 20. 10 50. 195 20. 10 101 . 497 34 . 523 20. 10 50. 069 20. 10 101 . 846 34 . 374 20. 10 49. 709 20. 10 102. 162 34. 164 20. 10 49. 514 20. 10 102 . 490 33. 933 20. 10 49. 255 20. 10 • 102 . 822 33. 916 20. 10 49. 109 20. 10 103. 158 33 . 868 20. 10 48 . 974 20. 10 103 . 495 33. 779 20. 10 48 . 849 20. 10 103 . 835 33. 691 20. 10 48 . 682 20. 10 104 . 157 33 . 633 20. 10 48 . 628 20. 10 104 . 501 33 . 443 20. 10 48 . 482 20. 10 104 . 833 33 . 436 20. 10 48 . ,316 20. 10 105. , 172 33. .347 20. 10 48 . 223 20. 10 105 . 494 33. 147 20. 10 48. .015 20. 10 105 . 836 33 . 140 20. 10 47 . 858 20. 10 106 . 168 32 . 980 20. 10 47. . 764 20. 10 106 . 499 32 . 953 20. 10 47 , .639 20. 10 106 . 836 32 . ,834 20. 10 47 . 515 20. 10 107 . 169 32 . 613 20. 10 47 . 581 20. 10 107 . 501 32 . 535 20. 10 47 . 507 20. 10 107 , .838 32 . 375 20. 10 108 , . 177 32 . 338 20. 10 108 , .507 32. . 239 20. 10 108 . 842 32. . 161 20. 10 45, . 183 30. 10 109. .506 31 .964 20. 10 42, .287 20. 10 109 .844 31 .895 20. 10 41 , . 364 20. 10 110 . 170 31 .705 20. 10 40. .441 20. 10 1 10 . 507 31 . 525 20. 10 39, .712 20. 10 1 10 .833 31 .508 20. 10 39. . 165 20. 10 111. . 171 31 . 389 20. 10 38. .609 20. 10 111 .494 31 . 301 20. 10 38 . 296 20. 10 111 .835 31 .406 20. 10 37 .984 20. 10 112 . 167 31 . 144 20. 10 37 . 580 20. 10 112 .503 31 .117 20. 10 37 .217 20. 10 112 .837 31 . 130 20. 10 36 .997 20. 10 999. 36 .664 20. 10 0 36 .413 20. 10 99 36 . 263 20. 10 1 18 .517 29 .920 30. 10 36 . 154 20. 10 118 .832 27 .711 20. 10 35 .934 20. 10 1 19 . 164 27 .089 20. 10 35 .845 20. 10 1 19 .497 26 .700 20. 10 35 .655 20. , 10 1 19 .830 26 .454 20. 10 35 .658 20. 10 120 . 164 26 .076 20. 10 35 . 376 20. 10 120 .491 25 .810 20. 10 35 . 298 20. . 10 120 .830 25 . 574 20. 10 999 0 3 30 .681 80 .903 20. , 10 31 .017 80 .573 20. , 10 31 .347 80 .446 20. , 10 31 .671 80 .422 20. . 10 32 .006 80 .245 20. 10 32 .338 80 .037 20. , 10 32 I. .676 79 .920 20. 10 32. .493 79. .946 30. 10 32. .835 76 . 122 20. 10 33, . 166 74 , .711 20. 10 33 . 500 73 . 717 20. 10 33, .832 72, .896 20. 10 34 , . 165 72 , . 269 20. 10 34 . 499 71 . 743 20. 10 34 .840 71 . 166 20. 10 35 . 174 70 .834 20. 10 35 .500 70 .441 20. 10 35 .842 70 . 159 20. 10 36 . 175 69. .878 20. 10 36 . 509 69 .637 20. 10 36 . ,845 69 . 416 20. 10 37 . 176 69 , .217 20. 10 37 . 510 69, .078 20. 10 37 . 846 68. .888 20. 10 38. , 181 68. ,739 20. 10 38. ,508 68. , 549 20. 10 38. ,852 68 . 471 20. 10 39. , 184 68. .342 20. 10 39. ,515 68. .255 20. 10 39. ,844 68. . 147 20. 10 40. , 176 67 . ,998 20. 10 40. ,515 67. ,909 20. 10 40. ,850 67 . 821 20. 10 41 . 186 67 . ,570 20. 10 41 . 512 67 . 513 20. 10 41 . 845 67. 385 20. 10 42. 177 67 . 297 20. 10 42 . 507 67 . 179 20. 10 42 . 845 67 . 213 20. 10 43 . 171 66 . 952 20. 10 43. 507 66. 895 20. 10 43 . 851 66. 846 20. 10 44 . 180 66 . 749 20. 10 44 . 511 66 . 600 20. 10 44 . 847 66. 440 20. 10 45. 185 66 . 342 20. 10 45. 516 66. 397 20. 10 45.852 66.227 20.10 46. 177 66.201 20.10 46.520 66.092 20.10 46.851 66.024 20.10 999. 0 99 2 1 1.202.302.403.209.999.99 10.0E- 10 RUN022; TEMPERATURE=35 C 7 164.0 3.343 0.3921 . 150 3.4 3.4 .175 29.2 29.2 .200 52.0 52.0 .225 67.3 67.3 .250 78.7 78.7 .275 86.9 86.9 .300 97.6 97.6 20.0 999 O 2 19 .983 89 . 189 30. 10 20 . 308 85 . 145 20. 10 20 .646 83 .901 20. 10 20 .991 83 .044 20. 10 2 1 . 327 82 .421 20. 10 21 .650 81 .921 20. 10 21 .983 81 .562 20. 10 22 . 326 81 . 326 20. 10 22 . 654 81 . 182 20. 10 22 . 993 80 .651 20. 10 23 .318 80. . 547 20. 10 23 , .648 80 .443 20. 10 23. .988 80, .085 20. 10 24 . 311 79. .910 20. 10 24 . 650 79. .857 20. 10 24 . 988 79. ,621 20. 10 25 . 323 79, , 579 20. 10 25. ,653 79, , 506 20. 10 25. ,984 79, ,443 20. 10 26 . , 327 79. ,115 20. 10 26 . 656 79. .032 20. 10 26 . 991 78 . 897 20. 10 27 . I . 332 78 . 794 20. 10 44 . 982 76. 261 30. 10 45. 332 73. 092 20. 10 45 . 653 71 . 923 20. 10 45 . 984 71 . 162 20. 10 46 . 323 70. 372 20. 10 46 . 661 69. 826 20. 10 46 . 992 69. 157 20. 10 47. 332 68. 733 20. 10 47 . 671 68 . 309 20. 10 48 . 000 67 . 873 20. 10 48 . 334 67. 591 20. 10 48. 671 67 . 228 20. 10 121 . , 163 25 . 328 20. 10 137 . 861 22 .453 20. 10 153 , .020 14 , 569 20. 10 121 . 501 25, .275 20. 10 138. . 199 22 . 359 20. 10 153 , . 349 14 , . 492 20. 10 121 . 836 25. .080 20. 10 138. .527 22 .389 20: '10 153, ,677 14 , .435 20. 10 122 . 177 24, .761 20. 10 138, .855 22 . 296 20. 10 154 , 012 14 , . 327 20. 10 122. 502 24, .740 20. 10 139, . 190 22 .325 20. 10 154 , .353 14. .363 20. 10 122 . 839 24 . 596 20. 10 139, .527 22 . 323 20. 10 154 , .688 14 , .205 20. 10 123 . 176 24. .390 20. 10 139, .852 22 .241 20. 10 155 , .020 14 . 056 20. •10 123. 503 24. . 328 20. 10 140. . 183 22 .076 20. 10 155 , . 351 14 . 020 20. 10 123 . 843 24 , .478 20. 10 140, .522 22 .064 20. 10 155. .687 13. .933 20. 10 124 . 176 24. .232 20. 10 140, .852 22 .022 20. 10 156. .02 1 13 .917 20. 10 124 . 503 24 . 059 20. 10 141 , .023 21 .990 20. 10 156 . 368 13 . 760 20. 10 124 . 832 23. ,813 20. 10 999 . 156 .691 13 .977 20. 10 125 . 162 23. .781 20. 10 0 157 .027 13 .778 20. 10 125. .500 23. .677 20. 10 6 157 . 359 13 .721 20. 10 125. .846 23. . 796 20. 10 140, .993 21 .934 30. 10 157 .690 13 . 746 20. 10 12G. . 170 23. .867 20. 10 141 , . 323 20 .118 20. 10 158 .011 13 .475 20. 10 126. .513 23. .7 12 20. 10 141 . 658 19 .431 20. 10 158 . 358 13 . 267 20. 10 126. , 849 23. .628 20. 10 141 , .997 19 .080 20. 10 158 .689 13 .413 20. 10 127. . 177 23. .515 20. 10 142 . 332 18 .647 20. 10 159 .020 13 . 255 20. 10 127 . 514 23 .472 20. 10 142, .667 18 . 133 20. 10 159 . 348 13 . 167 20. 10 127 . 837 23 . 533 20. 10 142, .999 17 .975 20. 10 159 .684 13 .019 20. 10 128 , . 183 23 . 469 20. 10 143 , .331 17 .694 20. 10 160 .023 12 .882 20. 10 128 . 513 23 . 325 20. 10 143. .670 17 .496 20. 10 160 . 363 12 . 734 20. 10 128 . 849 23 . 384 20. 10 143, .999 17 . 134 20. 10 160 .691 12 .677 20. 10 129 , . 171 23 . 323 20. 10 144 , . 336 16 .752 20. 10 161 .026 12 . 509 20. 10 129 . 508 23 . 250 20. 10 144 , .674 16 .533 20. 10 161 . 353 12 . 594 20. 10 129 , .842 23 .238 20. 10 145 , .006 16 .446 20. 10 161 .690 12 . 588 20. 10 130, . 176 23 . 185 20. 10 145, .342 16 . 298 20. 10 162 .021 12 .511 20. 10 130 . 509 23' .071 20. 10 145 . 669 16 .281 20. 10 162 . 352 12 . 444 20. 10 130. . 840 22 .999 20. 10 146 . 004 16 .052 20. 10 162 .685 12 . 306 20. 10 131 . 177 22 .885 20. 10 146 . ,345 15 .833 20. 10 163 .020 12 . 34 1 20. 10 131 .505 22 .996 20. 10 146 . 682 15. .634 20. 10. 163 . 361 1 1 . 848 20. 10 131 , .843 22 .882 20. 10 147. ,016 15 . 507 20. 10 163 .684 12 .045 20. 10 132 . 176 22 . 788 20. 10 147 . 351 15. .430 20. 10 164 .026 1 1 .918 20. 10 132 , . 507 22 .665 20. 10 147 , .683 15 .373 20. 10 999. 132 , .837 22 . 786 20. 10 148 , 018 15 . 255 20. 10 0 133. . 176 22 . 783 20. 10 148 , .346 15. .076 20. 10 99 133 , .510 22 .670 20. 10 148 . 683 14 . 918 20. 10 133 . 843 22 .729 20. 10 149 , .018 14 .862 20. 10 134 . .179 22 .615 20. 10 149 , 355 15. .039 20. 10 134 .507 22 .604 20. 10 149 , .687 14, .891 20. 10 134 .847 22 . 734 20. 10 150, .019 14. .906 20. 10 135 . 181 22 .641 20. 10 150, .353 14, .930 20. 10 135 . 508 22 .711 20. 10 150, ,679 14. .690 20. 10 135 .855 22 . 555 20. 10 151 , 015 14. .563 20. 10 136 . 186 22 .482 20. 10 151 , 350 14 , .679 20. 10 136 .517 22 .593 20. 10 151 , .682 14 . 632 20. 10 136 .847 22 .470 20. 10 152 , .010 14 , .514 20. 10 137 . 190 22 .487 20. 10 152 , 344 14 . 590 20. 10 137 .532 22 .454 20. 10 152, ,686 14 .453 20. 10 2 1 10.0E-10 RUN#23; TEMPERATURE=35 C 6 109.0 3.8795 0.3900 .150 28.0 0.0 .175 49.8 24.9 .200 67.9 48.0 .225 81.0 65.9 .250 89.7 79.8 .275 98.3 88.2 20.5 20. .483 95 . 1 15 30. 10 20. .815 89, .946 20. 10 21 , 154 88 .298 20. 10 21 . 486 87 , .158 20. 10 21 . 825 86 .212 20. 10 22 . 158 85 .622 20. 10 22. .497 84 .869 20. 10 22 .840 84 .482 20. 10 23 . 163 83 .883 20. 10 23. .503 83 .435 20. 10 23, .827 83 .069 20. 10 24 , . 176 82 .631 20. 10 24 , .505 82 .306 20. 10 24 . 835 81 .869 20. 10 25, . 174 81 . 370 20. 10 25, .502 81 . 259 20. 10 25, .837 80 .984 20. 10 26 , . 166 80 . 527 20. 10 26 , .503 80 .385 20. 10 26, .837 80 .212 20. 10 27; ; 164 79 .959 20. 10 27, , 495 79 .695 20. 10 27, .837 79, . 267 20. 10 28, . 170 79, . 176 20. 10 28 , .505 78, .809 20. 10 28, .833 78, .658 20. 10 29 , .171 78, .311 20. 10 29 , .507 78, .057 20. 10 29, ,840 77 , . 783 20. 10 30, . 166 77 , . 540 20. 10 30, ,508 77 , . 203 20. 10 30, .839 77 , .041 20. 10 31 , 173 76, .685 20. 10 31 . , 508 76 , .482 20. 10 31 . 836 76 , . 137 20. 10 32. , 175 75 , .923 20. 10 32 . 507 75 , .903 22. 00 999 . 2 999 3 32 .480 75 .782 30. 10 32 .822 70 .355 20. 10 33 . 155 67 .931 20. 10 33 .494 66 . 220 20. 10 33 .825 64 .968 20. 10 34, . 164 63 .857 20. 10 34 .497 62 . 798 20. 10 34, .822 62 .055 20. 10 35 . 160 61 .464 20. 10 35 .499 60 .863 20. 10 35 .834 60 . 180 20. 10 36 . 162 59 .722 20. 10 36, .498 59 . 151 20. 10 36 .824 58 .724 20. 10 37 . 153 58 . 367 20. 10 37, .499 57 . 786 20. 10 37 .822 57 . 369 20. 10 38 . 155 56 .849 20. 10 38 .507 56 . 379 20. 10 38 .831 56 . 196 20. 10 39, . 164 55 .687 20. 10 39 .498 55 . 391 20. 10 39 .837 55 .095 20. 10 40, . 175 54 .636 20. 10 40, .505 54 .452 20. 10 40 .840 54 .055 20. 10 41 , . 179 53 .636 20. 10' 41 , .505 53 . 301 20. 10 41 , .859 53, .013 20. 10 42 . 180 52 .729 20. 10 42 , .510 52, .260 20. 10 42, .841 52 .036 20. 10 43 , I . .020 52, .060 22 . 00 42 , .977 52, .218 30. 10 43 , .371 47 .703 20. 10 43, .667 46 . 256 20. 10 44 . 008 45, .019 20. 10 44 . 355 43 , .750 20. 10 44 . 697 42 , .645 20. 10 45. ,037 41 , .886 20. 10 45 . 377 41 , .280 20. 10 45. ,720 40. .561 20. 10 46. ,063 39, .822 20. 10 46. , 397 39, . 175 20. 10 46 . 742 38 , .619 20. 10 47 . ,085 38, . 154 20. 10 47 . ,420 37 , .812 20. 10 47 . , 753 37 . 429 20. 10 999 4 48 . 098 36 . 792 20. 10 48 . 442 36 . 500 20. 10 48 . 781 36 . 056 20. 10 49 . 126 35 . 652 20. 10 49. 463 35 . 148 20. 10 49. 815 34 . 946 20. 10 50. 151 34 . 615 20. 10 50. 495 34 . ,282 20. 10 50. 836 33 . 909 20. 10 51 . , 183 33 . ,648 20. 10 51.. 524 33 . 315 20. 10 51 . ,869 33 . 074 20. 10 52 . , 209 32 . , 803 20. 10 52 . ,552 32 . , 592 20. 10 52. ,897 32 . , 362 20. 10 53 . 228 32 . ,010 20. 10 53 . ,581 31 . 626 20. 10 53 , 920 31 , . 395 20. 10 54 , 251 31 , .074 20. 10 54 , . 591 30, .620 20. 10 54 , 946 30, .469 20. 10 55 , .281 30, . 168 20. 10 55 , .619 29 , .948 20. 10 55 , .957 29 .687 20. 10 56 . 302 29 . 385 20. 10 56 , .641 29 .083 20. 10 56 , .976 28 .934 20. 10 57 , .314 28 . 562 20. 10 57 .656 28 .402 20. 10 58 , .000 28, . 202 20. 10 58 .338 27 . 788 20. 10 58, .674 27 .538 20. 10 59, I. .007 27 .349 22 . 00 59 .012 27 . 739 30. 10 59 .339 23 . 434 20. 10 59 .663 22 . 283 20. 10 60 .006 21 .323 20. 10 60 .341 20 . 537 20. 10 60 .680 19 .903 20. 10 61 .013 19 .219 20. 10 61 . 344 18 .718 20. 10 61 .679 18 . 329 20. 10 62 .021 18 .021 20. 10 62 . 359 17 . 560 20. 10 62 .693 17 .313 20. 10 63 .018 16 .804 20. 10 63 . 353 16 .486 20. 10 63 .693 16 .279 20. 10 G4. .027 16, .023 20. 10 64 .362 15 .674 20. , 10 64. .684 15, .511 20. 10 65, .024 15, . 243 20. '10 65. . 358 14 , 905 20. 10 65. .690 14, .903 20. 10 66 .029 14 , .798 20. 10 66, . 359 14 , .593 20. 10 66. . 701 14 , .651 20. 10 67, .024 14, . 325 20. 10 67 , . 363 14 , . 332 20. 10 67, .700 14 , . 126 20. 10 68 .021 14 , .034 20. 10 68 . 358 13, .828 20. 10 68 . 691 13, . 704 20. 10 69, .031 13, .507 20. 10 69 .355 13 , . 120 20. 10 69! .689 13 . 178 20. 10 70, .023 12 , .861 20. 10 70, . 355 12 . , 777 20. 10 70, . 700 12 , 590 20. 10 7 1 , .021 12 , . 163 20. 10 71 . 356 12 , 170 20. 10 71 . 689 12, .056 20. 10 72, ,029 12 , 012 20. 10 72 . 358 1 1 , .899 20. 10 72 , .696 1 1 , . 754 20. 10 73 , 028 1 1 . 538 20. 10 73 , 358 1 1 . ,465 20. 10 73 , 698 1 1 . .472 20. 10 74 , 025 1 1 . , 196 20. 10 74; 361 10. ,746 20. 10 74 , .692 10. ,439 20. 10 75. .029 10. .620 20. 10 75. .360 10. ,597 20. 10 75. ,694 10. .809 20. 10 76. ,034 10. ,562 20. 10 76 . , 369 10. ,539 20. 10 76. ,703 10. 699 20. 10 77 . 030 10. 719 20. 10 77 . , 366 10. 645 20. 10 77 . 687 10. 665 20. 10 78. 035 10. 671 20. 10 78. 365 10. 588 20. 10 78 . 703 10. 554 20. 10 79. 031 10. 614 20. 10 109. 0 0. 10 22 . 00 999. 50 2 1 1.202.302.403.209.999.99 10.0E-10 RUN #24; TEMPERATURE=35 C 7 167.5 3.343 0.4200 .150 3.3 2.5 .175 18.0 16.4 .200 48.3 48.1 .225 ' 63.4 62.9 .250 75.4 74.9 .275 82.6 81.4 .300 94.8 93.3 20.0 999 0 2 19 . 987 94. 333 30. 10 20. 317 89. 445 20. 10 20. 657 87. 915 20. 10 20. ,983 87 . ,066 20. 10 21 . ,326 86 . 340 20. 10 21 . ,656 85. ,715 20. 10 21 . ,993 85. .304 20. 10 22. , 334 84 . ,914 20. 10 22 . 668 84 . ,544 20. 10 23. .007 84 , 153 20. 10 23. .331 83 . ,823 20. 10 23, .670 83 . 585 20. 10 24, .007 83 . 419 20. 10 24 , . 342 83 . 089 20. 10 24, .671 82 .912 20. 10 25 .002 82 .725 20. 10 25 . 340 82, .436 20. 10 25 .670 82 . 249 20. 10 25 .999 82 . 133 20. 10 26 .334 81 .936 20. 10 26 .666 81 .718 20. 10 27 .003 81 .450 20. 10 27 I. .338 81 .405 20. 10 32 .482 79 .591 30. 10 32 .819 76 .901 20. 10 33 .151 76 .013 20. 10 33 .488 75 .379 20. 10 33 .821 74 . 776 20. 10 34 . 164 74 . 397 20. 10 34 .487 73 .844 20. 10 34 .821 73 .547 20. 10 35 . 153 73 .218 20. 10 35 .490 72 .849 20. 10 35 .815 72 .561 20. , 10 36 . 153 72 . 203 20. 10 36 . 490 72 . 027 20. 10 36 . 829 71 . 617 20. 10 37 . 155 71 . 309 20. 10 37 . 486 70. 981 20. 10 37 . 820 70. 836 20. 10 38. 163 70. 569 20. 10 38 . 495 70. 322 20. 10 38. 824 70. ,004 20. 10 39 . 158 69 . ,787 20. 10 39 . 492 69 . ,500 20. 10 39. 836 69. ,294 20. 10 40. 167 69. , 128 20. 10 40. 496 68 . 922 20. 10 40. 836 68 . 655 20. 10 41 . 165 68 . 479 20. 10 41 . 505 68 .222 20. 10 41 . ,835 68 . 067 20. 10 42 . , 169 67 .911 20. 10 42 . 502 67 .664 20. 10 42 . ,834 67 . 397 20. 10 43 . , 171 67 .211 20. 10 43 . ,500 67 .015 20. 10 43 . 836 66 .840 20. 10 44 . 172 66 .847 20. 10 44 .839 66 .639 20. 10 45. . 176 66 .606 20. 10 45 . 502 66 .348 20. 10 45 .838 66 . 305 20. 10 46 3. . 182 66 . 130 20. 10 49 .488 64 . 478 30. , 10 49 .820 61 .094 20. 10 50 . 155 60 .221 20. , 10 50 .494 59 . 227 20. . 10 50 .826 58 . 537 20. . 10 51 . 169 58 .062 20. . 10 51 .499 57 .483 20. , 10 51 .831 57 . 170 20, , 10 52 . 170 56 . 796 20. . 10 52 .508 56 . 401 20 . 10 52 .843 56 .057 20 . 10 53 . 176 55 .693 20 . 10 53 .516 55 .400 20 . 10 53 .854 55 .046 20 . 10 54 . 188 54 .865 20 . 10 54 .518 54 .500 20 . 10 54 .856 54 .258 20 . 10 55 . 186 53 . ,913 20. 10 90. 160 55. 524 53, ,763 20. 10 90. 502 63. .4 49 , 5 20. 10 90. 833 i . 91 . 169 91 . 507 91 . 837 75. .489 45 , 269 30. 10 92 . 168 75 . 825 42 , .606 20. 10 92 . 844 76. . 158 - 41 . ,458 20. 10 93. 177 76 . 495 40, ,830 20. 10 93. 503 76 . 836 40. ,273 20. 10 93. 839 77. , 168 39, ,553 20. 10 94. 177 77. .495 39 , 178 20. 10 94. 511 77. ,828 38, ,641 20. 10 94. 848 78 . 170 38 , 409 20. 10 999. 78. 499 38 , 309 20. 10 0 78 . 832 37 , .894 20. 10 99 79. , 167 37 , 652 20. 10 123 . ,498 79 , . 507 37 . 543 20. 10 123. 839 79 . 834 37 . 117 20. 10 124. , 166 80. . 169 37 .018 20. 10 124 . ,499 80. .500 36. . 735 20. 10 124. ,842 80, .841 36 . 554 20. 10 125. 180 81 , . 175 36 . 302 20. 10 125. ,511 81 , .510 36, . 101 20. 10 125. ,842 81 , .840 36 .041 20. 10 126. , 174 82 . 172 35 .687 20. 10 126. ,503 82, .512 35 .578 20. 10 126. 839 82 . 840 35 . 366 20. 10 127. . 174 83. . 179 35 . 297 20. 10 127. ,496 83. .502 35 .349 20. 10 127. .838 83 , .836 35 . 199 20. 10 128 , 176 84. . 174 35 . 160 20. 10 128 , .499 84. .505 35 .091 20. 10 128, ,840 84, .833 35 .031 20. 10 129, . 172 85, . 168 34 .871 20. 10 129, .510 85. .500 34 .690 20. 10 129, .836 85 .840 34 .662 20. 10 130. . 168 86. . 166 34 .663 20. 10 130, . 505 86, .498 34 .523 20. 10 130. .836 86 .842 34 .383 20. 10 131 . 171 87 . 173 34 .416 20. 10 131 , . 507 87 .505 34 .397 20. 10 131 .839 87, .832 34 .246 20. 10 132, . 178 88. . 168 34 . 146 20. 10 132 .509 88. .506 34 .047 20. 10 132 .843 88 .837 33 .846 20. 10 133 . 185 89 . 171 33 . 705 20. 10 133 .513 89 . 501 33 .666 20. 10 133 .842 89 .831 33 .454 20. 10 134 . 173 33. 181 20. 10 134 . 508 14 . 009 20. 10 33. 001 20. 10 134 . 832 13 . 946 20. 10 33. 003 20. 10 135. 176 13. 812 20. 10 32. 832 20. •10 135 . 512 13 . 840 20. 10 32 . 824 20. 10 135 . 845 13. 614 20. 10 32 . 613 20. 10 136 . 177 13. 622 20. 10 32 . 665 20. 10 136 . 506 13. 569 20. 10 32. .650 20. 10 136 . 836 13 . 547 20. 10 32. ,652 20. 10 137 , 17 1 13, ,494 20. 10 32. .490 20. 10 137 , 503 13 . 248 20. 10 32. ,442 20. 10 137 , .838 13, ,073 20. 10 32. , 342 20. 10 138 , . 168 13 . 091 20. 10 31 . ,958 20. 10 138 . 504 12 .977 20. 10 31 , 991 20. 10 138 .830 12 .863 20. 10 139 . 166 12 .861 20. 10 139 .507 12 .676 20. 10 139 .84 1 12 .816 20. 10 20. .997 30. 10 140 . 167 12 . 580 20. 10 18 , .726 20. 10 140 .510 12 . 72 1 20. 10 18 . 245 20. 10 140 . 840 12 .647 20. 10 18 , .019 20. 10 141 . 177 12 . 503 20. 10 17. .824 20. 10 141 .506 12 .552 20. 10 17 .720 20. 10 141 .843 12 .560 20. 10 17 .352 20. 10 142 . 178 12 . 466 20. 10 16 .902 20. 10 142 .519 12 . 484 20. 10 16 .645 20. 10 142 .853 12 . 452 20. 10 16 .318 20. 10 143 . 187 12 .399 20. 10 16 . 163 20. 10 143 . 507 12 . 397 20. , 10 15 .937 20. 10 143 .847 12 .151 20. 10 15 .894 20. 10 167 .5 9 .0 20. 10 15 .566 20. 10 999 . 15 .656 20. 10 0 15 .542 20. 10 99 15 . 265 20. 10 15 .090 20. 10 14 .956 20. 10 14 .893 20. 10 14 .728 20. 10 14 . 522 20. 10 14 .479 20. 10 14 .457 20. 10 14 . 363 20. 10 14 .728 20. 10 14 .359 20. 10 14 .378 20. 10 14 .223 20. 10 14 . 1 19 20. 10 14 .117 20. 10 14 .217 20. . 10 14 . 154 20. . 10 2 1 0.752.584.499.999.999.99 10.0E-10 RUN #25; TEMPERATURE=35 C 8 112.5 3.343 0.4126 .150 3.0 3.0 .175 26.2 26.2 .200 45.0 45.0 .225 59.7 59.7 .250 71.8 71.8 .275 79.0 79.0 .300 87.1 87.1 .325 96.1 96.1 27.0 27 .021 88 , 801 30. 10 27 .319 81 , 981 20. 10 27, .655 79, .584 20. 10 27 .991 78, .417 20. 10 28 . 323 77 , 168 20. 10 28 .657 76, .387 20. 10 28 .995 75, , 788 20. 10 29, . 330 75 , 250 20. 10 29, .673 74 , .660 20. 10 30, .006 74 . , 174 20. 10 30, .341 73, .809 20. 10 30, .674 73 , .546 20. 10 31 , .003 73, , 100 20. 10 31 , . 337 72 . 806 20. 10 31 , .672 72, ,330 20. 10 32 . 009 72 , 218 20. 10 32 .342 72 , 108 20. 10 32 , .677 71 ; ,732 20. 10 33, .018 71 , .610 20. 10 33, .351 71 , 571 20. 10 33, .663 71 . , 301 20. 10 33. ,997 71 . , 129 20. 10 34 , 339 70. ,956 20. 10 34 , .674 71 . ,038 20. 10 35 ,006 70. ,927 20. 10 35, . 344 70. 866 20. 10 35. .675 70. .776 20. 10 36 , .01 1 70. ,716 20. 10 36 . 333 70. ,546 20. 10 36, .666 70. 323 20. 10 37 , .005 70. ,415 20. 10 37 , . 333 70. ,335 20. 10 37. ,665 70. 265 20. 10 38. ,000 70. .002 20. 10 38. , 328 70. ,034 20. 10 38 . 668 69 . 953 20. 10 0 2 38 . ,995 69 . 853 20. 10 39. ,330 69. 722 20. 10 39. ,658 69. 794 20. 10 39. ,997 69. 733 20. 10 40. , 337 69 . 693 20. 10 40. ,667 69. 603 20. 10 41 . ,000 69. ,594 20. 10 41 . , 337 69. ,482 20. 10 41 . 659 69. ,495 20. 10 42 . ,004 69. ,301 20. 10 42. ,329 69. ,364 20. 10 42 , .669 69. . 242 20. 10 43, ,000 69 . 223 20. 10 43 , .338 69. , 183 20. 10 43 , .675 69. . 163 20. 10 43, .999 69 , 003 20. 10 44 , .327 68 , 872 20. 10 44 , .674 68 . ,902 20. 10 44, .998 68, ,874 20. 10 45, . 340 68. .680 20. 10 45, .670 68 , .631 20. 10 46, .000 68 . 612 20. 10 46 .343 68 , .581 20. 10 46 .668 68 . 542 20. 10 47 .005 68, .472 20. 10 47 . 337 68 , .493 20. 10 47 .674 68, .311 20. 10 47, .995 68 . 151 20. 10 48, . 339 68, .079 20. 10 48 .666 68, .071 20. 10 48 .998 68 . 143 20. 10 49 .332 68 , .063 20. 10 49 .661 68 .085 20. 10 49 .995 68 .004 20. 10 50 .333 67 .943 20. 10 50 .670 68 .005 20. 10 51 .010 67 .964 20. 10 51 . 336 68 .007 20. 10 51 .667 67 .998 20. 10 52 .013 67 .875 20. 10 52 .343. 67 .897 20. 10 52 .677 67 .959 20. 10 53 .003 67 .940 20. 10 999 999 53 .050 66 . 192 30. 10 53 .325 62 .620 30. 10 53 .656 60 .633 30. 10 53 .991 58 .921 30. 10 54 . 330 57 . 828 30. 10 54 . 671 56 . 897 30. 10 54 . 994 56 . 180 30. 10 55. ,344 55 . 595 30. 10 55. 682 55. 060 30. 10 56 . ,012 54 . 576 30. 10 56 . , 334 54 . 305 30. 10 56. .668 53. ,751 30. 10 56 . ,997 53 . ,429 30. 10 57 . 332 53. 179 30. 10 57 , 670 52 . ,705 30. 10 57 , 999 52. 404 30. 10 58 . 336 52 . 266 30. 10 58 . ,671 51 . ,894 30. 10 59 . 001 51 . , 735 30. 10 59 , 330 51 . ,464 30. 10 59, .670 51 . ,468 30. 10 60, .003 51 . ,045 30. 10 60, . 34 1 51 . ,008 30. 10 60 .668 50. .951 30. 10 61 .003 50, ,894 30. 10 61 . 332 50. . 867 30. 10 61 .666 . 50. ,678 30. 10 62 .005 50. ,803 30. 10 62 . 332 50. . 705 30. 10 62 .679 50. .608 30. 10 63 .001 50, ,58 1 30. 10 63 . 333 50. . 595 30. 10 63 .672 50, .212 30. 10 64 .004 50, , 267 30. 10 64 . 334 49 .895 30. 10 64 .674 49 .858 30. 10 65 .006 49 .689 30. 10 65 . 329 49 . 753 30. 10 65 .669 49 .534 30. 10 66 .003 49 . 598 30. 10 66 . 335 49 .561 30. 10 66 .664 49 . 534 30. 10 66 .999 49 .447 30. 10 67 .332 49 ,379 30. 10 67 .665 49 .271 30. 10 67 .990 49 .112 30. 10 68 .318 49 .085 30. 10 68 .657 48 .724 30. 10 68 .989 48 .748 30. 10 69 . 329 48 .579 30. 10 69 .659 48 .450 30. 10 69 .997 48 .383 30. 10 70 . 334 48 . 255 30. 10 70 .664 48 . 228 30. 10 •71 .000 48 . 282 30. 10 86. ,455 34 . ,261 20. 10 102 . 950 27 . 616 20. 10 71 . 331 48 . 266 30. 10 86. , 795 33 . 929 20. 10 103 . 283 27 . 283 20. 10 7 1 .669 48 .229 30. 10 87 , 123 33 . 586 20. 10 103 . 604 27 . 267 20. 10 72 .003 48 .314 30. 10 87 , 441 33 . 375 20. 10 103 . 937 27 . 220 20. 10 72 . 335 48 . 155 30. 10 87 . , 774 33 . 155 20. 10 104 . 267 27. 163 20. 10 72 .666 48 .118 30. 10 88. ,116 32 . 700 20. 10 104 . 596 27 . 035 20. 10 73 .009 48 . 152 30. 10 88. . 440 32 . 449 20. 10 104 . 928 27. , 101 20. 10 73 . 347 48 . 176 30. 10 88 . , 765 32 . , 136 20. 10 105. 255 26. ,901 20. 10 73 .675 48 .048 30. 10 89 . 087 31 . ,987 20. 10 105. .587 26. ,752 20. 10 74 .007 47 .919 30. 10 89 . 430 31 . ,941 20. 10 105 . 909 26 , .858 20. 10 74 .337 47 .923 30. 10 89. .761 31 . ,435 20. 10 106. . 244 26 . 944 20. 10 74 .668 47 .795 30. 10 90. .092 31 , 541 20. 10 106 . ,573 26. .847 20. 10 74 .999 47, .646 30. 10 90. .425 31 , 311 20. 10 106, .898 26. . 749 20. 10 75 .336 47, .477 30. 10 90, .749 31 , 550 20. 10 107 , 242 26 .672 20. 10 75 .671 47 .542 30. 10 91 , .085 31 , .034 20. 10 107 , 560 26 . 574 20. 10 76 .007 47. .494 30. 10 91 , .407 31 , 068 20. 10 107. .893 26 . 323 20. 10 76 .338 47 . 386 30. 10 91 . 736 31 , 052 20. 10 108 , 229 26 .327 20. 10 76 .672 47 . 400 30. 10 92, .070 30, ,546 20. 10 108 , .554 26 . 158 20. 10 76 .999 47 .241 30. 10 92, . 398 30, .581 20. 10 108 .878 26 . 152 20. 10 77 . 335 47 . 143 30. 10 92 , . 737 30. .617 20. 10 109 . 205 26 .085 20. 10 77 .672 46 .995 30. 10 . 93, .060 30. . 570 20. 10 109 .539 25 .946 20. 10 78 .005 46 .968 30. 10 93, . 374 30. .635 20. 10 109 .867 25 . 705 20. 10 78 . 327 46 .819 30. 10 93. .717 30. .313 20. 10 1 10 .200 25 .689 20. 10 78 .666 46, .762 30. 10 94 . 040 30. .419 20. 10 1 10 . 524 25 .632 20. 10 78 .999 46 . 725 30. 10 94 . 375 30 .444 20. 10 1 10 .848 25 . 534 20. 10 79 .327 46. .790 30. 10 94. .700 30 .530 20. 10 111 . 197 25 . 376 20. 10 79 .661 46 , .722 30. 10 95. .031 30 .401 20. 10 111 .516 25 . 390 20. 10 79 .997 46. .675 30. 10 95, . 359 30. .395 20. 10 1 1 1 .850 25 . 364 20. 10 80 . 336 46 . 516 30. 10 95 .688 30. .287 20. 10 1 12 . 180 25 .042 20. 10 80 .667 46 .459 30. 10 96 .022 30. .455 20. 10 1 12 .507 25 .036 20. 10 80, .997 46, .473 30. 10 96 . 337 30. .418 20. 10 999 999 81 .331 46 . , 385 30. 10 96, .681 30. .474 20. 10 0 81 .664 46 . 501 30. 10 97, .012 30. .223 20. 10 99 82 .002 46, ,484 30. 10 97 . 336 29. .921 20. 10 26 .988 91 .823 30. 10 82 . 335 46 , . 366 30. 10 97 .668 29. .783 20. 10 52 .996 68 . 172 30. 10 999 999 . 97 . 996 29 .491 20. 10 82 . 504 46 . 334 30. 10 98 . 321 29. .474 20. 10 98 .650 29 .121 20. 10 82 .518 45 , 037 30. 10 98 .983 29 . 177 20. 10 82 .829 41 , . 149 30. 10 99 .313 28 .895 20. 10 83, . 153 39, .682 30. 10 99 .645 28 . 787 20. 10 83 , 485 38 , 573 30. 10 99 .975 28 .475 20. 10 83, ,819 38 . 138 30. 10 100 .305 28 .500 20. 10 84 . 154 37 . , 377 30. 10 100 .630 28 . 218 20. 10 84, .484 36 . 799 30. 10 100 .970 28 .019 20. 10 84 . 811 36. 221 30. 10 101 .297 27. .972 20. 10 85 , . 146 35. ,929 30. 10 101 .629 28 .007 20. 10 85. .481 35. . 393 30. 10 101 .961 27 .899 20. 10 85. ,811 35 . 131 30. 10 102 . 284 27 .975 20. 10 86. . 136 34. ,574 30. 10 102 .623 27 .714 20. 10 2 1 0.759.999.999.999.999.99 10.0E-10 RUN 26; TEMPERATURE=35 C 8 69.9 3.343 0.4020 . 150. 6 . 2 6.2 . 175 27 .3 27.3 .200 44 .4 44.4 .225 58 .8 58.8 . 250 69 .2 69.2 .275 76 .4 76 . 4 .300 86 .5 86 . 5 .325 97 .9 97 .9 42.5 42. 492 73. 763 30. 10 42 . 517 71 . 431 30. 10 42 . 823 64 . 538 30. 10 43. 166 60. 552 30. 10 43 . 502 58 . ,001 30. 10 43 . 841 56 . 081 30. 10 44 . 176 54. ,701 30. 10 44 . 509 53 . ,463 30. 10 44 . ,836 52. 338 30. 10 45 . , 168 51 . ,426 30. 10 45. ,502 50. ,595 30. 10 45. ,839 49. .998 30. 10 46. 166 49. 229 30. 10 46 . ,500 48 . , 754 30. 10 46. ,830 48 . ,249 30. 10 47 . 160 47 . 713 30. 10 47 . , 493 47 , . 198 30. 10 47 ; 830 46, .754 30. 10 48 . 169 46, .217 30. 10 48, .504 45 .783 30. 10 48 , .839 45, .512 30. 10 49, . 186 45, . 158 30. 10 49, .508 45 . 163 20. 10 49, .841 44 .861 20. 10 50, . 171 44 .458 20. 10 50, .514 44 . 369 20. 10 50, .839 44 . 149 20. 10 51 , . 171 44 .000 20. 10 51 , . 504 43 .800 20. 10 51 . 834 43 .519 20. 10 52 . 179 43 . 298 20. 10 52 .508 43 . 109 20. 10 52 ,844 42 .847 20. 10 53 . 183 42 .698 20. 10 53 . 509 42 .702 20. 10 53 .839 42 . 370 20. 10 54, . 172 42 .251 20. 10 54, .508 42 . 194 20. 10 54 , .839 42 , . 136 20. 10 55, . 166 41 .815 20. 10 55, .509 41 .828 20. 10 55, .835 41 .883 20. 10 67, .514 36 .042 20. 10 67 .837 35 .833 20. 10 68 . 168 35 .644 20. 10 68 .512 35 .677 20. 10 68 .836 35 .518 20. 10 69 . 171 35 . 237 20. 10 69 .505 34 .925 20. 10 69 .831 34 .868 20. 10 999. 999. 0 99 

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