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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 . S c , The University of B r i t i s h 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 t h i s t h e s i s 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 requirements  this thesis  British  it  freely available  for  that  f u l f i l m e n t of the  f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y  of  agree  in partial  Columbia,  I agree that f o r reference  permission  scholarly  the L i b r a r y  shall  and s t u d y .  I  f o r extensive  p u r p o s e s may  for  that  shall  Department o f  Date  P. —  10 - ^  gl  of this  Iti s thesis  n o t be a l l o w e d w i t h o u t my  permission.  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  thesis  be g r a n t e d by t h e h e a d o f my  copying or p u b l i c a t i o n  f i n a n c i a l gain  further  copying of t h i s  d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . understood  make  Columbia  written  ABSTRACT  The mechanical response under uniaxial d i s c s , made from f r e e z e - d r i e d tigated at 22, 2 9 . 5 , maintained  compression of collagen  collagen reconstituted at acid pH, was i n v e s -  and 35°C ( ± 0 . 3 C ° ) . The pH during compression was  near the p h y s i o l o g i c a l l e v e l of 7.40-5.  Connective t i s s u e s are known to be non-linear v i s c o e l a s t i c m a t e r i a l s . It  was f e l t , however, that the l i n e a r i z e d , f l u i d transport-based model  developed by Bert (1970) would adequately describe the behaviour of collagen "for small changes i n h y d r a t i o n .  [The model i s l i n e a r i z e d  assumption that the d i f f u s i o n c o e f f i c i e n t , h y d r a t i o n , and i s therefore  D(H),  the  i s a weak f u n c t i o n of  constant f o r small changes i n  The average d i f f u s i o n c o e f f i c i e n t ,  through  hydration].  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 o f hydration than expected i n the hydration range investigated have increased s c a t t e r  [1.9  to 5.5 g H 0/g c o l l a g e n ] , and t h i s may 2  in the r e s u l t s . Average values of D(H) and k/n at  hydration 3.0 g H 0 / g collagen [ i . e . 2  and ^ 6 . 0 x 1 0 "  11  skin hydration]  were ^ 3 . 5 x l 0 ~  7  cm /s 2  cmVdyne-s r e s p e c t i v e l y .  The compressive response of collagen was only weakly influenced by temperature,  and p o s s i b l e thermal  degradation of the molecules was indicated  at 3 5 ° C . Some creep was a l s o noted at times >5 t, , but no attempt was made to quantify  it.  11i  TABLE OF CONTENTS Page i i  ABSTRACT  iii  TABLE OF CONTENTS  v  LIST OF TABLES LIST OF FIGURES  vi  ACKNOWLEDGEMENT  vii 1  INTRODUCTION CHAPTER 1 1.1 1.2 1.3 1.4 1.5 1.6  BACKGROUND Connective Tissue Collagen Organization Collagen Hydration Reconstituted Collagen Methods for Measuring Soft Tissue Response The Mechanical Response of Collagenous Tissues  2 2 3 12 13 15 17  CHAPTER 2 2.1 2.2  MATHEMATICAL Formulation of the Model Determination of Model Parameters  22 22 26  CHAPTER 3 3.1 3.2 3.3  CHAPTER 4 4.1 4.2 CHAPTER 5 5.1 5.2  EXPERIMENTAL General Collagen Preparation 3.2.1 Solutions 3.2.2 Procedure 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  DATA AND ANALYSIS  42 42 45  RESULTS AND DISCUSSION  47 47 66 66 66 67 74 77 78  General Analysis  Results Discussion 5.2.1 S e n s i t i v i t y 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 V a l i d i t y of D(H) 5.2.6 The Relationship of D(H) and k/n to Hydration  iv  Page CONCLUSIONS  80  RECOMMENDATIONS FOR FURTHER WORK  81  NOMENCLATURE  82  REFERENCES  84  APPENDIX 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7  EQUIPMENT Linear Displacement Transducer Carrier Amplifier S t r i p Chart Recorder Recirculating Constant Temperature Bath Centrifuge Blender Digitizer  87 87 87 87 87 87 88 88  APPENDIX 2 2.1  SAMPLE CALCULATIONS Calculation of Hydration 2.1.1 Determination of Sample Thickness 2.1.2 Determination of Hydration Calculation of the Half-Time The Least Squares F i t Calculation of Model Parameters 2.4.1 The Diffusion Coefficient 2.4.2 The Flow Conductivity  89 89 89 89 91 91 94 94 94  COMPUTER PROGRAMS Program for Calculation and Plotting of Dimensionless Hydration Curves for Individual Sampl es Program for Calculation and Plotting of Dimensionless Hydration Curves for Lumped Data  96 97  2.2 2.3 2.4  APPENDIX 3 3.1 3.2  102  APPENDIX 4  DATA FOR GRAPHS PRESENTED  104  APPENDIX 5  RAW DATA  143  V  LIST OF TABLES  Table 1.2.1 1.3.1 3.2.1.1 3.3.3.1 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 5.2.3.1 5.2.4.1 A2.2.1 A4.1 A4.2 A4.3 A4.4 A4.5 A4.6 A4.7 A4.8 A4.9 A4.10 A4.ll A4.12 A4.13 A4.14 A4.15 A4.16 A5.1  Title  p  Molecular formulae and d i s t r i b u t i o n of various collagen types Hydration of collagen Compositions of solutions used Experiments performed Least squares f i t for dimensionless hydration-time data Model parameters for 22 C, sequence 1 Model parameters f o r 29.5 C, sequence 1 Model parameters for 35 C, sequence 1 Model parameters for 29.5 C, sequence 2 Model parameters for 35 C, sequence 2 Comparison between o r i g i n a l and recalculated values of t^ Errors due to approximation to the model Average half-times Data for figure 4.1.1 Data f o r figure 5.1.1 Data f o r figure 5.1.2 Data for figure 5.1.3 Data for figure 5.1.4 Data for f i g u r e 5,1.5 Data for figure 5.1.6 Data for f i g u r e 5.1.7 Data for figure 5.1.8 Data for figure 5.1.9 Data for figure 5.1.10 Data for figure 5.2.3.1 Data for figure 5.2.3.2 Data for figure 5.2.3.3 Data for figure 5.2.3.4 Data for f i g u r e 5.2.3.5 Raw data 2  a g e  5 12 31 41 58 61 62 63 64 65 75 77 92 105 106 108 110 112 114 116 119 120 122 126 127 129 132 135 138  vi  LIST OF FIGURES  Figure 1.1.1 1.2.1 1.2.2 1.2.3 1.2.4 1.6.1 2.1.1 3.2.1.1 3.2.2.2 3.3.1.1 3.3.2.1 3.3.2.2 4.1.1 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 5.1.7 5.1.8 5.1.9 5.1.10 5.1.11 5.1.12 5.2.3.1 5.2.3.2 5.2.3.3 5.2.3.4  Title Diagrammatic i l l u s t r a t i o n of connective t i s s u e matrix. Schematic representation of the structure of the procollagen molecule. Schiff-base type bonds between adjacent collagen molecules Current concept of the collagen molecule and p r o t o f i b r i l . Schematic drawing of a part of a tendon. Comparison between Jamison et aj_. and Sakata models. I l l u s t r a t i o n of the f l u i d transport-based model of Bert. Apparatus for n e u t r a l i z a t i o n of collagen/PBS mixture. Test-tube prepared for c e n t r i f u g a t i o n . Schematic representation of the experimental system. The main apparatus. Mounting for the l i n e a r transducer. Swelling pressure/hydration r e l a t i o n s h i p for samples tested in sequence 2 at 29.5°C. Response of sample tested in sequence 1, 29.5°C, 30 g weight. Response of sample tested in sequence 1, 29.5°C, 40 g weight. Response of sample tested in sequence 1, 29.5°C, 50 g weight. Response of sample tested in sequence 1, 29.5°C, 60 g weight. Response of sample tested in sequence 1, 22°C, 40 g weight. Response of sample tested in sequence 1, 35°C, 40 g weight. Response of sample tested in sequence 2, 29.5°C, 40 g weight. Response of sample tested in sequence 2, 29.5°C, 60 g weight. Response of sample tested in sequence 2, 29.5°C, 80 g weight. Response of sample tested in sequence 2, 35°C, 40 g weight. Relationship of D(H) to average hydration, H° Relationship of k/n to average hydration, H° Relationship of dimensionless hydration and time (cut o f f at 5 t^) for sample #10. Relationship of dimensionless hydration and time (cut o f f at 6 t i j for sample #10. Relationship of aimensionless hydration and time (cut o f f at 7 t j j for sample #10. Relationship of climensioniess hydration and time (cut o f f at 5 and compensated for H°) for sample #10. Relationship of dimensionless hydration (unsealed f o r time) for sample #10. Sample raw data curve.  Page 4 6 8 10 11 19 23 32 34 35 37 38 44 48 49 50 51 52 53 54 55 56 57 59 60 69 70 71 72  2  5.2.3.5 A2.1.1.1  73 90  vii  ACKNOWLEDGEMENTS I would l i k e to express my thanks to the following  individuals:  Dr. K.L. Pinder, for his patience and help during the course of t h i s work. Tony Paterson, for his support, and for timely help with various mathematical problems. Joel Bert, for l e t t i n g me draw on his considerable knowledge in the f i e l d . Marlene Woschee for her excellent typing under duress. My parents, for t h e i r love and support. In a d d i t i o n , I would l i k e to express appreciation for the e f f o r t s of the s t a f f of the Chemical Engineering Workshop and Stores. Financial support from the National is g r a t e f u l l y acknowledged.  Research Council of Canada  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 t i s s u e s , interact in vivo, and what s p e c i f i c 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 v i s c o e l a s t i c behaviour of samples, made from r e constituted, freeze-dried collagen [Chapters 1.3, 1.4], via the f l u i d transport-based model developed by Bert [Chapter 2]. b) Investigating the interaction of collagen with other constituents of skin.  This would involve adding, for example, e l a s t i n and proteoglycans  to the collagen samples, and determining changes in the f l u i d 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 using the apparatus [Chapter 3.3]. statistical 5].  [modified by the author] designed by Sakata  compression (1969)  Results from the experiments were then analyzed using  methods applied to the model derived by Bert (1970)  [Chapters 4,  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 c a r t i l a g e , to the corneal  stroma, spinal discs and a r t e r i a l walls.  A knowledge of the swelling  behaviour of collagen is thus indispensable to an adequate understanding of such phenomena, among others, as edema, c a r t i l a g e function in j o i n t s , peridontal membrane function, the e l a s t i c i t y of skin, and a r t e r i a l blood flow. Connective tissue may be regarded as consisting of three functiona l l y d i s t i n c t substances:  collagen f i b r e s , e l a s t i n , and the amorphous  ground substance, or proteoglycans.  Morphology  [that i s , gross s t r u c t u r e ] ,  composition and function vary greatly from tissue to t i s s u e . Several types of connective tissue are to be found in both man and animals.  Their s p e c i f i c functional properties - which allow the tissue to  f u l f i l l s p e c i f i c biological  functions - are largely dependent upon the macro-  molecular organization of the collagen molecules within the t i s s u e .  For  example, collagen f i b r e bundles in skin, tendon and bone are composed of collagen f i b r i l s of comparable diameter, but collagen in a r t i c u l a r c a r t i l a g e forms a fine meshwork of r e l a t i v e l y narrow f i b r i l s .  Furthermore, although  collagen may constitute up to 33% of skin [79% on a dry weight basis]  it  only forms about 23-35% of c a r t i l a g e (Lowther (.1963), Schubert and Hamermann (1968)).  3  In some connective t i s s u e s , both the collagen and the ground substance 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 H 0/g collagen. 2  Hence, in  most cases, the fibrous collagen network serves as a support structure which physically restrains the g e l - l i k e proteoglycans within the space between the f i b r e s , and provides the mechanical strength of the tissue 1.1.1].  [Figure  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 i s o l a t i o n .  A discussion of the swell-  ing behaviour of a l l connective tissues and t h e i r contributions to the overall response of s p e c i f i c tissues is c l e a r l y 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 c y c l i c a l step function 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 s i g n i f i c a n t deviation from the in vivo state of the collagen used, and therefore a b r i e f 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 t y p i c a l l y contain 1011 amino acid residues and the end  4  FIGURE 1.1.1  Diagrammatic i l l u s t r a t i o n of connective t i s s u e matrix. (Scott (1979))  5  regions from 9 to 25 residues (Fietzek and Ku'hn (1976)). Four morphological types of collagen, composed of f i v e g e n e t i c a l l y d i s t i n c t polypeptide chains all  [Table 1.2.1], have been i d e n t i f i e d so f a r and  are very s i m i l a r (Scott (1979)).  Fietzek and Kiihn (1976), in t h e i r  excellent review of collagen s t r u c t u r e , report that of these chains the structure of the a l ( I ) - and h a l f of the a2-chain are known.  Some preliminary  data has also been obtained on the sequence of the a l ( I I ) - and a l ( I I I ) chains.  Three of these polypeptide chains are brought together i n t r a -  c e l l u l a r by a complex chain of events which includes the "hydroxylation of c e r t a i n proline and l y s i n e residues by s p e c i f i c hydroxylases and attachment of carbohydrate moieties to some of the hydroxylysine residues by galactosyl  TABLE 1.2.1 Molecular formulae and d i s t r i b u t i o n o f various Collagen types (Fietzek and Kiihn (1976)) Morphological Type  and glycosyl  Molecular Formula  Distribution  I  [al(I)] a2  Skin, bone, tendon, a o r t a , lung, e t c .  II  [cdUI)]3  Hyaline c a r t i l a g e  III  [al(III)]  IV  [al(IV)]  2  transferases"  3  3  As type I,  reticulin  Basement membrane  (Fietzek and Kiihn (1976)).  This coming together  of three l e f t handed h e l i c a l molecules produces a r i g h t handed superh e l i c a l molecule with non-helical procollagen peptides attached [ F i g . 1.2.1]. The formation and correct alignment of t h i s s o - c a l l e d  'tropocollagen'  molecule i s assumed to be f a c i l i t a t e d by the i n t e r a c t i o n o f the procollagen peptides.  After the t r i p l e helix i s secreted into the e x t r a -  (MarOn GlcNac  N-TERMINAL PROPEPTIDE  COLLAGEN  ;,_C-TERMINAL PROPEPTIDE  MOLECULE  3000 A )  (150 A)  (100 A) (Man)n GlcNac  (20A)  (100A!  Globular Domain Triple - Helical Domain Nontriple- Helical Domain  Nontriple- Helical Domain  Nontriple - Helical Domain  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 c e l l u l a r f l u i d the procollagen peptides are enzymatically cleaved o f f , thus giving the molecule the a b i l i t y to aggregate into f i b r i l s (1972), Prockop et al_. (1979)).  It  (Grant  is important to note that a l l three  * polypeptide chains have a c h a r a c t e r i s t i c Gly-X-Y repeat sequence of amino acids throughout the t r i p l e h e l i c a l region.  This arrangement is  necessary  due to s t e r i c considerations encountered during formation of the t r i p l e helix and a f t e r .  Glycine is the smallest of the amino acids and lacks any  side chains, and i s thus p a r t i c u l a r l y suitable for occupying the  positions  located in the i n t e r i o r of the t r i p l e helix (Ramachandran and Kartha Rich and Crick It  (1955),  (1955)).  is assumed that the higher order organization of the collagen  molecules is also c o n t r o l l e d 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 s e l e c t i v e enzymes on segments of the chain.  For example,  c e r t a i n l y s i n e and hydroxylysine residues located in the n o n - t r i p l e h e l i c a l regions at both ends of the helices are deaminated by oxidation via a l y s i n e oxidase (Gallop et aj_. (1973), Robins et al_. (1973)).  This  results  in i n t e r a c t i o n between the carbonyl compounds thus created and the l y s i n e and hydroxylysine molecules in adjacent molecules via S c h i f f intermolecular bonds [ F i g . 1.2.2].  base-type  The n o n - t r i p l e h e l i c a l regions are  also notable for t h e i r 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 d i l u t e solutions o f neutral s a l t - s o l u b l e collagen to 37°C. cause the spontaneous  *  This was found to  p r e c i p i t a t i o n of collagen molecules and resulted  Glycine, an amino a c i d .  8  = 0  aldehyde  H N - R"  +  2  primary amine  condensation R, H0  NR II  +  2  R  S c h i f f base weakly basic  hydrolysis (H 0 + strong 2  carbonyl compound (aldehyde, ketone, e t c . )  Fig. 1.2.2:  acid)  H N - R II  +  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 s a l t - s o l u b l e collagen is a group of proteins which aggregates to t y p i c a l 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 substances such as urea and a r g i n i n e , which are known to prevent the formation of hydrogen bonds between molecules [in a d d i t i o n , they may also function as competitors for carboxyl and other charged groups]. r e s u l t s of Van Duzee (1978) also confirm t h i s .  Both pH and ionic  The strength  were also found, by Fessler (1960), to a f f e c t urea i n h i b i t i o n and t h i s was held to suggest that there is a " p a r t i c i p a t i o n of e l e c t r o s t a t i c forces in addition to hydrogen bonding in f i b r i l s a l t solution]  system."  formation in t h i s  [collagen/neutral  Furthermore, the established amino acid sequence  9 strongly suggests that hydrophobic interactions are also involved in establ i s h i n g bonds in which the C-terminal of the collagen molecule is involved. The C-terminal  i s strongly hydrophobic, and the quarter-stagger  within f i b r i l s  [see below] ensures that i t w i l l always be in contact with  hydrophobic regions of the surrounding chains.  arrangement  Since the a2-chain contains  many more hydrophobic residues than the c d ( I ) - c h a i n ,  i t contributes  to the hydrophobic character of type I collagen (Fietzek and Klihn .Current theory suggests that "the aggregation into f i b r i l s represents a self-assembly  greatly  (1976)).  of the molecules  process, regulated by the amino  acid sequence of the collagen molecule" (Fietzek and Kuhn  (1976)).  Several review a r t i c l e s have covered the h i s t o r y of the investigation collagen structure and properties.  To quote V i i d i k  of  (1973):  "Recently, an idea that the tropocollagen molecule consists of f i v e i d e n t i f i a b l e 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." [ F i g . 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 n o n - t r i p l e h e l i c a l regions of 16 and 25 residues  r e s p e c t i v e l y , f i t into the empty spaces of length 0.6D.  This over-  lapping arrangement gives r i s e to the t y p i c a l , r e g u l a r l y banded, appearance 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 l o n g i t u d i n a l l y to form f i b r e s [ F i g . 1.2.4].  Fibres may anasto-  mose at acute angles in t i s s u e 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  •  1  1  1 •  •  1  1  1 •  )»  1  1  1 •  ^  1  H H  •  •—t  1  (B)  FIGURE 1.2.3 Current concept of the collagen molecule and p r o t o f i b r 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 f i b e r bundles is cut (arrow), showing the wavy course of the f i b e r s . The group of primary bundles shown is surrounded by a sheath (also c u t ) . (Scott (1979))  12 "not considered to branch at a l l in the native s t a t e " .  1.3  (Viidik (1973)).  Collagen Hydration The interaction between collagen and water has received consider-  able attention l a t e l y .  Nomura and his coworkers (1977) have i d e n t i f i e d  four regimes in collagen hydration, and these are l i s t e d in Table 1.3.1.  TABLE  1.3.1  Hydration of Collagen  Water Content g H 0/g collagen 2  0 - 0.07  Characteristics structural water  0.07 - 0.25  bound water  0.25 - 0.45  bound-free t r a n s i t i o n zone  > 0.45  free water  They have gone on to suggest that the structural water is incorporated into the t r i p l e superhelix, the bound water is associated with the polar side chains within the i n t e r h e l i c a l regions of a f i b r e , and that the free water corresponds with the i n t e 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 H 0/g collagen, i t is assumed that the movement of water into and 2  out of the collagen matrix is r e l a t i v e l y unaffected by i n t e r f i b r i l l a r forces.  13 1.4  Reconstituted Collagen The collagen used for t h i s work was commercially a v a i l a b l e  l y o p h i l i z e d [freeze-dried] bovine a c h i l l e s tendon or rat t a i l tendon collagen [U.S. Biochemical Corporation], and therefore, according to the c l a s s i f i c a t i o n system given in Table 1.2.1, primarily type I c o l l a g e n . The method of preparation used by the manufacturers is that of Einbinder and Schubert (1951).  This method involves extraction of cleaned collagenous  t i s s u e for 6 days at 0°C with 3% ^ H P C s  to remove soluble p r o t e i n s , further  extraction for 6 days at 0°C with 25% KC1 solution to remove proteoglycans; and f i n a l l y , washing with water and dehydration of the t i s s u e using absolute alcohol.  This is followed by . l y o p h i l i z i n g the t i s s u e .  Collagen prepared  in such a manner has a dry, f l a k y appearance, with some comparatively large 'bundles' mixed i n . Reconstitution of the collagen to a state approximating in vivo collagen, was subject to the following considerations: a) Dried collagen does not swell e a s i l y at the pH of physiological s a l i n e (Veis (1964)).  It does, however, swell r a p i d l y at acid pH.  Accord-  ing to Schubert and Hamermann (1968) the " e f f e c t of lowering pH appears to favor a s h i f t of e q u i l i b r i a to the disordered forms because o f the disruptive e f f e c t of the repulsions among the accumulated c a t i o n i c charges on the ordered f i b r e s " .  Flory and Weaver (1959) report that  viscosities  of d i l u t e collagen solutions were considerably reduced by the addition of 0.4% acetic a c i d , and a t t r i b u t e d t h i s to the suppression of association of collagen molecules by e l e c t r o l y t e s present in the a c i d . by Weissman and Cocks (1978).  This was confirmed  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 a c i d base hydrolysis e q u i l i b r i a which exist for t h i s side group].  14 ii)  pH s e n s i t i v e intermolecular f o r c e s .  At pH l e v e l s below  the i s o e l e c t r i c point of c o l l a g e n , the net positive charge increases with decreasing pH and t h e r e f o r e , at low pH, the increased repulsive force between molecules along with freeing o f i o n i c groups on collagen by the high H concentration, establishes a Donnan potential inside the f i b r e s .  +  Hence  water flows in along i t s concentration gradient and equalizes the ion concentration inside the collagen and in the external solution  (Ramachandran  and Kartha (1955)). Low pH i s , t h e r e f o r e , desirable but strong acids damage the collagen structure by disrupting the matrix.  0.5M a c e t i c acid has been used (Gross  and Kirk (1958)) without damage to the tropocollagen molecule, and t h i s concentration of acid was used in the present study.  Damage done to the  molecules at low pH can be reversed by n e u t r a l i z a t i o n 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 r e c o n s t i t u t i o n i s necessary, the collagen sample once formed, must be kept at stable physiological 6 days at up to 37°C. physiological  pH [7.40-7.45] f o r up to  In order to e f f e c t t h i s a phosphate buffered  saline solution [PBS] was used (Dulbecco and Vogt (1954)).  This solution i s buffered with NaH P0ii and KH P0 i with an e f f e c t i v e range 2  2  H  centered near a pH of 6.8 (Hampel and Hawley (1973)). c) Proteins are open to thermal, biochemical and b i o l o g i c a l  attack  outside the body: i ) Collagen i s subject to thermal degradation at temperatures above 35°C, the maximum temperature encountered in t h i s study (Gustavson (1956), Schubert and Hamermann (1968), Veis (1964)).  15 ii). The molecular organization of collagen can be severely disrupted by the l y o t r o p i c action of certain e l e c t r o l y t e s and s t a b i l i z e d by the presence of others (Gustavson (1956), Veis (1964)). present in the PBS used in t h i s study, only CaCl  2  Of the s a l t s ,  has a moderately disrup-  t i v e e f f e c t on collagen when present at high concentrations.  This s a l t was  present at a very low concentration [0.001M] in the PBS and could not have caused any s i g n i f i c a n t iii)  disruption.  0.2% w/w sodium a z i d e , NaN , was used to prevent bacterial 3  growth in the PBS.  1.5  Methods for Measuring Soft Tissue* Response Soft t i s s u e s have been shown to be complex materials and t h e i r  mechanical behaviour is the r e s u l t of complex s t e r i c interactions within a matrix of e x t r a c e l l u l a r , l a r g e l y c o l l a g e n , f i b r e s imbedded in an aqueous proteoglycan g e l .  To the response of the matrix must be added e f f e c t s due  to the movement of free i n t e r s t i t i a l f l u i d under the influence of osmotic and hydrostatic concentration and pressure gradients, and matrix deformation. Beyond the necessary complexity of any soft tissue model, l i e problems of experimental technique. the following considerations a) In i t s natural  In s p e c i f i c , for the case of s k i n ,  arise:  s t a t e , skin is b i a x i a l l y , and unevenly  stressed, with the degree of preloading varying from point to point on the body. 'Langer's  Maps showing d i r e c t i o n s of minimum e x t e n s i b i l i t y - the s o - c a l l e d lines'  (Danielson  (1971)) - have been produced, and are extensively  v  * 'Soft t i s s u e ' is a term widely used to denote tissues with v i s c o e l a s t i c properties s i m i l a r to those of connective t i s s u e s .  16  used by surgeons. b) Whole skin is inhomogeneous.  Skin properties vary not only with  i t s l o c a t i o n 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 to determine skin thickness  (Alexander and Cook  (1977)).  d) If the experiment is to be done in v i t r o , then i t is to reproduce in vivo conditions as far as  possible  important  possible.  The majority of the skin and tendon investigations  done to date  have involved c h a r a c t e r i z a t i o n of tissue behaviour under tension and have generally been c a r r i e d out using one of two experimental techniques: a) Use of t r a d i t i o n a l m a t e r i a l s - t e s t i n g apparatus such as that made by Instron,  and other extensometer manufacturers (Fung (1967), Van  Duzee (1978), Diamant et al_. (1972), Elden  (1964)).  b) A p p l i c a t i o n 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 r o , and are p a r t i c u l a r l y useful  in investigating  behaviour of edematous  Cartilage i n v e s t i g a t i o n s ,  tissues.  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)). indentation methods used for tests that used in t h i s  The  performed on c a r t i l a g e are s i m i l a r to  paper.  One of the major problems with extensometric studies is that they are often destructive in nature, and must therefore be c a r r i e d out in v i t r o , with some care devoted to both extraction and preservation of the t i s s u e . For studies with immediate c l i n i c a l a p p l i c a t i o n s , p a r t i c u l a r 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 v i v o ] . due to the non-linear v i s c o e l a s t i c nature of the tissues t e r i z a t i o n of tissue behaviour based on stress  Furthermore,  involved, charac-  [force per unit area] be-  comes d i f f i c u l t due to changes in cross-sectional  area during t e s t i n g .  Also, expression of f l u i d s due to tight clamping of the samples can i n t e r fere with r e s u l t s , p a r t i c u l a r l y where swelling behaviour is being i n v e s t i gated . The hydrostatic pressure application method of Dick (1951), in i t s c l i n i c a l manifestation as a vacuum application technique, is also troublesome (Grahame (1969)).  To quote Alexander and Cook (1977):  "Reducing the raw data from such a technique to quantitatively valuable s t r e s s - s t r a i n information is complicated by a' number of factors: the skin is already b i a x i a l l y loaded in the natural state, the thickness of the test s i t e is not known, and any characterization in terms of material constants requires a multiaxial s t r e s s - s t r a i n law that is generally v a l i d 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 l a s t century.  half  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 e a s i l y accessible of t i s s u e s , but also often r e f l e c t s 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 formulations. 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 e s s e n t i a l l y 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 t e d to the water transport-based model derived by Bert  (1970). Many attempts at modelling the mechanical behaviour of so-called  "soft"  biological  approach.  tissues  have involved the t r a d i t i o n a l spring and dashpot  The models suggested by Jamison et al_. (1968) and Sakata  (1969)  are presented below [Fig. 1.6.1] and consist of ideal e l a s t i c and viscous elements - represented by springs and dashpots, respectively. of Sakata  In the case  (1969), an idealized plastic or f r i c t i o n element - the "ratchet"  element - has also been included.  V i i d i k (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 c l e a r l y i d e n t i f i a b l e 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 i n g methods. model of Veronda and Westman, presented below:  For example, the  FIGURE 1.6.1 Comparison between Jamison et al_. ( l e f t ) and Sakata (right) models. n i » n . = Viscous element. E = E l a s t i c element. Right: F = Force. A,C = E l a s t i c elements. B = Viscous element. D = E l a s t i c element with ratchet. X X , X = Displacement. A,B,C,D = Time dependent parameters. (Wilkins and Pinder (1979))  Left:  2  2  l s  3  2  20  3 W  =  Y,  1.6-1  °i 1 dA  i=l  where W i s the s t r a i n energy function per u n i t volume o f the undeformed body a., i s the s t r e s s i n the i d i r e c t i o n X. i s the r a t i o between p r i n c i p a l extensions o f the deformed body and the corresponding i n i t i a l b) an integral  dimensions i n the undeformed  state,  equation i s solved f o r the s t r a i n energy function  when oCt) and x(t) are known.  Such a model was suggested by Gou (1970), and  t h i s was tested by WiTkins and Pinder (1979) on various c o n s t i t u e n t s o f connective t i s s u e i n g e l a t i n g e l s .  This model involves the phenomenological  treatment o f continuum mechanics given by Mooney (1940), and the load extension r e l a t i o n f o r uniaxial tissue  [sartorius muscle].  stress proposed by Aubert (1955) f o r a s o f t It i s presented below:  a = 3ck(x -X~ )exp[k(x -3+2x)] 6  3  1.6-2  6  where c and k are parameters X i s the uniaxial  strain  and a i s the corresponding uniaxial S i m i l a r models have been proposed by o t h e r s .  stress. These models have one  drawback, however - they a r e u s u a l l y very s e n s i t i v e t o X at low s t r a i n s , and very small e r r o r s i n the measurement can lead t o large e r r o r s i n the predicted values o f o .  21  Some authors have also f i t t e d exponential and power series functions 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 j u s t i f i e d . 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 f e l t that  a model based on f l u i d transfer through a porous membrane would more closely approximate real i t y for a highly hydrated t i s s u e . d) It allows comparison of the swelling behaviour of d i f f e r e n t soft tissues  based on a measurable quantity - the hydration of the t i s s u e .  In his work, which will be expanded upon in the next chapter, Bert (1970) investigated the swelling behaviour of several different connective tissues.  These included corneal stroma, costal and a r t i c u l a r  c a r t i l a g e , spinal d i s c s , skin and aortic walls. t i v i t i e s near 7 x 1 0 ~  12  per gram of dry t i s s u e .  cm^s"^yne"  1  He reports flow conduc-  for skin at hydrations near 3 g H 0 2  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 dm is the incremental amount of water in a segment of membrane with w  dry mass dm, and 6 and y are the densities of collagen and water, respectively. The above assumes that the volumes of f l u i d and dry material are additive. Equation 2.1-1 can be rearranged to give 1  dx  1  dm  _ + _ .• _ !-TIT! HTT + yA 6A dm  V-m  2.1-2  or  dm where  is the hydration at a point, H g water/g collagen.  defined e = ^ o  0 to x. variable  and & = ^ ~ , where  Bert has  is the thickness of dry material from  6A  This allows the transformation of the space variable x to the which is based on the thickness of dry collagen in the sample:  FIGURE'2.1.1 I l l u s t r a t i o n of the f l u i d transport-based model of Bert. Hydration p r o f i l e s are assumed to be symmetrical about the l i n e ip = 0.  ro co  24  dx =  • o>  2.1-4  The continuity equation for the system can be shown to be  3  H  3t where f  x  Hm  9  f  v  dm = _ - ^ L . dm A 9m  2.1-5  is the water flux in the x d i r e c t i o n , -rr • T ~ is---the rate of change _ 3t A 3 f  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 i r e c t i o n .  Rearrangement of equation 2.1-5 gives  3H  3 f  2.1-6  x  . m A  9t  9  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  f  where f  c  that:  = v . T  •9x9P——  k — n  2.1-7  i s the convective flux g/cm -s and- k/n is the flow conductivity 2  The d i f f u s i v e flux f , d  by F i c k ' s f i r s t  associated with water a c t i v i t y gradients, is described  law:  9a f. = - D — ^ d 3X  2.1-8  25  For connective tissues at hydrations greater than 0.2 g water/g c o l l a g e n , the d i f f u s i v e flux has been shown by Bert to be n e g l i g i b l e  [less than 1%  of the convective f l u x ] . The equations of i n t e r e s t to us, are thus reduced to i ) The continuity equation:  9f  9H  4  x  2.1-6  x  at  i i ) The equation of motion:  k  =  f  x  =  f  9P  C  2.1-7  _ .— A n 9x  c  i i i ) An equation of state which is derived from experimental data and defines 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 d e f i n i t i o n of ^, gives 1  9H  9  f k  YE  3P  C  S  9t  Y  9* I n  dP  9P  Using the r e l a t i o n s h i p  3  (E+H)  =  2.1-9  1  T/J  9H  •  and substituting in equation 2.1-9  yields 9H  It  1 9 =  - Y  3*  f k  1  YE  n ' U+Hl *  dP  s  9H  dlT * a* ^  But E = Y/<S and is independent of ty. Hence  2  '" 1  10  26  9H 9t  d  =  e  k  C  dP  2  '  3 K V  n ' Te+Hl ' ciTT ' 3^ J  9^ 1"  •  2.1-11  Bert has defined the d i f f u s i o n c o e f f i c i e n t D(H) to be k -DCH) .  E  -  .  dp  2  ^  .  ^  2.1-12  and has rewritten equation 2.1-11 as  •• f If  •!*••{"«< >  2-1-13  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 i n e a r i z e d to  9H  _ DTHT . 9 £ H  ----^  at  where DCH) i s the c o e f f i c i e n t 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 H can be written for H:  Q  the f i n a l , hydration.  Equation 2.1-14  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 the dry thickness of the sample].  is thus  half  This system i s depicted in F i g . 2.1.1.  The solution i s given (Crank (1975)) as:  H - H.  ,  ~  , ,*n  -D(nT(2n+l) Tr t/4V 2  2  2  , o  n  +  n  ,  n=0 For n>0, a good approximation  0  is:  1  v  or -D(HTTT t/4f 2  H = H 0  + (H.-H ) - e 1  0  2  cosffr  2.2-5  2$  TT  and at any time, the average hydration across the membrane, H , is given g v  by  _  -rKITTr t/4^ 2  H =H + (H.-H ) - e av o l o TT  or  ^=^' 2  •V ^  f> /  cosffr dij; ^  2.2-6  28  -D{hTir t/V 2  H = H + CH.-H ) \ av o i o TT  Z  2  e  2.2-7  H -H A plot of l n ( T j r - n — ) versus time w i l l c l e a r l y give a straight l i n e of slope i o l (~z) - 4 " ^ ' ^ n  »  a  n  from t h i s  d  DCH) can e a s i l y be determined.  dP Once DCH) is determined, j p p swelling  1  S  experimentally determined from the  pressure - hydration r e l a t i o n s h i p  [the hydration of the membrane  at any time is calculated from measurements of i t s thickness, via the equation  Ap H  av  =  j  ~m~  1  ~ 6  2  - " 2  8  where A is the cross sectional area of the membrane, DW i t s dry weight, and T the thickness of the membrane]. k The parameter equation 2.1-12. H  i  +  H  the flow c o n d u c t i v i t y , can then be calculated from  Note that D(H) as determined is considered to be the value  o Also note that a l l values of H measured are in fact averages,  over i^=0 to ^=^'. from t h i s  point on.  The subscript w i l l  H , av = w  be l e f t o f f , for the sake of c l a r i t y ,  29  CHAPTER 3 EXPERIMENTAL  3.1  General Experiments were performed to measure the mechanical response, under  uniaxial compression, of discs made from r e c o n s t i t u t e d , f r e e z e - d r i e d , fibres.  collagen  The r e s u l t s were compared to the f l u i d transport-based model pro-  posed by Bert  (1970).  Considerable e f f o r t was invested in the preparation of collagen discs.  Two major objectives were i d e n t i f i e d in t h i s a) The discs  regard:  produced have to be both e a s i l y reproducible, and  homogeneous: i) The use of reconstituted collagen* eliminated some of the random errors associated with any experimentation involving soft [These large errors are a d i r e c t r e s u l t of the large variations and properties inherent in l i v i n g tissues  [Chapter 1.5]].  tissues. in structure  Also a r i g i d  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] d i l u t e acetic acid was used to cause r e hydration of the c o l l a g e n , and, a f t e r n e u t r a l i z a t i o n to the pH of ECF**,  * Taken from r e l a t i v e l y homogeneous, c o l l a g e n - r i c h , tissues such as bovine a c h i l l e s tendon and rat t a i l s . * * E x t r a c e l l u l a r or i n t e 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 r a t i o n 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 l e v e l . Centrifugation of the collagen/PBS mixture produced highly viscous l e t s of collagen  pel-  [at r e l a t i v e l y low hydrations], which were d i f f i c u l t to  deal with:  the discs produced by manually packing this material into p l e x i -  glass rings  [see below] invariably contained a i r 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. of the preparation procedure.  This was accomplished by the standardization 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 H 0/g collagen. 2  31  3.2  Collagen  Preparation  3.2.1  SOZ.UXA.OVU,:  TABLE 3.2.1.1 Compositions of Solutions Used Solution  Contents  acetic acid  CH3COOH  0,.50  sodium hydroxide  NaOH  5,.00  phosphate buffered saline  NaCl KCl NazHPO^ KH P0 CaCl MgCl -6H 0 NaN H0 2  Amount (grams)  4  2  2  2  3  2  Molarity  8..00 0..20 1;.15 0..20 0..10 0,.10 0,.20 990,.15  0,.1368 0,.0027 0,.0081 0,.0015 0..0009 0,.0005  1000.2  PBS was f i l t e r e d 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 d i l u t e 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 a c h i l l e s tendon c o l lagen.  32  FIGURE 3.2.2.1  Apparatus for neutralization of collagen/PBS mixture.  33  d) The collagen p e l l e t s 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 r e f r i g e r a t o r at 4°C. e) Steps c) and d) were repeated to give a t o t a l of 160 g of the collagen/PBS mixture, which was s u f f i c i e n t for about 9 samples of c o l l a g e n . The mixture was l e f t r e f r i g e r a t e d overnight before using. f) 18 g of collagen suspension  from e) were placed in a s p e c i a l l y  prepared test tube [see below, and Figure 3.2.2.2] and centrifuged at 1650 g f o r h hour, 10 minutes.  1100 g for a further h hour, and f i n a l l y  1100 g f o r  The collagen was s t i r r e d with a spatula a f t e r each c e n t r i f u g a -  t i o n step to release a i r trapped under the porous d i s c , and also in order to prevent packing gradients  from developing in the collagen d i s c .  The f i n a l  weight o f a collagen sample was about 3 g. g) The disc was removed from the tube, and the membrane was r e moved, leaving only the plexiglass  ring.  The disc was then placed on top  of a porous metal disc in a covered glass beaker containing just enough to wet the top of the metal d i s c .  1.5 ml of PBS,  This was r e f r i g e r a t e d f o r at  least two days before using in the apparatus described below.  3.3  Experiments  3.3.1  The, ExpthAjmzYital. SystemThe experimental system i s represented in Figure 3.3.1.1 and consists  of f i v e major elements [Appendix 1 ] : a.) The main apparatus, to uniaxial  in which the collagen discs are subjected  stress.  b) A l i n e a r t r a n s d u c e r / c a r r i e r a m p l i f i e r combination, the output of which is proportional to the thickness of the collagen disc under observation.  34  POLYCARBONATE TUBE  POROUS STEEL DISC  FIGURE 3.2.2.2  Test-tube prepared for centrifugation.  CONSTANT TEMPERATURE RECIRCULATING BATH  MAIN APPARATUS  STRIP CHART RECORDER  CARRIER AMPLIFIER  FIGURE 3.1:1.1 Schematic representation of the experimental system.  36 c) A s t r i p chart recorder, to record the output of the c a r r i e r a m p l i f i e r , and hence the thickness of the d i s c , 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. i f i c a t i o n s made were as follows  The mod-  [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 l i n e a r transducer c o i l  in order to reduce fluctuations in output caused by changes  in ambient temperature.  The c o i l was mounted in a threaded copper cylinder  that screwed into a s o l i d 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 t e s t s . iv) The copper heating c o i l  [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 i n e a r displacement transducer [4], a c y l i n d r i c a l vessel coil  [5], a heating  [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 c y l i n d r i c a l vessel [5] is shown in section. Figure is approximately to scale.  FIGURE 3.3.2.2  Mounting  for the l i n e a r transducer.  39  c) Water at constant temperature was c i r c u l a t e d through the bath surrounding the transducer [9], and also through a s t a i n l e s s coil  steel  heating  [6], immersed in the PBS tank [5], by means of a constant temperature  bath. d) Calibrated weights were placed on the arm, d i r e c t l y over the probe, to apply pressure to the collagen  3.3.3  discs.  ?fL0C.2.duAZ:  a) C a l i b r a t i o n of l i n e a r 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 c y l i n d r i c a l v e s s e l .  Temperatures used were  22, 29.5 and 37°C. ii)  PBS was added to the v e s s e l , and the e n t i r e system was  allowed to e q u i l i b r a t e for 20 minutes. i i i ) C a l i b r a t i o n of the transducer was accomplished by i n s e r t i n g one or more machined, s t a i n l e s s  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 p o s i t i o n , which corresponds to a sample thickness of 0.125"]. were used:  One-inch diameter discs of the following  thicknesses  0.050", 0.100", 0.125", 0.275", a l l to a tolerance of ± 0.001.  Calibrations were performed both before and a f t e r each test  series  [see below]. b) S t r e s s - s t r a i n  determination  i ) A f t e r c a l i b r a t i o n , the collagen d i s c , contained in the plexiglass  ring [Figure 3.2.2.2], was placed on the disc support, and held  in place by the r e s t r a i n i n g c y l i n d e r .  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 r e s t r i c t movement of the probe to the v e r t i c a l during t e s t i n g , and t h i s was made possible by a bar - 5 mm below the p a r a l l e l to the supporting arm - which connected the probe to the arm support.  A l l four  v e r t i c e s of the parallelogram thus formed allow rotation about an axis perpendicular to i t s plane, and thus the probe remained p a r a l l e l to the fixed arm" support. The arm was about 24 cm in length - long enough to neglect horizontal displacement of the probe, since v e r t i c a l displacement of the probe was always less than 0.25" from the n u l l p o s i t i o n . ponded to a sample thickness of 0.125".] hollow s t a i n l e s s  [The null position c o r r e s -  The probe i t s e l f was a p a r t i a l l y  steel c y l i n d e r 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 s c , and consisted of a porous s i n tered s t a i n l e s s  steel disc that allowed r e l a t i v e l y free passage of the PBS.  S i m i l a r l y , the anvil had a porous top of the same m a t e r i a l .  A roller  bearing at the juncture of the arm and the arm support served to reduce f r i c t i o n 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 i n e a r transducer was a v a r i a b l e permeance, electromechanical instrument in which the a.c. current produced was roughly proportional to the probe displacement from a null position [the h o r i z o n t a l ] .  The maximum  allowable displacement was 0.25 inches. The output of the transducer was amplified by a c a r r i e r a m p l i f i e r with a maximum output of 10 V d.c.  It was discovered that at high a m p l i f i -  cations noise was considerably reduced, as was n o n - l i n e a r i t y of the output.  41  A near-maximum setting was thus used throughout the experiments.  The  output of the amplifier was recorded on a s t r i p chart recorder. ii)  PBS was added to bring the level of the l i q u i d 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 t h i c k ness was r e l a t i v e l y stable [Chapter 4].  The time taken to ' e q u i l i b r a t e '  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  ~-^Step Sequence  Number  1  2  —^_  3  4  5  6  Sample Number  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  35.0  1  30  40  50  35.0  2  40  60  80  * A l l samples were preloaded to 20 g.  8,9,10,11 60  70  80  19,20,21,22,24 16,18,25,26  42  CHAPTER 4 DATA AND ANALYSIS 4.1  General Due to the large scatter inherent in b i o l o g i c a l  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 r e s u l t s : a) Experiments at each condition [e.g.. 35°C, Sequence 1] were repeated f i v e times. b) A completely randomized experimental design would have been ideal:  t h i s would have ensured a minimum of systematic errors a r i s i n g from,  for example, a malfunction in the constant temperature bath or some mistake in the preparation of a p a r t i c u l a r batch of collagen. practical  for the following reasons:  This was, however, not  experiments could not be c a r r i e d out  to equilibrium because a creep component in the response of the collagen was noticed.  It was, t h e r e f o r e , decided to carry out experiments for at  f i v e half-times  least  [Chapter 5.2], to ensure as complete a measurement of the  v i s c o e l a s t i c component of the response as possible.  However, in order to  do t h i s , i t was necessary to f i r s t ascertain the h a l f - t i m e , and t h i s was only possible a f t e r a number of i d e n t i c a l runs had been performed [due to s c a t t e r , the r e s u l t s of only one run could not be applied to an e n t i r e series]. Because i t was necessary to determine the half-time for each new c o n d i t i o n , a compromise was reached:  at least one of the f i v e  identical  runs at each condition would be done using collagen from a new batch [and  43  hence at a d i f f e r e n t time from the other runs]. Note that runs were not c a r r i e d out for exactly f i v e h a l f - t i m e s , but for at least f i v e h a l f - t i m e s * [this was i n e v i t a b l e , since half-times were calculated only a f t e r a l l runs were complete].  The response curves  were r e l a t i v e l y f l a t in t h i s region [at times greater than f i v e  half-times]  and therefore the half-times were not greatly affected by t h i s .  Results  were adjusted by extrapolation to an ' e q u i l i b r i u m ' 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 g h t l y denser packing was  noted at the bottom of each disc produced.  To investigate the magnitude of  the e f f e c t of t h i s anomaly on the r e s u l t s , 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 i d e n t i c a l conditions with the discs normally o r i e n t e d ] , [Figure 4.1 1 ] .  [but  No excessive scatter  resulted from t h i s , and hence the e f f e c t was neglected. d) The power supply was subject to some i s o l a t e d and r e l a t i v e l y fast changes in voltage.  This was e a s i l y 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 e a s i l y detected. Recall that c a l i b r a t i o n s of the chart recorder were c a r r i e d out both before and a f t e r each weight sequence.  If a voltage f l u c t u a t i o n was detected  during any step of the weight sequence [Table 3.3.3.1], that step example, step 3] was discarded.  [for  Steps prior to the disturbance [steps 1  and 2 in our example] were r e f e r r e d t o the f i r s t c a l i b r a t i o n , and steps a f t e r the disturbance [steps 4, 5 and 6] were refered to the end c a l i b r a t i o n .  * The half-times of most sequence runs at steps 5 and 6 were found to be l a r g e , and since data had not been taken for 5 t^, these runs were, d i s carded. 2  (  In  45 the absence of a disturbance, beginning and end calibrations differed only slightly.  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 i g i t -  izer to a form suitable for computer analysis [Appendix 1].  F i t t i n g the  data to the model was done by computer [Appendix 2 ]. a) Chart recorder readings were converted to hydrations, and H H-H , 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 a  v  Q  f i t t e d via a weighted, linear least-squares method [LSF; UBC-program "LQF"] Weighting of the LSF was held to be necessary because, although H, H  Q  were known quite accurately, the error became p a r t i c u l a r l y s i g n i f i c a n t  and hL at  values of H close to H . o The theory of the weighted l i n e a r LSF requires that points be weighted according to the inverse of the variance of each point et al_. (1969)).  (Carnahan  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 i n t e r p o l a t i o n , 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 „—u~ were truncated to f i v e half-times and, a f t e r compensation for  and In  V o H  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. H.+H a function of H° = — ^ — dPs —  APs  ^  w  e  r  e  prepared  [Figure 5.1.11].  Plots of D(H) The value  as  of  APS  =  H  _  H  was calculated for each weight step from Tables 5.1.2 to  5.1.6. f) The flow c o n d u c t i v i t y , k/n, for each weight step was also c a l c u lated [Appendix 2.4.2]. [Figure  5.1.12].  A plot of k/n as a function of H° was also prepared  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. runs with 40 g weights.  They include a l l runs at 29.5°C and a l l  [The time axis of each graph has been kept to 20  hours, regardless of the length of the run, to f a c i l i t a t e comparisons between 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 t e d in Table 5.1.1. tj  and 5 t  5  was least squares f i t t e d .  in Chapter 5.2].  [Only data between  The reasons for this are explained  It is clear from both the graphs and the errors l i s t e d 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 t . 1  Values of D(H) and k / n were also calculated and plotted as funcH.+H tions of average hydration [H° - - ^ ^ ^ 9 t step [Figures o r  e  a  c  n  w e i  n  5.1.11 and 5.1.12, and Tables 5.1.2 to 5.1.6].  The plots show c l e a r l y 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  12.0  ]6.0  Time (hours) FIGURE 5.1.2  Response of sample tested in sequence 1, 29.5 C, 40°g weight.  20.  \  Time (hours) FIGURE 5.1.3  Response of sample tested in sequence 1, 29.5°C, 50 g weight.  ^  o  o o  I  1  I  1  1  1  1  1  0 +  o  \.  +  +  CD \ ^ CD \ O  re  + + \  +  +  * +  CD zc  0  +  \ . + U  1 33,  +  CD \ . O °CD  ^ "~  sample #7 sample #12  + \ .  o  1  + + + \  .  +  ° . 00 1  _  —  ++ <s  <D?° **\CD  —  0  PO 1  T 0.0  1  1  1  4.0 FIGURE 5.1.4  1 1  1 1  8.0  1 1  I1 12.0  I1  I1  1  I  16.0  Time (hours) Response of sample tested in sequence 1, 29.5°C, 60 g weight.  r 20.0 cn  4.0  8.0  12.0  16.0  Time (hours) FIGURE 5.1.6  Response of sample tested in sequence 1, 35 C, 40°g weight.  20.0 co  o o © sample #8 A sample #9 + sample #10  i  T  -  0.0  1  1 4.0  n  I  i  8.0  i 12.0  i  i  I  16.0  Time (hours) FIGURE 5.1.7  Response of sample tested in sequence 2, 29.5°C, 40 g weight.  ' 20.0  o sample #8 A sample #9 + sample #10 x sample #11  0.0  4.0  1  8 . 00  1  1  ..1122..00  1  16.0  T  Time (hours) 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  12.0  8.0  0.0  •  T  16.0  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 F i t For Hydration-Time Data  Sequence No  Slope hr i  Temp °C  Weight 9  22  30 40 50 60  -  .389 .284 .179 .169  ± ± ± ±  .015 .009 .003 .003  .188 .201 .180 .191  ± ± ± ±  .040 .032 .017 .017  29.5  30 40 50 60  -  .443 .336 .170 .144  ± ± ± ±  .019 .006 .005 .008  .451 .439 .427 .597  ± ± ± ±  .040 .017 .028 .040  35  30 40 50 60  -  .352 .177 .171 .115  ± ± ± ±  .013 .008 .010 .003  .489 .428 .745 .488  ± ± ± ±  .035 .040 .054 .020  29.5  40 60 80  .450 ± .018 .343 ± .014 .135 ± .003  .470 ± .041 .446 ± .038 .070 ± .026  35  40 60 80  ,514 ± .062 .130 ± .010 ,079 ± .003  .772 ± .113 .687 ± .061 .361 ± .027  Intercept  i  1—I  1—i—i  1  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  v  x A  A  YA  V  A  X A X  A  V  x A V  7  X  A  X X X  X  X  A 7  v  • 1  1.5  2  * ' v  1A  '  I  3  4  I  I  I 5  6  I L 8  Average Hydration, H° (g HfO/g collagen) FIGURE 5.1.11  Relationship of D(H) to average hydration, H ° .  10  r10 10 8  |-  T  i—r  x s e q . 1, 22°C A s e q . 1, 29.5°C A s e q . 1, 35°C vseq.  2,  • V A A  29.°C  •  X  & AA  T s e q . 2, 35°C  A A  *  1  A  CO  I 0)  Xy  c  >>  TJ  A  d-  E O  Ji  151-  A  * X  V  A A  X V  AT x  10  V  T V  T  +-> o C o C_)  V  • •  1.5h  10 121  J 1 I I L 1.5 2 3 4 5 6 8 10 Average Hydration, H° Cg H Q/g; collagen) 2  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 No.  V xl0 cm  DW g  2  H  i  50g  40g  30g  3  2  H  o  H  i  H  o  60g  H.  H  H.  1  0  H  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  k/nxlO cmVdyne-s  Run No.  D(H)xl0 cm /s  30  2 3 5  10.19 12.18 10.32  4.78 4.40 4.26  5538 6988 4892  6.19 5.50 6.49  2 3 5  7.435 8.889 7.527  4.23 3.95 3.72  4734 5435 5149  4.82 4.76 4.07  50  2 3 5  4.699 5.618 4.757  3.72 3.50 3.26  5870 6522 7159  2.23 2.29 1.68  60  2 .3 5  4.419 5.283 4.474  3.31 3.14 2.92  7724 8386 9468  1.46 1.55 1.11  40 -  2  8  H° g H20/g collagen  dP  Weight g  11  62  TABLE.5.1.3 Model Parameters For 29.5°C, Sequence 1  No.  DW 9  V xl0 2  cm  30g  3  2  H  i  40g H  H. l  0  H  H.  3.78  3.76  V  0  60g  50g H  .3994  1.958  4.76  4.23  4.16  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  30  40  x  n  50  60^  dP.  3.50 3.13  2.90  2.95  2.72  k/nxlO  Run No.  DllTxlO  6 7 12 14 15  9.771 10.72 8.813 12.90 10.21  4.50 4.35 4.13 3.82 3.93  5538 4811 4381 8153 4734  5.66 6.97 6.05 4.50 6.25  6 7 12 14 15  7.415 8.139 6.688 9.794 7.749  3.97  7724  2.80  3.55 3.45 3.38  7159 7724 6522  2.51 3.34 3.08  6 7 12 14 15  3.739 4.104 3.372 4.938 3.907  3.63  11288  3.02 2.88  6670 7526  6 7 12 14 15  3.181 3.492 2.869 4.202 3.324  3.02 2.84  12761 12761  cm /s 2  8  g H 0/g collagen dH av 2  H  0  6  Weight  H.  1 1  cmVdyne-s  9.05xl0  _1  1.78 1.20 6.56xl0 5.17xl0  _1 _1  * Blanks are l e f t where runs were discarded due to voltage supply fluctuations or other e r r o r s . [Chapter 4.1]  63  TABLE 5.1.4 Model Parameters for 35°C, Sequence 1  iample No.  DW g  V xl0 2  cm  3  2  3 0  R._  9  4 0  H  H•  0  50g  9  H  1  0  H  60g  i  H  H.  0  1  H  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 g  Run No.  D(H)xl0  cm /s 2  8  H° g H 0/g collagen 2  dP  s  dH  k/nxl0"  cmiVdyne-s  ia  20 21 22 24  7.952 7.754 7.555 7.718 8.266  4.87 4.86 5.09 5.01 5.03  4975 4515 5755 4515 5336  5.46 5.85 4.64 5.97 5.42  19 20 21 22 24  4.000 3.900 3.800 3.882 4.158  4.16 4.21  4447 4586  2.72 2.59  4.26 4.26  4811 4134  2.48 3.10  50  19 20 21 22 24  3.865 3.768 3.672 3.751 4.017  3.56 3.69 3.87 3.70 3.44  6988 5870 5241 6522 3579  1.49 1.78 2.01 1.59 2.95  60  19 20 21 22 24  2.593 2.528 2.464 2.517 2.695  3.20 3.31  8894 8894  7.28xl0  7.27X10"  3.27  8894  7.17X10"  30  40  -1  1  1  64  TABLE .5.1.5 Model Parameters For 29.5°C, Sequence 2  40g  60g  DU  V xl0  9  cm  8  .4061  2.024  4.49  3.34  9  .3847  1.817  5.12  10  .4325  2.296  11  .3832-  1.802  Sampl e No.  2  3  z  80g H  o  0  i  3.13  2.71  2.69  2.39  4.04  3.78  3.42  3.27  2.97  4.55  3.33  3.04  2.59  2.06  1.89  4.48  3.41  3.21  2.87  2.78  2.37  H  o  H° g H 0/g collagen  H  dP^  H  k/nxlO"  Weight g  Run No.  DlrTTxlO cm /s  40  8 9 10 11  10.25 9.202 11.63 9.126  3.92 4.58 3.94 3.95  5104 5435 4811 5486  60  8 9 10 11  7.811 7.012 8.860 6.954  2.92 3.60 2.82 3.04  13976 16306 13044 17265  1.31 1.17 1.55 9.70X10"  8 9 10 11  3.065 2.751 3.477 2.729  2.54 3.12 1.98 2.58  19567 19567 34529 14317  3.34X10"  80  2  8  2  dH  cmVdyne-s 5.81 5.51 7.02 4.84  1  1  3.45X10" 1.84x10"! 4.11x10"!  1  65  TABLE .5.1.6 Model Parameters For 35°C, Sequence 2  Sam pi e No.  DW g  V xl0 cm 2  40g  3  2  H  i  5.37  rt  3.91  .4262  2.230  18  .4054  2.017  25  .4126  2.090  5.53  4.45  26  .4020  1.984  4.87  3.57  40  60  80  Run No. 16 18 •25 26  D(.H)xlO cm /s 2  3.264 2.953 3.059 2.904  16 18 25 26  1.972 1.784 1.849 1.755  H o  3.61  2.75  3.86  3.14  3.13  2.59  4.17  3.48  3.38  2.84  H° g H 0/g collagen 2  12.91 11.68 12.10 11.49  16 18 25 26  H.  1  0  16  Weight g  80g  60g H  H  i  H  o  k/nxlO cm^/dyne-s 11  dH  4.64  4021  10.6  4.99 4.22  5435 4515  7.74 7.78  3.18 3.50 3.83  6826 8153 8507  1.19 0.964 1.02  2.86 3.11  10870 10870  0.379 0.416  •5-' .  66 5.2  Discussion  5.2.1  Se-YiAsOLLvAAy ofi the. ModeZ to H^: The model is moderately s e n s i t i v e to the value of H .  Although  Q  i t was not possible - due to time constraints  - to carry out runs to  e q u i l i b r i u m , i t was f e l t that consistency in a p p l i c a t i o n of the model would still  allow useful conclusions to be drawn from the data.  This was accomp-  l i s h e d as described in sections 5.2.2 to 5.2.4.  5.2.2  Slgyvi^Xjcanaz Ojj the. hoJL^-tme.'. .  H-H  By d e f i n i t i o n the h a l f - t i m e , t, , occurs at the point where  *  0.50.  Because the runs were not c a r r i e d out to e q u i l i b r i u m , H  determined exactly. all  TJ—n—  =  V o could not be H  Q  This did not greatly a f f e c t the value of t  }  because in  cases tj occurred during the steep portion of the response curve. The half-time is d i r e c t l y related to the time constant, x , of the  model.  Recall  H  H  that  8  - W t / 4 f  2  1 0  Bearing in mind the d e f i n i t i o n of t^, manipulation of equation 2.2-7  results  in  4V  K  2  TT^DTHJ  ln(\)  K  -h = 1_ - In 0.5 0.4831  TT  Insertion of equation 5.2.2-1 into 2.2-7 gives  5.2.2-1  67  H-H  -0.4831t/V  0  £- = — r e H.-H i o  5.2.2-2  The time constant, T , is defined by  H-H  8  •t/x  and, t h e r e f o r e , 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 r a p i d l y  approaches i t s f i n a l value, H .  This is shown below:  H-H time  H  0  r o H  !  H  H  " 0 H  i" o H  0.500  0.500  K  0.308  0.692  3 t.  0.190  0.810  V  0.117  0.883  0.072  0.928  0.045  0.955  K  'a  2  4  "2. 6 t.  h  etc.  In other words, by the time f i v e half-times have elapsed, the response should be 92.8% complete. reasons noted below:  In f a c t , only data upto 5 tj was considered, for p r a c t i c a l  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 i t was not possible to carry out tests to equilibrium.  runs,  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 i r r e g u l a r i t i e s in the voltage supply [Chapter 4.1]. The  true value of H was calculated from that measured at the end o of f i v e half-times as follows:  (H)  = H. true  H. - (H ) 1  (  0  ° g 9 2  e a S U r e d  )  , 5.2.3-1  This was possible due to the l i n e a r relationship between In ( The  H-H _^ ) and time. i o u  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. part vindicated by the r e s u l t s :  The modification is in  the plots show progressive l i n e a r i z a t i o n  when carried on for longer times, as the model would predict. the  In some of  few runs carried out to beyond 7 tj , hydration continues to decrease  with time beyond the predicted value, and this indicates that creep becomes s i g n i f i c a n t 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. lie  The curves for 40, 60 and 80 g weights  close together, and this is not surprising - time scaling cuts o f f the  creep component before i t becomes s i g n i f i c a n t and causes separation of the curves.  That creep should occur is also to be expected, since soft tissues  are known to be non-linear, v i s c o e l a s t i c materials.  [However, few i n v e s t i -  0 0  4.0  8.0  12.0  16.0  20.0  Time (hours) FIGURE 5.2.3.1  Relationship of dimensionless hydration and time (cut o f f 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 o f f at 6 t  1  ) for sample #10.  0.0  4.0  8.0  12.0  16.0  20.0  Time (hours) FIGURE 5.2.3.3  Relationship of dimensionless hydration and time (cut o f f at 7" tj,) for sample #10.  i 0.0  4.0  1  8.0  1 12.0  r 16.0  20.0  ; Time (hours) FIGURE 5.2.3.4 Relationship of dimensionless hydration and time (cut o f f at 7 tj_) for sample #10, and compensated for H . 2  Q  T  0.0  4.0  B.O  12.0  16.0  20.0  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 t h e i r behaviour].  The creep e f f e c t would be masked at shorter times by the  r e l a t i v e l y steep nature of the hydration curve in that region.  No attempt  is made in t h i s 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 r e c a l c u l a t i o n of t,  by means of equation 5.2.2-1, which is  rewritten as  (0.4831)(V*)  •  The values of ^  S  m  2  M  TT • D W  H  2  and DCH) are known for each sample [Tables 5.1.2 to 5.1.6]  2  and were calculated by curve f i t t i n g the hydration-versus-time graphs. Results of t h i s r e c a l c u l a t i o n are presented in Table 5.2.3.1. case the recalculated t,  is higher than the o r i g i n a l  In nearly every  value by 8 to 32%.  This is to be expected in the case of creep because the modified H higher than the H  produced at the "end" of creep, and therefore t  :  Q  is  still  will  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 j u s t i f i e d for time greater than t  1  .  The solution to the boundary value problem [Chapter 2] as given by Crank (1975)  H-H.  is:  1  TT  2n+l n=0  e  c  o  s  2*'  2  ' " 2  3  TABLE 5.2.3.1 Comparison Between Original and Recalculated Values  Sequence No.  oft,  4g  Temp °C  Weight g  t  hr  hr  22  30 40 50 60  .1.14 1.56 2.46 2.61  1.24 1.70 2.69 2.86  29.5  30 40 50 60  0.95 1.22 2.15 2.97  1.09 1.44 2.85 3.35  35  30 40 50 60  1.20 2.30 2.40 3.20  1.37 2.72 2.82 4.20  29.5  40 60 80  0.99 1.29 3.79  1.07 1.41 3.59  35  40 60 80  0.75 2.58 4.49  0.94 3.72 6.15  t  "2  t , Recalculated t  '2  76  LetMLli^k. 4V  Then  2  H-H.  4  n - = 1  H^HT "  1  -kt  TTIJ)  - - Ccos^-r e  " TT ^ 2 * '  ^ -  c  3THJJ  -9kt  cos^-r e  3 " °2^' u  5mjj  -25kt  + -F COS-OTT e ' 5 2,|,  c  -  vua  ...)  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" The approximation made [Chapter 2] was 1  H-H.  1_ _ i  -kt  1  H-H.  ,  ._TjjL_  rr  TT  C 0 S  2^'  .  Both 2.2-3 and 2.2-4 were integrated over $ from 0 to V » are presented below [note  J*cosax.dx „  H  av  =  H  o  +  ( H  i" o H  )  e  +  c  -  c  *  d the r e s u l t s  = j sinax] :  -kt (  a n  2 2-4  , i  e  -9kt +  . k  e  -25kt +  S- - " 2  4  1  for the rigorous case, and  ft  H = H + (H.-H ) \ av o i o TT  for the approximation. [Table 5.2.4.1].  e  -kt  5.2.4-2  The approximation is acceptably accurate f o r t  >  \  77 TABLE 5,2,4.1 Errors Due to Approximation to the Model (H-H )/(Hi -Ho). Approximation Rigorous  Time  0  K  Deviation %  .5000  .5012  0.23  .6366  .6469  1.62  1/2  t  1/4  t  .7183  .7503  4.45  1/8  t  .7631  .8234  7.91  .7685  .8741  11.14  p  1/16 t.  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 c o e f f i c i e n t , D(.H), was defined by Bert as  = 4~ S (H) n  3t  3ijj I  •  2.1-13  • 3^ '  v  An average diffusion c o e f f i c i e n t , D(H), was then defined by assuming  D(H)  to be a weak function of hydration over the hydration range in question:  ft  = TJITO  •'  f  2.1-14  This assumption is j u s t i f i e d 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 H] Q  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 s t e p s ] . 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 i o n 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 f o r 35°C tends to give lower values of D(H) and k/n for any given hydration.  This e f f e c t is more pronounced at low hydrations.  The dependency of DCH) and k/n on hydration is to be expected because as the hydration decreases the area a v a i l a b l e for f l u i d transport reduced due to compaction of the collagen f i b r e s .  is  This w i l l cause a de-  crease in flow c o n d u c t i v i t y .  ; .•'  ,'  The s h i f t due to high temperature is more d i f f i c u l t to e x p l a i n . Two possible explanations for t h i s 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 k e l y that the bulk of f l u i d transport occurs quite quickly [ i . e .  while the value of D(H)  is s t i l l  relatively.high].  Any averaging  process  based on i n i t i a l and f i n a l values of D(H) is therefore l i k e l y to underestimate D(H) or k/nb) 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-  t i o n 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 w i l l not chemically degenerate.  The physical un-  r a v e l l i n g of collagen molecules w i l l cause a decrease in the area a v a i l able for f l u i d transport, and thus lower D(.H) and k/n.  This e f f e c t w i l l be  independent of hydration. The second of the two explanations i s , in f a c t , the more l i k e l y . If the f i r s t e f f e c t predominated, one would expect the s h i f t to be most pronounced for step 1 than for subsequent steps during the i n i t i a l weight steps].  [hydration changes most  This i s not the case.  If,  however,  collagen was indeed degenerating at 35 C, one would expect the e f f e c t 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 t h i s is indeed the case. Values of k/n obtained in t h i s study range from 3.6x10"  12  to 2 x 1 0 "  1 1  cmVdyne-s at H°=3.0. These figures may be compared with values, obtained by B e r t , of 0 . 9 x l 0 ~ , 3 x l 0 " 12  1 3  and 5 x l 0 "  1 3  cmVdyne-s for human s k i n , steer  corneal stroma and rabbit corneal stroma, r e s p e c t i v e l y . Bert also found k/n for human spinal discs to be ^ 8 x l 0 ~  12  cmVdyne-s, for a subject of age 50  years at death. Note that the samples tested by Bert were a l l natural  tissues,  and hence structured and constituted d i f f e r e n t l y from the collagen samples tested in t h i s  study.  80  CONCLUSIONS 1) The f l u i d transport-based model considered in this  study,  describes collagen behaviour adequately for small changes in hydration, and within certain l i m i t s  [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 e s s e n t i a l l y the same.  Some breakdown of collagen is the l i k e l y cause of  changes in collagen behaviour at 35°C. 4) A creep component in the response of collagen was noticed.  This  l i m i t s a p p l i c a b i l i t y of the model to conditions under which the hydration changes r e l a t i v e l y rapidly - that i s , at times less than 5 ^ .  81  RECOMMENDATIONS FOR FURTHER WORK The model is promising, and further investigation of the behaviour of collagen in i s o l a t i o n and in combination with proteoglycans and e l a s t i n is c a l l e d f o r .  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 c a l l for a reduction in the  range of hydration studied [increasing chart recorder s e n s i t i v i t y would necessarily decrease the range] but w i l l 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 f a c t , 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 (cm )  dm  differential mass of dry membrane (g)  dmw  differential mass of water in dm (g) ^'  D(H)  diffusion coefficient (cm /s)  D(H)  average diffusion coefficient (cm /s)  DW  dry weight of membrane (g)  f  convective flux (g/cm -s)  fj  diffusive flux (g/cm -s)  f  flux in the x-direction (g/cm -s)  2  2  2  2  2  2  X  H  hydration at a point (g H 0/g collagen)  H°  average hydration,  H  dimensionless hydration, T T — r r -  H av  average hydration [integrated] (g H 0/g collagen)  H.j  i n i t i a l hydration (g H 0/g collagen)  H  final hydration (g H 0/g collagen)  H +H.  °  1 ?  2  (g H 0/g collagen) H-H.  2  V i H  Q  2  2  2  k/n  flow conductivity (cmVdyne-s)  P  swelling pressure (dynes/cm ) 2  s  t,  half-time (hours, seconds)  T  sample thickness (cm)  x  space variable  NOMENCLATURE (CONTINUED)  density of collagen (g/cm ) 3  ratio of water to collagen densities, y/6 C(e  -e  H  H  )/(H.-H ))xlOO* o  error associated with measured hydration Cg H 0/g collagen) 2  error associated with i n i t i a l hydration (g H 0/g collagen) 2  error associated with final hydration (g H 0/g collagen) 2  CCe +e H  £  T  +  H  e  )/(H-H ))xl00% o  B  density of water (g/cm ) 3  thickness of dry material from 0 to x, 7 7 (cm) oM  value of i|> at surface of sample (cm) density of water (g/cm ) 3  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., P h y s i o l . Chem. and Phys. II (1979).  3.  Bert, J . , Ph.D. D i s s e r t a t i o n , UCLA, Berkeley (1970).  4.  Carnahan, B., Luther, H.A. and Wilkes, J . O . , John Wiley and Sons, New York (.1969).  5.  Chapman, J . A . , quoted by Fietzek, P.P. and Kiihn, K.,  Applied Numerical Methods, in H a 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 H a l l , D.A. (ed.), The Methodology of Connective Tissue Research, Academic Press, New York (1976).  7.  Crank, J . ,  8.  Danielson, D.A.,  9.  Diamant, J . , K e l l e r , A., Baer, E., L i t t , M. and A r r i d g e , R.G.C., Proc. R. Soc. Lond. B., 180, 293 (1972).  The Mathematics of Diffusion,  Clarendon Press, London (1975),  J . Biomechanics, 6_, 539 (1973).  10.  Dick, J . C . , J . P h y s i o l . , U 2 , 102 (1951).  11.  Dulbecco, R. and Vogt, M., J . Exper. Med., 99, 167 (1954).  12.  Einbinder, J . and Schubert, M., J . B i o l . Chem., 188, 335 (1951).  13.  Elden, H.R.,  14.  Fessler, J . H . , Biochem. J . , 76, 452 (1960).  15.  Fietzek, P.P., and Kuhn, K., in H a l l , D.A. (ed.) The Methodology of Connective Tissue Research, Academic Press, New York, (1976).  16.  Flory, P.J. and Weaver, E.S.,  17.  Fung, Y.C.B., Amer. J . of P h y s i o l . , 213, 1532 (1967).  18.  Gallop, P.M., Blumenfeld, 0. and S e l f t e r S., Ann. Rev. Biochem., 41, 617 (1973). ~~  Biochem. Biophys. Acta, 79, 592 (1964).  J . Exper. Med., 82, 4518 (1959).  85 19.  Gon, P.F., J . Biomech., 3, 547 (1970).  20.  Grahame, R., Ann. Phys. Med., 10, 130 (1969).  21.  Grant, M.E. and Prockop, D.J., N. Engl., J . Med., 286, 194 (1972).  22.  Gross, J . , J . Exp. Med., 107, 265 (1958).  23.  Gross, J . and Kirk, D., J . B i o l . Chem., 233, 355 (1958).  24.  Gustavson, K.H., The Chemistry and Reactivity  Press, New York, (.1956).  of Collagen,  Academic  25.  Hampel, C A . and Hawley, G.G., The Encyclopaedia of Chemistry, Nostrand Reinhold Co., New York (1973).  26.  Harkness, R.D., Marko, A.M. Muir, H.M. and Neuberger, A., Biochem. 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. S c i . , 3_5, 1011 (1972).  29.  Jackson, D.S.,  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 i o l . , 20, 699 (1975).  32.  Lowther, D.A., in H a l l , D.A. and Jackson, D.S. (eds.), International Review of Connective Tissue Research , Volume 1, Academic Press, New  Van  Biochem. J . , 65, 277 (1957).  York, Volume 1, Academic Press, New York, (1963).  33.  Mooney, M., J . Appl. Phys., 11, 583 (1940).  34.  Nomura, S., H i l t n e r , 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., K i v i r i k k o , K.I., 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., B r i t . J . Derm., 77, 639 (1965).  40.  Robins, S.P., (1973).  Tuderman, L., and Guzman, N.A., N.  Shimokomaki, M. and Bailey, A . J . , Biochem. J . , 131, 771  86 41.  Sakata, K., M.A.Sc. Thesis, .The University of B r i t i s h Columbia, (1969).  42.  Schubert, M. and Hamerman, D., A Primer Lea and Felsiger, New York (1968).  43.  Schwartz, N.J., Mackay, R.S. 28, 585 (1966).  44.  Scott, J . E . , Chem. in Gr. B r i t a i n , 15_, 13 (.1979).  45.  Van Duzee, B., J . Invest. Derm., 7l_» 140 (1978).  46.  Veis, A., The York (1964).  47.  Veronda, D.R. and Westmann, R.A., J . Biomech., _3, 111 (1970).  48.  V i i d i k , A., in H a l 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).  on Connective Tissue Biochemistry,  and Sackman, J . L . , B u l l . Math. Biophys.,  Macromolecular Chemistry of Gelatin, Academic Press, New  87  APPENDIX 1 EQUIPMENT  1.1  Linear Displacement Transducer The l i n e a r displacement transducer used [Crescent Technology  Corporation, Model ZD25] was a v a r i a b l e permeance transducer which produced an a.c. current proportional to the probe displacement from the null position.  1.2  C a r r i e r Amplifier The a m p l i f i e r used [Crescent Technology Corporation, Model 85-N-4]  was a t r a n s i s t o r i z e d c a r r i e r a m p l i f i e r , with a maximum output of 10V d.c. A maximum gain [setting 100] was used throughout the experiments.  1.3  S t r i p Chart Recorder The s t r i p chart recorder used [Watanabe Servocorder, Model SR652]  was operated with an input s e n s i t i v i t y of 5 v o l t s / c h a r t width and a chart speed of 30 mm/min.  1.4  Recirculating Constant Temperature Bath The constant temperature bath [Colora, Model K] had an e f f e c t i v e  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 o u t f i t t e d 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 j a r s .  1.7  Digitizer Numerical data was obtained from the skip charts by means of a  digitizer  [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 i n e a r i n t e r -  polation between the c a l i b r a t i o n : points immediately above and below the data point in question [ F i g . 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 av  where  Ap T 1 w DW " 6  2.2-8  A is the x-sectional area of the sample, cm  2  DW* is the dry weight of the sample T is the thickness of the sample, cm  *  Dry weight was determined by drying at 40 C for 36 hours. P  91  2.1.3  Elastic  Rz£>povu>2. jon. Sequence. 2 CUAVQA  An " e l a s t i c " component become s i g n i f i c a n t curves.  in sequence 2 response  This may have represented a real e l a s t i c 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 t h i s component showed no consistent pattern, and was always r e l a t i v e l y small, i t was simply ignored.  That i s , the i n i t i a l hydration point, H , was Q  considered to occur at the end of the e l a s t i c response. was not noticeable for sequence  2.2  The e l a s t i c  response  1 runs.  Calculation of the Half-Time  H-H The h a l f - t i m e , by d e f i n i t i o n , occurs at ln(,„ ) [Chapter i~ o  Once thickness and hydration c a l c u l a t i o n s were completed, t weight step could be c a l c u l a t e d .  5.2.1].  for each  t  Half-times calculated for individual  steps were averaged for each step in each set of indentical runs  [Table  A2.2.1], and t h i s figure was used in further c a l c u l a t i o n s . A t y p i c a l plot H-H of l n - f n — n — ) for a sample, before scaling to 5 t , is presented in Figure V o * 5.2.3.5. 5  2.3  The Least Squares Fit The computerized least squares f i t package, LQF, a v a i l a b l e at the  U n i v e r s i t y ' s computer centre, was used for f i t t i n g data. weights was done as i)  Calculation of  follows:  The chart reading and i t s associated error (±0.1%) were con-  verted into a hydration and error according to equation 2.2-8. H-H i i ) Error terms were combined to give the error in r j — r r as i" o shown below. Q  H  H  92  TABLE A2.2.1 Average Half-Times (error figures are root mean square errors).  Sequence No.  1  Temp. °C  22  30  35  2  30  35  Weight g  Average Half-Time hr.  30  1.14 ± .30  40  1.56:+ .26  50  2.46 ± .25  60  2.61 ± .09  30  0.95 ± .36  40  1.22 ± .22  50  2.15 ± .37  60  2.97 ± .50  30  1.20 ± .38  40  2.30 ± .39  50  2.40 ± .97  60  3.20 ± .09  40  0.99 ± .22  60  1.29 ± .47  80  3.79 ± 2.16  40  0.75 ± .29  60  2.58 ± 2.42  80  4.49 ± 1.68  93  The percentage errors  e  e  T  H  +  e  R  H  H-H  °- x 100%  =  +  A2.4-2  o  H. H ^ - H ° i " o  £  and  £  e  x 1  0  0  A2.4-3  %  were then added to give  Hence, we have  H ± e  H  H  i  ±  £  - H  o  H . - H l  ±  O  H - H  ±  — e  0  =17—u ± e„ Cu _ u ) i - o " i - o H  H  H - H  Q  u  H  t  %  V  H  A2.4-5  H  Q  Or, substituting f i c t i t i o u s numbers H = 4.5, H  Q  = 4.0, H.. = 5.0 and e  M  ± 0.005,  4.5 ± .005 - 4.0 ± .005 _ 0.5 ± 0 . 0 1 _ r . 5.0 ± .005 - 4.0 ± .005 " 1.0 ± 0.01 " ' ° " n  n  u  U  n q  "  U  R 1  3  When logs are taken, i t is somewhat more d i f f i c u l t to c a l c u l a t e the absolute error.  The method used was to c a l c u l a t e ln(0.5 + 0.015) and ln(0.5 - 0.015),  94  and c a l c u l a t e the larger deviation from l n t 0 . 5 ) .  The inverse square of t h i s  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)  weight =  = -  .724  L-fifiY = 1040  2.4  Calculation of Model  Parameters  2.4.1  The.  Vllluu-lon  The  d i f f u s i o n c o e f f i c i e n t , D(H),  Coz^XjcLzYit for each weight step, was calculated  from lumped data for i d e n t i c a l runs, by using the r e l a t i o n s h i p expressed in equation 2.2-7.  This can be rewritten as:  H-H  dOnyr^-) 1  dt  °  DIHJTT  2  "  In^-^rr^ 4<j,'  IT  A2.4.1-1  :  H-H  DUiT = ^ ( l n §  dCln^J-) -IT -* 2  7  H-H  A2.4.1-1  H-H  where d(ln,, _° ) is simply the slope of the graph of 1n( _ ) plotted as a i~ o i o dt H  function of time.  2.4.2  \  .. Values of D(H) are shown in tables 5,1.2 to 5.1.6.  T h z Flow The  The values of D(H) calculated here considered to apply _  H.+H  at H° =  H  Conductivity  flow conductivity at each value of H° was calculated by means  95  of equation 2.1-12, rewritten below:  D(H)^ n  A2.4.2-1  dP /dH s  dP Values of -rrr- were approximated by segmented slopes dn  dP AP ' _ _ i «b dH H -H.  A2.4.2-1  s  o  where A P = 2935 dynes/cm  2  f o r sequence 1  = 5870 dynes/cm  2  f o r sequence 2  s  Calculated values of - are presented in tables 5.1.2 to 5.1.6, n  APPENDIX 3 COMPUTER PROGRAMS  APPENDIX  1 36 2 C C C C C C  403  6  10 20 11 101  21  77 76  3.1:  P r o g r a m f o r c a l c u l a t i o n a n d p l o t t i n g o f d1 mens 1 on 1 e s s h y d r a t i o n curves f o r Individual samples.  REAL T H ( 1 5 0 ) , P C I ( 1 5 0 ) , P C E ( 1 5 0 ) . D T I ( 1 5 0 ) , D P C ( 1 5 0 ) . 1DTHI(150),DTHE(150),PP(2)/0.0,0.0/,PXX(150),PYY(150) 1,TTH(150),H(150),LHAVE(150),TIME(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 F0RMAT(3I5) READ(5,36) (OTH(I),I=1,6) F0RMAT(6F4.2) READ(5,2)EPS F0RMAT(E8.4)  THE FOLLOWING COMMANDS D R E A D IN THE T I T L E OF THE GRAPH OF TO BE P L O T T E D , AND 2 ) P L 0 T THE AXES, AXIS LABELS,AND T I T L E .  READ(5,403)BCD WRITE(8,403)BCD FORMAT(20A4) C A L L PLTAX C A L L OUTLAB READ(5,6)N,TMAX,A,DW FORMAT(12,2X,F5.1,2X,F6.4,2X,F6.4) D020 1=1,N READ(5,10) T H ( I ) , P C I ( I ) . P C E ( I ) F0RMAT(F4.3,2X,F4.1,2X,F4.1) CONTINUE R E A D ( 5 , 1 1)DOT FORMAT(F4. 1 ) L=0 D030 K = 1 , 1 5 0 READ(5,21) DTI(K),DPC(K),DY(K) F0RMAT(G9.3,G9.3,2X,F4.2) IF((DTI(K)-DTI(1)).LT.(5*0TH(0)))GOTO I F ( L . G T . O ) G 0 T 0 77 L=K-1 IF(DTI(K)-900.)30,76,76 I F ( L . G T . O ) G 0 T 0 52 L = K-1 GOTO 52  77  LHAVE/TIME  APPENDIX  30 52 23  34 50 31 32 33  24 25  51  95 91 96  94 93 97  3.1:  (Continued)  CONTINUE READ(5,23)DRIFT FORMAT(11) DOT=DTI( 1 ) d=0 DO 34 KK= 1 ,L I F ( D P C ( K K ) . G T . D P C ( L ) ) G O T O 34 DPC(L)=DPC(KK)-0.01 CONTINUE 1= 1 d = d+1 IF(DRIFT.GT.O)PCI(I)=PCE(I) IF(DPC(J ) -PCI(I))33,33.32 1=1+1 GOTO 31 DTHI(d)=TH(I-1) + ((DPC(J)-PC I(I- 1 ) ) / ( P C I ( I ) - P C I ( I - 1)))*.025 D T H E ( J ) = T H ( I - 1) + ( ( D P C ( J ) - P C E ( I - 1 ) ) / ( P C E ( I ) - P C E ( I - 1 ) ) ) * . 0 2 5 I F ( D R I F T . G T . O ) G O T O 24 TTH(d)=DTHI(d) GOTO 25 TTH( J ) =DTHE (d) H(d)=(A*2.54*TTH(d)/DW)-.7409 DELH(d)=(DY(d)/DPC(d))*H(J) IF(J-L)50.51,51 M=L-1 HX=H(1)-(H(1)-H(L))/.928 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) IF(A2-DELH(d))91,91,96 DELH(d)=A2-.001 ETOP(d)=DELH(d)+DELH(L) EPCT(J)=((ET0P(d)/A2)+(EB0T/A1))*(A2/A1) HPLUAV(d)=AL0G((A2/A1)+EPCT(d)) IF(((A2/A1 )-EPCT(d))-0. )93,93,94 HMINAV( J)=ALOG( (A2/A1 )-EPCT(<J) ) GOTO 97 HMINAV(«J) = -100. PYY(d)=2*LHAVE(J)+6.0 I F ( LHAVE ( d ) '. LT . R )RX ( d ) = 1 I F ( R X ( d ) . G T . 0 ) G 0 T 0 98 PY(Z)=PYY(d)  ^ 00  APPENDIX  98 55  99 350 351 352  35 889 888 401  4  5  7 8  22  3.1:  (Continued)  Z = Z+1 W1=Z TIME(d)=DTI(d)-DOT WRITE(7,55)TIME(d),TTH(d),H(d).LHAVE(J) FORMAT(4X.F4. 1 , 8 X , F 5 . 3 , 9 X , F 4 . 2 , 8 X , F 6 . 3 ) PXX(d)=((TIME(J)-0.0)/2.0) I F ( T I M E ( d ) . G T . 2 0 . 0 ) G 0 T 0 99 I F ( R X ( J ) . G T . O ) G O T O 99 PX(Z-1)=PXX(d) W2=Z-1 CONTINUE IF(W1-W2)350,350,351 W3=W1 GOTO 352 W3 = W2 CALL P L O T ( P X ( 1 ) , P Y ( 1 ) , 3 ) C A L L S Y M B 0 L ( P X ( 1 ) , P Y ( 1 ) , 0 . 1 0 , S Y M ( O ) , 0 . , - 1) DO 888 W=1,W3 I F ( W . G T . 1 ) G O T O 35 WW= 1 IF(PX(W)-PX(WW)-0.25)888,889,889 CALL SYMB0L(PX(W),PY(W),.10,SYM(O),0..-1) WW = W CONTINUE NN = W3 DO 4 11=1,M X(11)=TIME(II) Y(11)=LHAVE(II) CALL WEIGHT(Y,HPLUAV,HMINAV,M,WT) EXTERNAL AUX CALL LOF(X , Y , Y F , W T , E 1 , E 2 , P P , 1.0,M.MM,NI,ND,EPS,AUX) I F ( N D . N E . 1 ) G 0 TO 103 WRITE(6,5) F O R M A T ( ' ESTIMATES OF ROOT MEAN SQUARE TOTAL ERROR ' , 1 ' I N THE PARAMETERS') WRITE(6,7) (E2(II),11=1.MM) F0RMAT(8G15.3) WRITE(6,8) 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) F0RMAT(6X,F5.2,9X,F5.2,10X,F6.2.9X,F7.2) P X ( I )=PX(I ) * 2 . PY(I ) = P Y ( I ) * 0 . 8 - 5 . <£>  APPENDIX  58 56 113 102 103  THE FOLLOWING IS AN AUXILIARY SQUARES F I T PACKAGE, L Q F .  10  C C C C  15  11 12 13 10  (Continued)  WRITE(8,353)PX(I).PY(I),WT(I) F0RMAT(3F8.3) CONTINUE TIME(L)=DTI(L)-DOT WRITE(7,58)TIME(L),TTH(L).HX FORMAT(4X,F4.1,8X,F5.3,9X,F4.2) READ(5,5G)0 FORMAT(12) IF(0-10)101,102.102 C A L L PLOTND STOP END  353 9  C C C C  3.1:  FUNCTION CALLED UPON BY THE LEAST  FUNCTION A U X ( P P . D , X , L ) DIMENSION P P ( 1 ) , D ( 1 ) COMMON MM D( 1 ) = 1 .0 AUX=PP( 1 ) DO 10 d=2,MM D(d)=D(d-1)*X AUX=AUX+PP(d)*D(d) RETURN END  SUBROUTINE WEIGHT THE LEAST SQUARES  CALCULATES THE R E L A T I V E WEIGHTS F I T PROGRAM, L Q F .  OF THE POINTS FOR  SUBROUTINE WEIGHT(Y,YPLUS,YMINUS , NN , WT) DIMENSION Y ( 1 0 0 ) . Y P L U S ( 1 0 0 ) , Y M I N U S ( 1 0 0 ) , E R R P L U ( 1 0 0 ) , 1ERRMIN(100),WT(100),ERROR(100) DO 10 1=1,NN ERRPLU(I)=ABS(YPLUS(I)-Y(I)) ERRMIN(I)=ABS(YMINUS(I)-Y(I)) IF(ERRPLU(I)-ERRMIN(I))11.11,12 ERROR(I )=ERRMIN(I) GOTO 13 ERROR(I)=ERRPLU(I) WT(I ) = 1 . / ( E R R O R ( I ) * E R R O R ( I ) ) CONTINUE RETURN END  5 o  APPENDIX  C C C  3.1:  (Continued)  SUBROUTINE PLTAX PLOTS THE AXES FOR THE GRAPHS OF LOG DIMENSIONLESS HYDRATION VS. TIME, WITH AXIS LABELS AND T I T L E . 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 A X C T R L ( ' X O R I G I N ' , 0 . 0 0 ) CALL A X C T R L ( ' S Y M S I Z E ' , 0 . 1 5 ) CALL A X P L O T ( 9 0 . 0 , 6 . 0 , - 3 . 0 , 0 . 5 ) CALL S Y M B O L ( 1 . 0 , 9 . 5 , 0 . 2 0 , B C D , 0 . 0 , 8 0 ) CALL A X C T R L ( ' S I D E ' , - 1) CALL A X C T R L ( ' Y O R I G I N ' , 0 . 0 0 ) CALL A X P L 0 T ( 0 . 0 , 1 0 . 0 , 0 . 0 , 2 . 0 ) RETURN END  C C C  200 201 202  SUBROUTINE  OUTLAB PRINTS THE COLUMN HEADINGS FOR F I L E  SUBROUTINE OUTLAB WRITE(7,200) WRITE(7,201) WRITE(7,202) FORMAT( ' TIME FORMAT( ' FORMAT( ' (HOURS) RETURN END  SAMPLE THICKNESS (INCHES)  HYDRATION (G COLLAGEN/ G WATER) ' )  0UTPUT2.  LN(H)') (AVERAGE)')  APPENDIX  53  1 14  51  10 11  21  19 15  4  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 h y d r a t i o n c u r v e s f o r lumped d a t a .  dimensionless  DIMENSION P X ( 2 5 0 ) , P Y ( 2 5 0 ) . B C D ( 2 0 ) , W T ( 2 5 0 ) , P P X ( 2 5 0 ) , 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 SYM(G)/1,2,3,4,5,6/.W,RX(250)/250*0/,0/1/.NI/1/ 1.RR.KK/2/ EXTERNAL AUX MM = 2 L=0 RR = 0 READ(8,53)BCD FORMAT(20A4) C A L L PLTAX READ(8,1)THALF . F0RMAT(F4.2) HALF = T H A L F / 2 . LL=L+1 DO 10 d = L L , 2 5 0 R E A D ( 8 . 51 ) P X ( d ) . P Y ( d ) , W W T ( d ) F0RMAT(3F8.3) I F ( P X ( d ) . G T . 9 0 0 ) G O T O 11 X(d)=PX(d)/2. Y(d)=2*PY(d)+6. CONTINUE L=d-1 d=LL-RR DO 19 I = L L , L I F ( X ( I ) . G T . H A L F ) G O T O 21 RR = RR+ 1 GOTO 19 CALL SYMB0L(X(I),Y(I).O.10.SYM(0).0..-1) PPX(d)=PX(I) PPY(d)=PY(I) WT(d ) =WWT(I) d = d+ 1 CONTINUE I F ( 0 . L T . 5 0 ) G O T O 12 CONTINUE dd=d-1 CALL L Q F ( P P X , P P Y , Y F . W T , E 1 , E 2 , P P . 1 . 0 , d d , M M , N I . N D , E P S , A U X ) IF(ND.NE.1)STOP WRITE(6,4) F O R M A T C ESTIMATES OF THE ROOT MEAN SQUARE TOTAL ERROR ' , 1'IN THE PARAMETERS') WRITE(6,62)(E2(I),1=1.MM)  O  ro  APPENDIX  62 60  61 17  12 52  13  18  3.2:  (Continued)  F0RMAT(F6.3,4X,F6.3) WRITE(6,60) F O R M A T ( ' V A L U E S OF X VALUES OF Y FITTED 1' WEIGHTS') DO 17 I = 1 , d d WRITE(6,61 ) P P X ( I ) , P P Y ( I ) , Y F ( I ) , W T ( I ) F0RMAT(3X,F5.2,9X,F5.2,10X,F6.2,10X,F7.1) CONTINUE PX(1)=0. PY( 1 )=2*PP( 1 )+6. PX(2) = ((3 ,+PP(1))/ABS(PP(2)))/2. PY(2)=0. CALL LINE(PX,PY,KK,1) GOTO 13 READ(8,52)0 FORMAT(12) I F ( 0 . G T . 5 O ) G 0 T 0 15 GOTO 14 C A L L PLOTND STOP END SUBROUTINE PLTAX DIMENSION B C D ( 2 0 ) COMMON BCD CALL P L C T R L ( ' S C A L ' , 0 . 8 ) C A L L PLOT( 1 . 0 , 1 . 0 , 3 ) CALL AXCTRL('SIDE',1) CALL A X C T R L ( ' X O R I G I N ' , 0 . 0 ) CALL A X C T R L ( ' S Y M S I Z E ' , 0 . 15) CALL A X P L 0 T ( ' ; ' , 9 0 . 0 , 6 . 0 , - 3 . 0 , 0 . 5 ) CALL SYMBOL(0.0.9.5,0.20,BCD,0.0,80) CALL AXCTRL('SIDE',-1) CALL AXCTRL('YORIGIN',0.00) C A L L AXPLOT( ' ; ' , 0 . 0 , 1 0 . 0 , 0 . 0 , 2 . 0 ) RETURN END FUNCTION A U X ( P P , D , X , L ) DIMENSION P P ( 1 ) , D ( 1 ) COMMON MM D(1)=1.0 AUX=PP(1) DO 18 d=2,MM D ( d ) = D ( d - 1 )*X AUX=AUX+PP(d)*D(d) RETURN  VALUES OF  Y',  APPENDIX 4 DATA FOR GRAPHS PRESENTED  TABLE A4.1 Data for Figure 4.1.1 Sample No.  Swelling Pressure 10 dynes/cm  Hydration g H 0/g collagen  8  5.87 11.74 17.61 23.48  4.49 3.13 2.69 2.39  9  5.87 11.74 17.61 23.48  5.12 3.78 3.27 2.97  10  5.87 11.74 17.61 23.48  4.55 3.04 2.06 1.89  11  5.87 11.74 17.61 23.48  4.48 3.21 2.78 2.37  3  2  2  TABLE A4.2 D a t a f o r F i g u r e 5.1.1 Time (Hours)  ln(Hdl)  In(Hdl) (Fitted)  Weight  RUN 6  1 .00 1 .34 1 .67 2.00 2.34 2.66 3.00 3.33 3.67 4.01 4.34  -0.84 -0.98 -1.13 -1 .30 -1.42 -1 .52 -1 .70 -1 .88 -2.08 -2.20 -2.46  -0.89 -1.04 -1.19 -1 .34 -1 .49 -1 .63 -1 .78 -1 .93 -2.08 -2.23 -2.37  233.6 190.9 150.7 116.0 94. 1 79.7 57.0 40.9 28.3 22.2 13.0  RUN 7  1 .00 1 .34 1 .67 2.01 2.35 2.69 3.02 3.34 3.68 4.02 4.35  -0.87 -1 .02 -1.16 -1 .31 -1 .44 -1.62 -1 .81 -1 .99 -2.16 -2.30 -2.46  -0.90 -1 .04 -1.19 -1 .34 -1 .49 -1 .64 -1 .79 -1 .93 -2.08 -2.23 -2.38  338.3 272.4 216.5 170.9 138.0 101.1 72.0 51 .3 37.5 28.0 20.4  RUN 12  1 .00 1 .34 1 .68 2.01 2.34 2.68 3.01 3.34 3.68 4.01 4.35  -0.89 -1 .05 -1 .21 -1 .37 -1 .50 -1 .63 -1.81 -1 .93 -2.08 -2.21 -2.39  -0.89 -1 .04 -1.19 -1 .34 -1 .49 -1 .64 -1 .78 -1 .93 -2.08 -2.23 -2.38  304.4 237.8 185.2 143.2 114.8 90.3 65.2 52.6 39.5 30.6 21 .4  RUN 14  1 .00 1 .33 1 .68 2.00 2.34 2.67  -0.75 -0.90 -1 .02 -1.16 -1 .22 -1 .45  -0.89 -1 .04 -1.19 -1 .34 -1 .49 -1 .64  162.4 131.9 109. 1 87.2 79.3 54.6  *  Hdl i s the dimensionless  hydration, (H-H )/(.H.-H ) 5  o  TABLE  A4.2  (Continued) Time (Hours)  ln(Hdl)  RUN 14  3.01 3.34 3.67 4.01 4.34  -1 .59 -1 .74 -1 .89 -2.05 -2.26  -1 .78 -1 .93 -2.08 -2.23 -2.38  42.5 32.5 24.2 17.8 1 1 .7  RUN 15  1 .00 1 .33 1 .66 2.00 2.33 2.66 3.00 3.33 3.66 4.00 4.33  -1.10 -1 .30 -1 .43 -1 .58 -1 .71 -1 .86 -1 .97 -2.10 -2.23 -2.36 -2.49  -0.89 -1 .04 -1.19 -1 .34 -1 .48 -1 .63 -1 .78 -1 .93 -2.07 -2.22 -2.37  229.3 167.0 133.2 103.0 81.5 62.4 50. 1 39.0 30.2 23.4 17.7  ln(Hdl) (Fitted)  Weight  108  TABLE  A4.3  D a t a f o r F i g u r e 5.1.2 Time (Hours)  ln(Hdl)  ln(Hdl) (Fitted)  Weight  RUN 6  1.31 1 .65 1 .99 2.32 2.65 2.99 3.32 3.65 3.98 4.32 4.65 4.99 5.32 5.65  -0.83 -0.94 -1.10 -1 .20 -1 .34 -1 .44 -1 .58 -1 .68 -1 .86 -2.00 -2.16 -2.23 -2.34 -2.42  -0.88 -1 .00 -1.11 -1 .22 -1 .33 -1 .44 -1 .56 -1.67 -1 .78 -1 .89 -2.00 -2.12 -2.23 -2.34  109.6 91 .7 71 .4 61 .1 48. 1 40.4 31.5 26. 1 18.4 13.9 10.0 8.6 6.9 5.7  RUN 7  1 .34 1 .67 2.00 2.33 2.67 3.00 3.33 3.66 4.00 4.34 4.67 5.00 5.34 5.68  -0.93 -1.06 -1 .20 -1.31 -1 .44 -1 .55 -1.61 -1 .73 -1 .89 -1 .96 - 2 . 14 -2.25 -2.41 -2.51  -0.89 -1 .00 -1.11 -1 .22 -1 .34 -1 .45 -1 .56 -1 .67 -1 .79 -1 .90 -2.01 -2.12 -2.23 -2.35  87.9 70.9 56.7 46.6 36.9 30.7 27. 1 21.7 15.7 13.9 9.6 7.4 5.2 4. 1  RUN 14  1 .34 1 .67 2.01 2.34 2.67 3.00 3.33 3.68 4.01 4.34 4.67 5.01 5.34 5.68  -0.89 -1 .02 -1.14 -1 .22 -1 .28 -1 .44 -1.52 -1 .59 -1 .69 -1.81 -1 .93 -2.06 -2.23 -2.46  -0.89 -1 .00 -1.11 -1 .23 -1 .34 -1 .45 -1 .56 -1 .68 -1 .79 -1 .90 -2.01 -2.12 -2.24 -2.35  1 56.3 129.8 1 07.8 94.8 85.3 65.0 56.4 49.7 41 .4 33.2 26.4 20.5 14.6 9.0  109  TABLE  A4.3  (Continued) Time (Hours) 1 .35 1 .68 2.01 2.34 2.68 3.01 3.35 3.68 4.02 4.35 4.68 5.01 5.35 5.68  In(Hdl) -0.89 -1 .00 -1.10 -1 .23 -1 .32 -1 .42 -1 .55 -1 .60 -1 .73 -1 .87 -1 .98 -2.1 1 -2.28 -2.46  ln(Hdl) (Fitted) -0.89 -1 .00 -1.12 -1 .23 -1 .34 -1.45 -1 .56 -1 .68 -1 .79 -1 .90 -2.01 - 2 . 13 -2.24 -2.35  Weight 142.9 119.1 1 02.2 82.9 70.9 60.0 47.7 43.6 34. 1 26. 1 21 .0 16.3 11.4 7.7  110  TABLE  A4.4  D a t a f o r F i g u r e 5.1.3 Time (Hours)  ln(Hdl)  2.34 2.67 3.00 3.34 3.67 4.00 4.34 4.66 5.00 5.34 5.67 6.00 6.34 6.67 7.00 7.34 7.67 8.01 8.34 8.68 9.01 9.34 9.68 10.01 10.34  -1 .02 -1.11 -1.19 -1 .27 -1 .41 -1 .49 -1 .56 -1 .64 -1 .69 -1 .71 -1 .82 -1 .83 -1 .81 -1 .78 -1 .79 -1 .80 -1 .85 -1 .87 -2.05 -2.26 -2.36 -2.40 -2.39 -2.50 -2.46  -0.82 -0.88 -0.94 -0.99 -1 .05 -1.11 -1.16 -1 .22 -1 .28 -1 .33 -1 .39 -1 .45 -1 .50 -1 .56 -1 .61 -1 .67 -1 .73 -1 .79 -1 .84 -1 .90 -1 .95 -2.01 -2.07 -2.13 -2.18  34.4 29.5 26.1 22.6 17.6 15.2 13.2 11.3 10.2 9.8 8.0 7.7 8.0 8.6 8.4 8.2 7.4 7.2 4.8 3.0 2.3 2.0 2.1 1 .6 1 .7  2.33 2.66 3.00 3.33 3.66 3.99 4.33 4.66 5.00 5.33 5.67 6.00 6.33 6.67 7.00 7.34  -0.78 -0.85 -0.93 -1 .00 -1.05 -1.10 -1.13 -1.18 -1 .25 -1 .29 -1 .36 -1 .40 -1 .45 -1 .52 -1 .56 -1 .64  -0.82 -0.88 -0.94 -0.99 -1 .05 -1.10 -1.16 -1 .22 -1 .27 -1 .33 -1 .39 -1 .44 -1 .50 -1 .56 -1 .62 -1 .67  232. 1 212.0 186.3 1 68.5 1 56.8 1 43. 1 136.6 126.7 1 12.8 1 04.8 94.4 87.5 79.7 71.1 65.7 57.4  ln(Hdl) (Fitted)  Weight  TABLE  A4.4  (Continued) Time (Hours)  ln(Hdl)  7.67 8.01 8.34 8.67 9.00 9.34 9.68 10.01 1 0.35  -1 .70 -1 .79 -1 .89 -1 .98 -1 .92 -1 .97 -2.07 -2.18 -2.38  -1 .73 -1 .79 -1 .84 -1 .90 -1 .95 -2.01 -2.07 -2.12 -2.18  50.9 43.5 35.9 30.4 34.0 30.6 25.5 20.3 13.5  2.34 2.67 3.00 3.34 3.67 4.01 4.34 4.68 5.02 5.35 5.68 6.01 6.35 6.68 7.02 7.35 7.69 8.02 8.35 8.69 9.02 9.35 9.68 10.02 10.35  -0.82 -0.87 -0.93 -0.97 -1 .02 -1 .07 -1.11 -1.17 -1 .20 -1 .26 -1.31 -1 .38 -1.41 -1 .48 -1 .53 -1 .62 -1 .66 -1.71 -1 .79 -1 .88 -1 .98 -2.08 -2.17 -2.27 -2.45  -0.82 -0.88 -0.94 -0.99 -1 .05 -1.11 -1.16 -1 .22 -1 .28 -1 .33 -1 .39 -1 .45 -1 .50 -1 .56 -1 .62 -1 .67 -1 .73 -1 .79 -1 .84 -1 .90 -1 .96 -2.01 -2.07 -2.13 - 2 . 18  80.4 74.6 68.0 64.2 58.5 54.3 50.4 45.6 43.4 39.3 35.8 31 .6 29.9 25.9 23.9 20.0 18.6 16.8 14.4 11.9 9.7 7.8 6.3 5.0 3.2  In(Hdl) (Fitted)  Weight  TABLE  A4.5  D a t a f o r F i g u r e 5.1.4 Time (Hours) 2.99 3.33 3.66 • 4.00 4.33 4.66 5.00 5.33 5.66 6.00 6.33 6.66 7.00 7.33 7.67 8.00 8.34 8.67 9.01 9.34 9.67 10.01 1 0.34 10.67 1 1 .00 1 1 .34 1 1 .67 12.01 12.34 1 2.67 12.99 1 3.33 1 3.67 1 3.99 1 4.34 3.01 3.34 3.67 4.00 4.34 4.67  ln(Hdl)  ln(Hdl) (Fitted)  Weight  -1.11 -1.19 -1 .27 -1 .37 -1 .46 -1 .52 -1 .53 -1 .56 -1 .55 -1 .52 -1 .60 -1 .69 -1 .79 -1.82 -1 .86 -1 .91 -1 .91 -2.06 -2.05 -2.05 -2.13 -2.02 -1 .99 -2.29 -2.33 -2.25 -2.32 • -2.47 -2.60 -2.53 -2.43 -2.49 -2.43 -2.48 -2.58  -1 .03 -1 .08 -1.13 -1.17 -1 .22 -1 .27 -1 .32 -1 .37 -1.41 -1 .46 -1.51 -1 .56 -1.61 -1 .66 -1 .70 -1 .75 -1 .80 -1 .85 -1 .90 -1 .95 -1 .99 -2.04 -2.09 -2.14 -2.18 -2.23 -2.28 -2.33 -2.38 -2.43 -2.47 -2.52 -2.57 -2.62 -2.67  14.9 13.0 11.1 9.3 7.8 6.8 6.8 6.4 6.5 6.9 5.8 4.8 3.8 3.6 3.2 2.9 2.9 2.0 2.0 2. 1 1 .7 2.2 2.4 1 .0 0.9 1 .2 0.9 0.6 0.3 0.4 0.7 0.5 0.6 0.5 0.3  -0.85 -0.90 -0.97 -1 .04 -1.12 -1.19  -1 .03 -1 .08 -1.13 -1.18 -1 .22 -1 .27  14.4 13.2 11.6 10.3 8.9 7.8  113  TABLE A4.5 (Continued) Time (Hours)  In(Hdl)  In(Hdl) (Fitted)  5.00 5.34 5.68 6.00 6.34 6.67 7.01 7.35 7.68 8.01 8.35 8.68 9.02 9.35 9.68 10.02 10.35 10.69 11.02 1 1 .35 1 1 .68 1 2.02 12.35 12.69 1 3.02 13.35 13.68 14.01 14.34  -1.21 -1 .23 -1 .27 -1 .32 -1 .40 -1.45 -1 .49 -1.51 -1 .56 -1 .60 -1 .59 -1.71 -1 .79 -1 .88 -1 .94 -1 .92 -2.04 -2. 14 -2.19 -2.25 -2.29 -2.49 -2.60 -2.52 -2.46 -2.56 -2.49 -2.34 -2.32  -1 .32 -1 .37 -1 .42 -1 .46 -1 .51 -1 .56 -1 .61 -1 .66 -1.71 -1 .75 -1 .80 -1 .85 -1 .90 -1 .95 -1 .99 -2.04 -2.09 -2.14 -2.19 -2.24 -2.28 -2.33 -2.38 -2.43 -2.48 -2.52 -2.57 -2.62 -2.67  Weight 7.5 7.2 6.7 6.0 5.1 4.6 4.2 4.1 3.7 3.4 3.4 2.5 2.1 1 .7 1 .4 1 .5 1. 1 0.8 0.6 0.5 0.4 0.1 0.0 0.1 0.2 0.0 0.1 0.4 0.4  114  TABLE A4.6 Data Time (Hours)  for Figure In(Hdl)  5.1.5  In(Hdl) (Fitted)  Weight  1 .65 1 .99 2.33 2.66 3.00 3.34 3.67 4.00 4.34 4.67 5.01 5.34 5.68 6.01 6.34 6.67 7.01 7.34  -0.74 -0.83 -0.98 -1 .09 -1.17 -1 .25 -1 .33 -1.41 -1 .47 -1 .57 -1 .63 -1 .71 -1 .78 -1 .90 -1 .97 -2. 12 -2.22 -2.40  -0.67 -0.77 -0.86 -0.96 -1 .05 -1.15 -1 .24 -1 .34 -1 .43 -1 .53 -1.62 -1 .72 -1.81 -1 .91 -2.00 -2.10 -2.19 -2.29  363.0 320.2 256.4 217.8 191 .8 167.9 147.9 128.7 116.2 97.7 88.4 76.8 67.2 53.8 47.2 35. 1 28.8 20. 1  1 .67 2.00 2.34 2.68 3.02 3.35 3.68 4.02 4.35 4.69 5.02 5.35 5.69 6.03 6.36 6.70 7.03 7.36  -0.61 -0.69 -0.78 -0.87 -0.96 -1 .05 -1.12 -1.21 -1.31 -1 .39 -1 .50 -1 .60 -1.77 -1 .89 -2.03 -2.20 -2.30 -2.53  -0.68 -0.77 -0.86 -0.96 -1 .06 -1.15 -1 .25 -1 .34 -1 .44 -1 .53 -1 .63 -1 .72 -1 .82 -1 .91 -2.01 -2.10 -2.20 -2.29  380.8 339.0 302.7 266.7 231 . 1 201 .4 180.2 156.0 132.6 116.6 96.9 81 .2 60.3 48.5 37. 1 26.6 21.6 13.4  115  TABLE  A4.6  (Continued) Time (Hours) 1 .67 2.01 2.34 2.68 3.02 3.35 3.68 4.02 4.35 4.68 5.02 5.36 5.69 6.02 6.35 6.69 7.03 7.36  ln(Hdl) -0.69 -0.81 -0.91 -1 .00 -1.12 -1 .22 -1 .33 -1 .44 -1 .58 -1 .68 -1.81 -1.91 -2.00 -2.13 -2.26 -2.34 -2.42 -2.50  ln(Hdl) (Fitted) -0.68 -0.77 -0.87 -0.96 -1 .06 -1.15 -1 .25 -1 .34 -1 .44 -1 .53 -1 .63 -1 .72 -1 .82 -1 .91 -2.01 -2.10 -2.20 -2.29  Weight 167.6 141.9 120.8 103.8 85.9 72.2 60.2 49. 1 38.0 31.7 24.6 20. 1 16.8 12.8 9.7 8.0 6.7 5.6  116  TABLE Data  A4.7  f o r F i g u r e 5.1.6  Time (Hours)  ln(Hdl)  In(Hdl) (Fitted)  2.33 2.66 2.99 3.32 3.65 3.99 4.33 4.67 5.00 5.34 5.66 6.00 6.34 6.67 7.00 7.34 7.68 8.02 8.35 8.68 9.01 9.34 9.68 10.01 10.34 10.68 11.01  -0.76 -0.84 -0.90 -0.98 -1 .05 -1.11 -1.18 -1 .24 -1 .31 -1 .38 -1.46 -1 .52 -1 .57 -1 .64 -1 .70 -1 .77 -1 .82 -1 .89 -1 .95 -2.03 -2.10 -2.20 -2.23 -2.34 -2.40 -2.46 -2.48  -0.84 -0.90 -0.96 -1 .02 -1 .08 -1.14 -1.19 -1 .26 -1 .31 -1 .37 -1 .43 -1 .49 -1 .55 -1.61 -1 .67 -1 .73 -1 .79 -1 .85 -1 .91 -1 .97 -2.02 -2.08 -2.14 -2.20 -2.26 -2.32 '-2.38  288.5 259.0 235. 1 209. 1 189.6 172.0 153.3 137.5 123. 1 110.4 95.9 86.5 79.2 69.7 61 .6 54.5 49.7 43.4 39. 1 33.4 29.3 23.5 22.5 17.8 15.8 13.8 13.3  2.34 2.68 3.00 3.34 3.67 4.02 4.35 4.68 5.02 5.35 5.69 6.02 6.36 6.69  -1 .06 -1.13 -1 .20 -1 .26 -1.31 -1 .39 -1 .45 -1 .50 -1 .58 -1.61 -1 .63 . -1.72 -1 .76 -1 .83  -0.84 -0.90 -0.96 -1 .02 -1 .08 -1.14 -1 .20 -1 .26 -1 .32 -1 .38 -1 .44 -1 .49 -1 .56 -1.61  224.9 203.7 1 79.8 164.0 1 50.4 133. 1 118.5 109.9 95. 1 90.5 86.8 73.8 69.0 60.8  Weight  117  TABLE  A4.7  (Continued) Time (Hours)  ln(Hdl)  RUN 20  7.03 7.36 7.69 8.03 8.37 8.70 9.04 9.37 9.71 1 0.03  -1 .87 -1.93 -1 .96 -2.13 -2.16 -2.29 -2.26 -2.35 -2.44 -2.45  -1 .67 -1 .73 -1 .79 -1 .85 -1.91 -1 .97 -2.03 -2.09 -2.15 -2.21  55.9 50.8 47.9 34.6 32.3 24.7 26.6 21 .9 18.4 18.1  RUN 21  2.35 2.69 3.02 3.35 3.69 4.02 4.35 4.69 5.03 5.35 5.68 6.01 6.36 6.69 7.02 7.35 7.68 8.02 8.34 8.68 9.01 9.35 9.67 1 0.02 10.34 10.68  -0.89 -0.97 -1 .07 -1.14 -1 .22 -1 .29 -1 .33 -1 .43 -1 .48 -1 .55 -1 .60 -1 .67 -1 .77 -1 .82 -1 .85 -1 .92 -1 .97 -2.02 -2.08 -2.11 -2.22 -2.27 -2.30 -2.45 -2.39 -2.61  -0.84 -0.90 -0.96 -1 .02 -1.08 -1.14 -1 .20 -1 .26 -1 .32 -1 .38 -1 .44 -1 .49 -1 .55 -1.61 -1 .67 -1 .73 -1 .79 -1 .85 -1.91 -1 .97 -2.03 -2.09 -2.14 -2.20 -2.26 -2.32  190.0 167.4 144.6 130.2 112.9 100.8 93.7 80. 1 72.4 64.3 59.0 52.0 43. 1 39.3 37.0 32.6 29.2 26.9 23.5 22.4 17.8 16.1 15.0 10.9 12.4 7.6  RUN 24  2.34 2.67 3.01 3.33  -0.75 -0.79 -0.84 -0.88  -0.84 -0.90 -0.96 -1 .02  357.0 336. 1 312.7 294.6  ln(Hdl) (Fitted)  Weight  118  TABLE  A4.7  (Continued) Time (Hours)  ln(Hdl)  3.67 4.01 4.35 4.67 5.00 5.34 5.68 6.01 6.34 6.68 7.01 7.35 7.69 8.01 8.35 8.68 9.02 9.35 9.69 10.02 10.35 10.69 1 1 .02  -0.94 -0.96 -1 .03 -1 .08 -1.14 -1.17 -1 .22 -1 .27 -1 .34 -1 .39 -1 .46 -1 .52 -1 .56 -1 .63 -1.71 -1 .77 -1 .86 -1 .93 -1 .99 -2.11 -2.25 -2.36 -2.49  In(Hdl) (Fitted) -1 .08 -1.14 -1 .20 -1 .26 -1 .31 -1 .37 -1 .43 -1 .49 -1 .55 -1 .61 -1 .67 -1 .73 -1 .79 -1 .85 -1.91 -1 .97 -2.03 -2.09 -2.15 -2.20 -2.26 -2.32 -2.38  Weight 272.3 261 .4 236.3 217.8 198.3 189.8 174.4 160.4 142.9 131.2 116.1 105.7 97.5 87.6 75.3 67.5 56.7 50.6 44.6 35.8 27. 1 21 .7 16.5  119  TABLE Data Time (Hours)  A4.8  f o r F i g u r e 5.1.7  ln(Hdl)  ln(Hdl) (Fitted)  Weight  RUN 8  0.99 1 .32 1 .65 1 .99 2.32 2.67 3.00 3.33 3.66 3.99 4.32  -0.87 -1 .06 -1 .23 -1 .40 -1 .56 -1 .69 -1 .86 -2.02 -2.13 -2.26 -2.50  -0.92 -1 .07 -1.21 -1 .37 -1 .52 -1 .67 -1 .82 -1 .97 -2.12 -2.27 -2.42  1040.9 776.4 594.3 452.5 344.3 273.0 198.6 148. 1 120.5 95.2 58.4  RUN 9  1 .28 1 .62 1 .95 2.29 2.63 2.96 3.30 3.63 3.97 4.31  -1.18 -1 .34 -1 .48 -1.63 -1 .78 -1 .93 -2.06 -2.22 -2.37 -2.49  -1 .05 -1 .20 -1 .35 -1 .50 -1 .65 -1 .80 -1 .95 -2.10 -2.26 -2.41  552.4 431.5 342. 1 265.0 204.9 154.6 122.2 90.4 68.2 53.4  RUN 10  1.31 1 .65 1 .97 2.30 2.62 2.96 3.29 3.62 3.95 4.27 4.60  -0.94 -1.13 -1 .29 -1 .43 -1 .55 -1 .69 -1 .83 -1 .95 -2.12 -2.31 -2,46  -1 .06 -1.21 -1 .36 -1 .51 -1 .65 -1 .80 -1 .95 -2.10 -2.25 -2.39 -2.54  1341.5 1019.5 790.4 628.5 513.1 406. 1 316.9 252.4 186.8 128.4 97.2  RUN 1 1  1.31 1 .64 1 .98 2.32 2.66 2.99 3.32 3.65 3.99 4.33  -1.17 -1 .37 -1 .52 -1 .67 -1.81 -1 .95 -2.10 -2.24 -2.36 -2.52  -1 .06 -1.21 -1 .36 -1.51 -1 .67 -1.81 -1 .96 -2.1 1 -2.27 -2.42  495.3 353.2 271 .5 209.7 162.9 126.2 95.4 71.9 56.6 41 .8  •  120  TABLE  A4.9  D a t a f o r F i g u r e 5.1.8 Time (Hours)  ln(Hdl)  ln(Hdl) (Fitted)  Weight  RUN 8  1 .32 1 .65 2.00 2.34 2.67 3.00 3.32 3.67 4.00 4.34 4.67 5.00 5.33 5.66 6.00  -1.01 -1.13 -1 .25 -1.41 -1 .56 -1 .67 -1 .88 -2.07 -2.21 -2.30 -2.34 -2.35 -2.40 -2.47 -2.51  -0.90 -1.01 -1.13 -1 .25 -1 .36 -1 .47 -1 .59 -1 .70 -1 .82 -1 .93 -2.05 -2.16 -2.27 -2.39 -2.50  58.2 47.0 38, 28, 21 .8 17.5 1 1 3 7 6 5 4 4.4 4.0 4, 0 3, 4 2, 9 2 6  RUN 9  1 .33 1 .66 2.01 2.33 2.66 3.00 3.33 3.67 4.01 4.34 4.68 5.01  -1 .02 -1.14 -1 .23 -1 .32 -1 .44 -1 .54 -1 .64 -1 .75 -1 .90 -2.05 -2.26 -2.40  -0.90 -1 .02 -1.13 -1 .25 -1 .36 -1 .48 -1 .59 -1.71 -1 .82 -1 .93 -2.05 -2.16  53, 4 43, 4 36, 9 31 .8 25. 1 21 , 17, 13.9 10.1 7.5 4.6 3.3  RUN 10  1.31 1 .65 1 .98 2.31 2.66 2.99 3.31 3.65 3.99 4.32 4.65 4.98 5.32 5.66 5.98  -0.80 -0.89 -1 .02 -1.13 -1 .27 -1 .39 -1 .52 -1 .62 -1 .76 -1 .84 -1 .93 -2.03 -2.14 -2.22 -2.48  -0.90 -1.01 -1.12 -1 .24 -1 .36 -1 .47 -1 .58 -1 .70 -1.81 -1 .93 -2.04 -2.15 -2.27 -2.39 -2.50  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 (Hours) 1 .30 1 .65 1 .98 2.31 2.65 2.97 3.31 3.64 3.97 4.30 4.65 4.97 5.30 5.64 5.97  In(Hdl) -0.94 -1 .07 -1.21 -1 .32 -1 .40 -1.51 -1 .60 -1 .66 -1 .82 -1 .93 -2.03 -2.16 -2.25 -2.50 -2.60  In(Hdl) (Fitted) -0.89 -1.01 -1.13 -1 .24 -1 .35 -1 .46 -1 .58 -1 .69 -1.81 -1 .92 -2.04 -2.15 -2.26 -2.38 -2.49  Weight 38.6 31.0 24. 1 19.8 17.1 13.8 1 1 .4 10.1 7.2 5.7 4.5 3.3 2.7 1 .4 1 .0  122  TABLE  A4.10  D a t a f o r F i g u r e 5.1.9 Time (Hours)  ln(Hdl)  3.89 7.79 8.11 8.45 8.78 9.1 1 9.45 9.78 10.11 10.45 10.78 11.12 1 1 .45 1 1 .78 12.12 12.44 1 2.78 13.12 13.45 1 3.79 14.12 1 4.45 14.79 15.12 1 5.45 1 5.79 16.12 16.47 16.80 17.12 1 7.46 17.79 18.12 18.46  -1 .20 -1 .70 -1 .77 -1 .71 -1 .67 -1 .66 -1 .65 -1 .67 -1 .60 -1 .70 -1 .68 -1 .74 -1 .77 -1.81 -1 .94 -2.06 -2.20 -2.32 -2.45 -2.42 -2.59 -2.46 -2.28 -2.13 -2.10 -2.17 -2.21 -2.22 -2.34 -2.51 -2.50 -2.56 -2.61 -2.55  -0.59 -1.12 -1.16 -1 .21 -1 .25 -1 .30 -1 .34 -1 .39 -1 .43 -1 .48 -1 .52 -1 .57 -1.61 -1 .65 -1 .70 -1 .74 -1 .79 -1 .83 -1 .88 -1 .92 -1 .97 -2.01 -2.06 -2.10 -2.15 -2.19 -2.24 -2.29 -2.33 -2.37 -2.42 -2.46 -2.51 -2.55  3.99 4.33 4.65 4.99 5.32 5.66 5.99  -0.54 -0.57 -0.61 -0.68 -0.73 -0.77 -0.87  -0.61 -0.65 -0.70 -0.74 -0.79 -0.83 -0.88  ln(Hdl) (Fitted)  Weight 3.9 2.9 2.4 2.8 3.1 3.2 3.2 3. 1 3.6 2.9 3.0 2.6 2.4 2.2 1 .5 1. 1 0.7 0.4 0.2 0.3 0.0 0.2 0.5 0.9 1 .0 0.7 0.7 0.6 0.4 0.1 0.1 0.0 0.0 0.1 33.8 32.3 30.2 27.3 25. 1 23.7 20. 1  123  TABLE A4.10 (Continued) Time (Hours) 6.32 6.65 6.98 7.31 7.65 7.98 8.32 8.65 8.98 9.32 9.65 9.98 10.32 10.65 10.99 1 1 .32 1 1 .65 1 1 .98 12.31 1 2.66 12.99 1 3.33 1 3.65 1 3.98 14.31 1 4.65 1 4.98 15.31 15.65 15.98 16.32 1 6.64 1 6.98 1 7.32 17.65 1 7.98 18.31  In(Hdl) -0.91 -1 .01 -1 .00 -1 .09 -1.14 -1.19 -1 .26 -1 .27 -1 .42 -1 .33 -1 .51 -1 .58 -1 .63 -1 .66 -1 .76 -1 .76 -1 .69 -1 .80 -1 .86 -1 .88 -1 .83 -1 .90 -2.12 -2.30 -2.32 -2.37 -2.51 -2.41 -2.31 -2.39 -2.28 -2.16 -2.38 -2.31 -2.33 -2.58 -2.46  ln(Hdl) (Fitted) -0.92 -0.96 -1.01 -1 .05 -1.10 -1.14 -1.19 -1 .23 -1 .28 -1 .32 -1 .37 -1.41 -1 .46 -1 .50 -1.55' -1 .59 -1 .64 -1 .68 -1 .73 -1 .77 -1 .82 -1 .86 -1.91 -1 .95 -2.00 -2.04 -2.09 -2.13 -2.17 -2.22 -2.26 -2.31 -2.35 -2.40 -2.44 -2.49 -2.53  Weight 18.7 16.0 16.2 13.8 12.7 11.5 10.1 10.0 7.4 8.9 6.1 5.3 4.8 4.5 3.6 3.6 4.2 3.3 2.8 2.7 3.1 2.6 1 .4 0.8 0.8 0.7 0.4 0.6 0.8 0.6 0.9 1 .3 0.6 0.8 0.8 0.2 0.5  TABLE  A4.10  (Continued) Time (Hours)  ln(Hdl)  3.98 4.31 4.66 4.99 5.32 5.65 5.98 6.32 6.65 6.98 7.32 7.66 7.99 8.32 8.66 8.99 9.32 9.65 10.00 10.32 10.66 10.99 11.32 1 1 .65 12.00 12.33 12.65 1 2.99 13.28 1 3.67 1 3.99 14.33 14.65 14.98 15.32 1 5.66 15.98 16.32 16.66 16.99 17.32 1 7.66 17.99 18.33  -0.82 -0.87 -0.89 -0.95 -0.96 -1 .02 -1 .05 -1 .04 -1 .03 -1 .03 -0.99 -0.96 -1 .06 -1.12 -1 .22 -1 .23 -1 .32 -1 .35 -1 .44 -1 .49 -1 .48 -1 .52 -1 .63 -1 .67 -1 .74 -1 .85 -1 .85 -1 .87 -1 .87 -1 .68 -1 .72 -1 .72 -1 .74 -1 .78 -1 .88 -1 .96 -2.07 -2.09 -2.32 -2.29 -2.52 -2.39 -2.58 -2.57  *  ln(Hdl) (Fitted) -0.61 -0.65 -0.70 -0.74 -0.79 -0.83 -0.87 -0.92 -0.96 -1 .01 -1 .05 -1.10 -1.14 -1.19 -1 .23 -1 .28 -1 .32 -1 .37 -1.41 -1 .46 -1 .50 -1 .55 -1 .59 -1 .64 -1 .68 -1 .73 -1 .77 -1 .82 -1 .86 -1.91 -1 .95 -2.00 . -2.04 -2.09 -2.13 -2.18 -2.22 -2.26 -2.31 -2.36 -2.40 -2.44 -2.49 -2.53  Weight 1 .6 1 .4 1.3 1. 1 1. 1 0.9 0.8 0.9 0.9 0.9 1.0 1. 1 0.8 0.7 0.5 0.5 0.3 0.3 0.2 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  125  TABLE A4.10 (Cont inued) Time (Hours) 3.97 4.30 4.63 4.97 5.29 5.62 5.94 6.28 6.61 6.94 7.28 7.60 7.94 8.27 8.61 8.92 9.25 9.57 9.90 10.23 10.56 10.90 1 1 .22 1 1 .56 1 1 .88 12.22 12.54 12.88 13.20 13.53 1 3.88 1 4.20 1 4.54 1 4.87 1 5.20 1 5.52 15.86 16.18 16.53 16.85 17.18 17.51 17.84 18.17 18.50  In(Hdl) -0.68 -0.73 -0.75 -0.77 -0.79 -0.82 -0.85 -0.89 -0.92 -0.93 -0.99 -1 .03 -1 .06 -1.10 -1.11 -1 .22 -1 .22 -1 .29 -1 .29 -1 .28 -1 .30 -1 .34 -1.41 -1 .48 -1 .57 -1 .65 -1 .69 -1 .64 -1 .66 -1 .70 -1 .74 -1 .77 -1 .87 -1 .91 -1 .99 -2.14 -2.20 -2.20 -2.19 -2.35 -2.38 -2.33 -2.45 -2.50 -2.56  ln(Hdl) (Fitted) -0.60 -0.65 -0.69 -0.74 -0.78 -0.83 -0.87 -0.91 -0.96 -1 .00 -1 .05 -1 .09 -1.14 -1.18 -1 .23 -1 .27 -1.31 -1 .36 -1 .40 -1 .45 -1 .49 -1 .54 -1 .58 -1 .62 -1 .67 -1.71 -1.76 -1 .80 -1.85 -1 .89 -1 .94 -1.98 -2.03 -2.07 -2.11 -2.16 -2.20 -2.25 -2.29 -2.34 -2.38 -2.43 -2.47 -2.51 -2.56  Weight 27.3 25.2 24.5 23.3 22.7 21 .3 20.4 19.1 17.8 17.7 15.8 14.4 13.8 12.8 12.4 10.0 10.1 8.7 8.6 8.8 8.5 7.8 6.7 5.7 4.7 3.8 3.5 3.9 3.8 3.4 3.1 2.8 2.2 2.0 1 .6 1 .0 0.8 0.8 0.8 0.5 0.4 0.5 0.3 0.2 0.1  126  TABLE A4.11 Data f o r F i g u r e 5.1.10 Time (Hours)  ln(Hdl)  In(Hdl) (Fitted)  •  Weight  RUN 16  1.01 1 .35 1 .69 2.03 2.36 2.69 3.02 3.36  -1 .44 -1.63 -1 .80 -1 .93 -2.11 -2.23 -2.35 -2.46  -1 .29 -1 .46 -1 .64 -1.81 -1 .98 -2.15 -2.33 -2.50  594.4 430.5 316.8 250.3 182.0 1 45.2 115.1 92.7  RUN 25  0.97 1 .30 1 .64 1 .97 2.31 2.65 2.98 3.32  -0.93 -1.16 -1 .35 ' -1.51 -1 .69 -1 .92 -2.17 -2.41  -1 .27 -1 .44 -1.61 -1 .79 -1 .96 -2.14 -2.31 -2.48  585.5 411.2 308.4 234.7 173.6 113.8 71.7 45.3  1.01 1 .35 1 .69 2.03 2.36 2.69 3.02 3.36  -1 .44 -1 .63 -1 .80 -1 .93 -2.11 -2.23 -2.35 -2.46  -1 .29 -1 .46 -1 .64 -1 .81 -1 .98 -2.15 -2.33 -2.50  594.4 430.5 316.8 250.3 182.0 1 45.2 115.1 92.7  RUN 26  127  TABLE Data Time (Hours)  A4.12  for Figure  ln(Hdl)  5.2.3.1  In(Hdl) (Fitted)  Weight  40 g  0.0 0.32 0.65 0.98 1.31 1 .65 1 .97 2.30 2.62 2.96 3.29 3.62 3.95 4.27 4.60  0.0 -0.42 -0.63 -0.85 -1 .07 -1 .30 -1 .52 -1.71 -1 .89 -2.10 -2.34 -2.59 -2.95 -3.54 -4.23  -0.09 -0.32 -0.57 -0.80 -1 .05 -1 .29 -1 .52 -1 .77 -2.00 -2.24 -2.49 -2.73 -2.96 -3.20 -3.44  3620.27 2314.99 1761.84 1304.14 951.92 664.67 467.39 334.31 243.83 164.89 104.36 65. 10 30.91 8.42 1 .41  60 g  0.0 0.31 0.65 0.98 1.31 1 .65 1 .98 2.31 2.66 2.99 3.31 3.65 3.99 4.32 4.65 4.98 5.32 5.66 5.98  0.0 -0.34 -0.55 -0.73 -0.90 -1.01 -1.17 -1 .30 -1 .49 -1 .66 -1 .85 -1 .99 -2.23 -2.36 -2.55 -2.75 -3.02 -3.23 -4.34  -0.11 -0.28 -0.46 -0.64 -0.82 -1 .00 -1 .36 -1 .55 -1 .73 -1.91 -2.09 -2.28 -2.45 -2.64 -2.82 -3.00 -3.18 -3.36  349.24 234.84 176.91 137.39 106.68 89.40 69.05 54.88 39.12 28.52 19.97 1 4.84 9.06 6.72 4.36 2.64 1 .21 0.59 0.00  0.0 0.31 0.64 0.98 1 .32 1 .65 1.99 2.31 2.65  0.0 -0.23 -0.34 -0.45 -0.52 -0.58 -0.66 -0.70 -0.73  -0.21 -0.26 -0.31 -0.37 -0.42 -0.48 -0.53 -0.58 -0.64  5.96 4.18 3.48 2.86 2.50 2.22 1 .86 1 .71 1 .60  80 g  -1.18  128  TABLE  A4.12  (Continued) Time (Hours)  ln(Hdl)  2.99  -0.79 -0.83 -0.89 -0.92 -0.98 -1 .01 -1 .08 -1 .09 -1.16 -1 .21 -1.19 -1.18  3.32 3.65 3.98 4.32 4.66 4.99 5.32 5.65 5.98 6.32 6.65 6.98 7.32 7.66 7.99 8.32 8.66 8.99 9.32 9.65 10.00 1 0.32 10.66 10.99 1 1 .32 1 1 .65 12.00 12.33 1 2.65 12.99 1 3.28 1 3.67 1 3.99 14.33 14.65 1 4.98 1 5.32 1 5.66 15.99 16.32 1 6.66 16.99 17.32 17.66  -1.18  -1.13 -1.10 -1 .22 -1 .29 -1 .42 -1 .43 -1.56 -1 .59 -1 .72 -1 .81 -1 .79 -1 .85 -2.02 -2.08 -2.20 -2.39 -2.39 -2.43 -2.42 -2.10 -2.16 -2.15 -2.20 -2.26 -2.44 -2.60 -2.83 -2.88 -3.56 -3.46 -4.74 -3.86  ln(Hdl) (Fitted) -0.69 -0.74 -0.80 -0.85 -0.90 -0.96 -1 .01 -1 .06 -1.12 -1.17 -1 .22 -1 .28 -1 .33 -1 .39 -1.44 . -1.49 • -1 .55 -1 .60 -1 .65 -1 .71 -1 .76 -1.81 -1 .87 -1 .92 -1 .97 -2.03 -2.08 -2.13 -2.19 -2.24 -2.29 -2.34 -2.40 -2.45 -2.51 -2.56 -2.61 -2.67 -2.72 -2. 77 -2.83 . -2.88 -2.93 -2.99 -3.04  Weight 1 .37 1 .24 1 .06 0.98 0.82 0.75 0.59 0.58 0.45 0.37 0.40 0.42 0.41 0.50 0.56 0.35 0.25 0.08 0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00  129  TABLE A4 . 13 Data Time (Hours)  f o r F i g u r e 5.2.3.2  In(Hdl)  In(Hdl) (Fitted)  Weight  40 g  0.0 0.32 0.65 0.98 1.31 1 .65 1 .97 2.30 2.62 2.96 3.29 3.62 3.95 4.27 4.60 4.94 5.26 5.58  0.0 -0.40 -0.61 -0.82 -1 .02 -1 .23 -1 .42 -1 .59 -1 .74 -1 .91 -2.10 -2.28 -2.52 -2.85 -3.13 -3.51 -3.83 -4.42  -0.11 -0.32 -0.53 -0.75 -0.97 -1.18 -1 .39 -1.61 -1 .82 -2.04 -2.26 -2.47 -2.68 -2.89 -3.11 -3.33 -3.54 -3.75  3834.13 2497.50 1930.66 1460.15 1095.61 795.05 585.12 440.37 339.61 248.93 176.25 126.22 78.42 40.30 22.66 9.80 4.48 0.81  60 g  0.0 0.31 0.65 0.98 1.31 1 .65 1 .98 2.31 2.66 2.99 3.31 3.65 3.99 4.32 4.65 4.98 5.32 5.66 5.98 6.31 6.65 6.99  0.0 -0.33 -0.53 -0.70 -0.85 -0.95 -1.10 -1 .22 -1 .39 -1 .53 -1 .69 -1.81 -1 .99 -2.09 -2.23 -2.36 -2.54 -2.65 -3.11 -3.43 -4.04 -4.07  -0.13 -0.28 -0.44 -0.60 -0.76 -0.92 -1 .08 -1 .24 -1.41 -1 .57 -1 .73 -1 .89 -2.05 -2.21 -2.38 -2.54 -2.70 -2.86 -3.02 -3.18 -3.34 -3.50  370.10 252.85 193.50 152.88 121.17 103.22 81 .92 66.93 50.01 38.39 28.75 22.79 15.78 12.79 9.62 7.11 4.78 3.58 0.99 0.25 0.00 0.00  TABLE  A4.13  (Continued) Time (Hours)  ln(Hdl)  0.0 0.31 0.64 0.98 1 .32 1 .65 1 .99 2.31 2.65 2.99 3.32 3.65 3.98 4.32 4.66 4.99 5.32 5.65 5.98 6.32 6.65 6.98 7.32 7.66 7.99 8.32 8.66 8.99 9.32 9.65 10.00 10.32 1 0.66 10.99 1 1 .32 1 1 .65 12.00 12.33 1 2.65 12.99 13.28 13.67  0.0 -0.23 -0.33 -0.44 -0.51 -0.56 -0.65 -0.68 -0.71 -0.77 -0.81 -0.87 -0.90 -0.96 -0.99 -1.05 -1 .06 -1.13 -1.17 -1.16 -1.15 -1.15 -1.10 -1 .07 -1.19 -1 .25 -1 .37 -1 .38 -1 .50 -1 .53 -1 .65 - 1 .73 -1.71 - 1 .76 - 1 .92 -1 .98 -2.08 -2.24 -2.25 -2.28 -2.27 -1 .99  ln(Hdl) (Fitted) -0.21 -0.26 -0.31 -0.36 -0.42 -0.47 -0.52 -0.57 -0.62 -0.67 -0.72 -0.77 -0.82 -0.87 -0.92 -0.97 -1 .02 -1 .07 -1.12 -1.18 -1 .23 -1 .28 -1 .33 -1 .38 -1 .43 -1.48 -1 .53 -1 .58 -1 .63 -1 .68 -1 .74 - 1 .79 -1 .84 -1 .89 -1 .94 -1 .99 -2.04 -2.09 -2.14 -2.19 -2.24 -2.30  Weight 6.10 4.31 3.61 2.98 2.62 2.34 1 .97 1 .82 1.71 1 .48 1 .34 1.16 1 .07 0.92 0.84 0.68 0.66 0.53 0.45 0.48 0.50 0.49 0.59 0.65 0.42 0.32 0.15 0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00  131  TABLE  A4.13  (Continued) Time (Hours)  In(Hdl)  ln(Hdl) (Fitted)  Weight  13.99 1 4.33 14.65 14.98 1 5.32 1 5.66 15.99 1 6.32 16.66 16.99 1 7.32 17.66 17.99 18.33 18.66 19.01 19.33 1 9.66  -2.04 -2.04 -2.08 - 2 . 13 -2.28 -2.42 -2.60 -2.64 -3.12 -3.05 -3.70 -3.30 -3.92 -3.85 -4. 06 -4.02 -3.78 -4.25  -2.34 -2.40 -2.45 -2.50 -2.55 -2.60 -2.65 -2.70 -2.75 -2.80 -2.85 -2.90 -2.95 -3.01 -3.06 -3.11 -3.16 -3.21  0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00  132  TABLE A4.14 Data f o r F i g u r e Time (Hours)  In(Hdl)  5.2.3.3 ln(Hdl) (Fitted)  40 g  0.0 0.32 0.65 0.98 1.31 1 .65 1 .97 2.30 2.62 2.96 3.29 3.62 3.95 4.27 4.60 4.94 5.26 5.58 5.92 6.25 6.57  0.0 -0.39 -0.58 -0.78 -0.96 -1.16 -1 .33 -1 .48 -1 .60 -1 .75 -1 .90 -2.04 -2.23 -2.45 -2.62 -2.83 -2.98 -3.18 -3.50 -3.86 -4.77  - 0 . 13 -0.31 -0.51 -0.69 -0.89 -1 .08 -1 .26 -1 .46 -1 .64 -1 .83 -2.03 -2.22 -2.40 -2.59 -2.78 -2.98 -3.16 -3.34 -3.54 -3.73 -3.91  60 g  0.0 0.31 0.65 0.98 1.31 1 .65 1 .98 2.31 2.66 2.99 3.31 3.65 3.99 4.32 4.65 4.98 5.32 5.66 5.98 6.31  0.0 -0.31 -0.50 -0.66 -0.80 -0.89 -1 .02 -1.13 -1 .28 -1 .40 -1 .53 -1 .63 -1 .77 -1 .85 -1 .95 -2.05 -2.16 -2.24 -2.51 -2.66  -0.15 -0.28 -0.42 -0.55 -0.69 -0.83 -0.97 -1.11 -1 .26 -1 .39 -1.53 -1 .67 -1.81 -1 .95 -2.09 -2.22 -2.37 -2.51 -2.64 -2.78  Weight 4062.17 2693.37 2112.63 1629.21 1252.58 939.16 717.32 561.71 451.43 350.05 266.34 206.64 146.72 94.76 67.77 44.85 33.05 21 .58 1 0.67 4.45 0.15 396.79 276.06 214.97 173.05 140.16 121.43 99.05 83. 1 3 64.91 52. 1 6 41 .34 34.48 26. 16 22.48 18.45 15.12 1 1 .82 1 0.03 5.52 3.82  133  TABLE  A4.14  (Continued)  " 8 0  g  Time (Hours)  ln(Hdl)  ln(Hdl) (Fitted)  Weight  6.65 6.99 7.32 7.65 7.98 8.31 8.65  -2.89 -2.90 -3.13 -3.24 -3.42 -3.61 -4.77  -2.92 -3.06 -3.20 -3.33 -3.47 -3.61 -3.75  2.10 .2.04 1 .04 0.69 0.32 0.00 0.00  0.0 0.31 0.64 0.98 1 .32 1 .65 1 .99 2.31 2.65 2.99 3.32 3.65 3.98 4.32 4.66 4. 99 5.32 5.65 5.98 6.32 6.65 6.98 7. 32 7.66 7.99 8.32 8.66 8.99 9.32 9.65 10.00 10.32 10.66 10.99  0.0 -0.22 -0.33 -0.43 -0.50 -0.55 -0.63 -0.66 -0.69 -0.75 -0.79 -0.84 -0.87 -0.93 -0.96 -1 .02 -1 .03 -1 .09 -1.13 -1.12 -1.11 -1.11 -1 .06 -1 .03 -1.15 -1 .21 -1 .32 -1 .33 -1 .44 -1 .47 -1 .58 -1 .65 -1 .64 -1 .68  -0.22 -0.26 -0.31 -0.36 -0.41 -0.45 -0.50 -0.55 -0.60 -0.65 -0.70 -0.74 -0.79 -0.84 -0.89 -0.94 -0.98 -1 .03 -1 .08 -1.13 -1.17 -1 .22 -1 .27 -1 .32 -1 .37 -1 .42 -1.46 -1.51 -1 .56 -1 .61 -1 .66 -1.71 -1 .75 -1 .80  6.26 4.46 3.75 3.11 2.75 2.47 2.10 1 .94 1 .84 1 .60 1 .46 1 .27 1.19 1 .02 0.94 0.78 0.76 0.62 0.54 0.57 0.59 0.58 0.68 0.75 0.51 0.40 0.23 0.22 0.08 0.03 0.00 0.00 0.00 0.00  134  TABLE  A4.14  (Continued) Time (Hours)  ln(Hdl)  1 1 .32 1 1 .65 12.00 12.33 12.65 12.99 13.28 1 3.67 13.99 1 4.33 1 4.65 1 4.98 15.32 1 5.66 15.99 1 6.32 16.66 16.99 17.32 17.66 17.99 18.33 18.66 19.01 19.33 19.66 19.99  -1 .82 -1 .87 -1 .96 -2.10 -2.11 -2.13 -2.12 -1 .88 -1 .93 -1 .92 -1 .96 -2.00 -2.14 -2.25 -2.40 -2.43 -2.80 -2.75 -3.17 -2.92 -3.29 -3.25 -3.36 -3.34 -3.21 -3.45 -3.39  In(Hdl) (Fitted) -1.85 -1 .90 -1 .95 -1 .99 -2.04 -2.09 -2.13 -2.19 -2.23 -2.28 -2.33 -2.38 -2.43 -2.47 -2.52 -2.57 -2.62 -2.67 -2.71 -2.76 -2.81 -2.86 -2.91 -2.96 -3.00 -3.05 -3.10  Weight 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00  135  TABLE Data Time (Hours)  A4.15  f o r F i g u r e 5.2.3.4  ln(Hdl)  ln(Hdl) (Fitted)  Weight  0.0 0.32 0.65 0.98 1.31 1 .65 1 .97 2.30 2.62 2.96 3.29 3.62 3.95 4.27 4.60  0.0 -0.38 -0.57 -0.76 -0.94 -1.13 -1 .29 -1 .43 -1 .55 -1 .69 -1.83 -1 .95 -2.12 -2.31 -2.46  -0.14 -0.31 -0.49 -0.67 -0.86 -1 .04 -1 .22 -1 .40 -1 .58 -1 .76 -1 .95 -2.13 -2.31 -2.49 -2.67  4208.88 2813. 1 1 2220.67 1727.03 1341.52 1019.51 790.41 628.53 513.08 406.11 316.87 252.44 186.78 1 28.45 97.24  0.0 0.31 0.65 0.98 1.31 1 .65 1 .98 2.31 2.66 2.99 3.31 3.65 3.99 4.32 4.65 4.98 5.32 5.66 5.98  0.0 -0.31 -0.50 -0.65 -0.80 -0.89 -1 .02 -1.13 -1 .27 -1 .39 -1 .52 -1.62 -1.76 -1 .84 -1 .93 -2.03 -2.14 -2.22 -2.48  -0.15 -0.28 -0.42 -0.55 -0.69 -0.83 -0.97 -1.11 -1 .25 -1 .39 -1 .52 -1 .66 -1 .80 -1 .94 -2.08 -2.21 -2.35 -2.49 -2.63  407.13 283.57 221.07 178. 18 144.52 125.34 102.42 86. 10 67.42 54.32 43.20 36. 1 4 27.56 23.76 19.58 16.12 12.70 1 0.83 6.10  0.0 0.31 0.64 0.98 1 .32 1 .65  0.0 -0.21 -0.31 -0.41 -0.47 -0.52  -0.22 -0.26 -0.30 -0.35 -0.39 -0.43  7.16 5.20 4.42 3.73 3.33 3.02  TABLE A 4 . 1 5 (Continued) Time (Hours) 1 .99 2.31 2.65 2.99 3.32 3.65 3.98 4.32 4.66 4.99 5.32 5.65 5.98 6.32 6.65 6.98 7.32 7.66 7.99 8.32 8.66 8.99 9.32 9.65 10.00 1 0.32 1 0.66 1 0.99 1 1 .32 1 1 .65 12.00 12.33 12.65 12.99 1 3.28 1 3.67 13.99 14.33 14.65 14.98 1 5.32 15.66  In(Hdl) -0.59 -0.63 -0.65 -0.71 -0.74 -0.79 -0.82 -0.87 -0.89 -0.95 -0.96 -1 .02 -1 .05 -1 .04 -1 .03 -1 .03 -0.99 -0.97 -1 .06 -1.12 -1 .22 -1 .23 -1 .32 -1 .35 -1 .44 -1 .49 -1 .48 -1 .52 -1 .63 -1 .67 -1.74 -1 .85 -1.85 -1 .87 -1 .87 -1 .68 -1 .72 -1.71 -1 .74 -1 .78 -1 .88 -1 .96  In(Hdl) (Fitted) -0.48 -0.52 -0.56 • -0.60 -0.65 -0.69 -0.73 -0.77 -0.82 -0.86 -0.90 -0.94 -0.99 -1 .03 -1 .07 -1.11 -1.16 -1 .20 -1 .24 -1 .28 -1 .33 -1.37 -1.41 -1 .45 -1 .50 -1 .54 -1 .58 -1 .62 -1 .67 -1.71 -1 .75 -1.79 -1 .84 -1 .88 -1 .92 -1 .97 -2.01 -2.05 -2.09 -2.13 -2.18 -2.22  Weight 2.61 2.44 2.32 2.05 1 .89 1 .69 1 .59 1 .40 1 .32 1.13 1.11 0.94 0.85 0.88 ' 0.91 0.90 1.01 1 .09 0.82 0.69 0.48 0.47 0.31 0.28 0. 15 0.08 0.09 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00  137  TABLE  A4.15  (Continued) Time (Hours)  ln(Hdl)  ln(Hdl) (Fitted)  Weight  15.99 16.32 16.66 16.99 17.32 17.66 17.99 18.33  -2.07 -2.09 -2.32 -2.29 -2.52 -2.39 -2.58 -2.57  -2.26 -2.30 -2.35 -2.39 -2.43 -2.47 -2.52 -2.56  0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00  138  TABLE Data  -  A4.16  f o r F i g u r e 5.2.3.5  Time (Hours)  ln(Hdl)  ln(Hdl) (Fitted)  0.0 0.32 0.65 0.98 1.31 1 .65 1 .97 2.30 2.62 2.96 3.29 3.62 3.95 4.27 4.60 4.94 5.26 5.58 5.92 6.25 6.57 6.91 7.24 7.57 7.90 8.22 8.55 8.89 9.20 9.54 9.87 10.20 10.53 1 0.85 11.18 11.51 1 1 .84 12.17 12.51 12.83 13.16 13.49  0.0 -0.30 -0.44 -0.58 -0.70 -0.81 -0.91 -0.99 -1 .05 -1.11 -1.18 -1 .23 -1 .29 -1 .36 -1 .40 -1 .45 -1 .47 -1.51 -1 .55 -1 .59 -1 .64 -1 .67 -1.71 -1 .77 -1 .80 -1 .86 -1 .91 -1 .97 -2.02 -2.03 -2.05 -2.11 -2.15 -2.20 -2.25 -2.31 -2.35 -2.41 -2.47 -2.54 -2.56 -2.60  -0.36 -0.42 -0.48 -0.54 -0.60 -0.67 -0.73 -0.79 -0.85 -0.91 -0.97 -1 .03 -1 .09 -1.15 -1 .22 -1 .28 -1 .34 -1 .40 -1 .46 -1 .52 -1 .58 -1 .64 -1.71 -1 .77 -1 .83 -1 .89 -1 .95 -2.01 -2.07 -2.13 -2.19 -2.26 -2.32 -2.38 -2.44 -2.50 -2.56 -2.62 -2.69 . -2.74 -2.81  -2.87  Weight  5888.64 4314.39 3646.39 3085.27 2639.18 2255.78 1971.83 1760.54 1602.98 1449.68 1313.99 1209.55 1094.71 981.44 913.62 847.40 808.03 763.60 710.30 667.59 611 .43 575.75 534.64 488.51 455.61 409.79 375.68 339.33 310.71 302.98 289.42 262.44 244.82 220.50 200.68 179.19 165.71 147.40 130.72 114.22 109.83 101.39  139  TABLE A 4 . 1 6 (Continued) Time (Hours)  ln(Hdl)  1 3.80 14.14 14.47 1 4.80 15.13 1 5.45 15.78 16.11 16.44 16.77 17.09 17.43 17.76 18.09 18.42 18.74 19.08 19.41 1 9.73  -2.67 -2.72 -2.70 -2.73 -2.81 -2.83 -2.86 -2.99 -3.01 -3.07 -3.15  0.0 0.31 0.65 0.98 1.31 1 .65 1 .98 2.31 2.66 2.99 3.31 3.65 3.99 4.32 4.65 4.98 5.32 5.66 5.98 6.31 6.65 6.99  0.0 -0.25 -0.39 -0.50 -0.60 -0.66 -0.75 -0.81 -0.90 -0.97 -1.03 -1 .08 -1.14 -1.18 -1 .22 -1 .26 -1 .30 -1 .32 -1 .40 -1 .44 -1 .49 -1 .50  -3.19  -3.26 -3.2.7 -3.37 -3.43 -3.53 -3.56 -3.69  ln(Hdl) (Fitted) -2.93 -2.99 -3.05 -3.11 -3.17 -3.23 -3.29 -3.36 -3.42 -3.48 -3.54 -3.60 -3.66 -3.72 -3.79 -3.85  Weight  -3.97 -4.03  89.49 80.95 84.35 79.58 67.26 63.75 59.97 46.69 44.09 39.24 33.45 30.35 26.03 25.64 20.68 18.00 1 4.66 13.56 10.15  -0.35 -0.39 -0.44 -0.49 -0.54 -0.59 -0.64 -0.69 -0.74 -0.79 -0.83 -0.88 -0.93 -0.98 -1 .03 -1 .08 -1.13 -1.18 -1 .22 -1 .27 -1 .32 -1 .37  553.88 415.92 346.41 298.34 260.09 237.94 210.93 191.21 167.85 150.77 135.54 125.38 112.33 106.20 99. 1 4 92.96 86.40 82.58 71 .73 66.81 60.91 60.68  -3.91  140  TABLE  A4.16  (Continued) Time (Hours)  ln(Hdl)  7.32 7.65 7.98 8.31 8.65 8.98 9.31 9.64 9.97 10.30 10.64 10.98 11.31 1 1 .64 1 1 .97 12.31 12.64 12.97 1 3.30 13.64 13.97 14.31 14.64 14.97 15.30 15.63 15.97 16.31 16.63 16.97 17.30 17.63 17.96 18.30 18.63 18.97 19.30 1 9.63 19.96  -1 .54 -1 .56 -1 .58 -1 .60 -1 .68 -1 .72 -1 .74 -1.81 -1.83 -1 .86 -1.91 -1 .93 -1 .93 -1 .97 -1 .99 -2.01 -2.03 -2.04 -2.10 -2.12 -2.13 -2.14 -2.17 -2.21 -2.21 -2.31 -2.33 -2.36 -2.40 -2.40 -2.44 -2.48 -2.61 -2.64 -2.66 -2.72 -2.85 -2.92 -2.98  ln(Hdl) (Fitted) -1 .42 -1 .47 -1 .52 -1.57 -1 .62 -1 .66 -1.71 -1 .76 -1.81  -1 .86 -1 .91 -1 .96 -2.01 -2.06 -2.10 -2.15 -2.20 -2.25 -2.30 -2.35 -2.40 -2.45 -2.50 -2.54 -2.59 -2.64 -2.69 -2.74 -2.79 -2.84 -2.89 -2.94 -2.98 -3.03 -3.08 -3.13 -3.18 -3.23 -3.28  Weight 56.21 54.34 51 .86 49.64 42.82 40.00 38.69 33.38 32.33 30.30 27.51 26.70 26.21 24.65 23.56 22.50 21 .75 21.16 18.77 17.93 17.79 17.10 16.31 15.03 14.76 12.14 1 1 .56 10.88 9.92 9.80 8.98 8.19 6.10 5.68 5.51 4.72 3.38 2.82 2.41  141  TABLE A4 . 1 6 (Continued) Time (Hours)  ln(Hdl)  0.0 0.31 0.64 0.98 1 .32 1 .65 1 .99 2.31 2.65 2.99 3.32 3.65 3.98 4.32 4.66 4.99 5.32 5.65 5.98 6.32 6.65 6.98 7.32 7.66 7.99 8.32 8.66 8.99 9.32 9.65 10.00 1 0.32 10.66 10.99 1 1 .32 1 1 .65 12.00 12.33 12.65 12.99 13.28 13.67  0.0 -0.22 -0.33 -0.43 -0.49 -0.55 -0.62 -0.66 -0.68 -0.75 -0.78 -0.84 -0.86 -0.92 -0.95 -1.01 -1 .02 -1 .08 -1.12 -1.11 -1.10 -1.10 -1 .05 -1 .02 -1.14 -1 .20 -1.31 -1 .32 -1 .42 -1 .45 -1 .56 -1 .63 -1.61 -1 .66 -1 .79 -1 .84 -1 .93 -2.06 -2.07 -2.09 -2.09 -1 .85  ln(Hdl) (Fitted) -0.22 -0.26 -0.31 -0.36 -0.41 -0.45 -0.50 -0.55 -0.59 -0.64 -0.69 " -0.74 -0.78 -0.83 -0.88 -0.92 -0.97 -1.02 -1 .07 -1.11 -1.16 -1.21 -1 .26 -1 .30 -1 .35 -1 .40 -1 .44 -1 .49 -1 .54 -1 .59 -1 .63 -1 .68 -1 .73 -1 .77 -1.82 -1 .87 -1 .92 -1 .96 -2.01 -2.06 -2.10 -2.15  Weight 6.30 4.50 3.80 3.16 2.79 2.51 2.14 1 .98 1 .87 1 .63 1 .49 1.31 1 .22 1 .05 0.98 0.81 0.79 0.65 0.57 0.60 0.62 0.61 0.71 0.78 0.54 0.43 0.26 0.25 0.11 0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00  142  TABLE  A4.16  (Continued) Time (Hours) 13.99 1 4.33 14.65 1 4.98 1 5.32 15.66 15.99 1 6.32 16.66 16.99 17.32 17.66 17.99 18.33 " 18.66 19.01 19.33 19.66 19.99  ln(Hdl)  ln(Hdl) (Fitted)  Weight  -1 .90 -1 .89 -1.93 -1 .97 -2.10 -2.20 -2.35 -2.38 -2.72 -2.67 -3.05 -2.83 -3.16 -3.13 -3.22 -3.20 -3.09 -3.29 -3.24  -2.20 -2.25 -2.29 -2.34 -2.39 -2.44 -2.48 -2.53 -2.58 -2.62 -2.67 -2.72 -2.77 -2.81 -2.86 -2.91 -2.96 -3.00 -3.05  0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00  APPENDIX 5 RAW DATA  144  Sample format for Table A5.1 [following  # calibration points; maximum time  Initial  .300 98.5 —20.0 19.982 20.319  time  Time (hours); chart reading  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  pages]:  MM; NI 1\ Parameters EPS J for LSF Title A; DW T; I n i t i a l and final c a l i b r a t i o n readings,  99.8' 91.507 30.10 88.557 20.10  D i g i t i z e r a r t i f a c t ; Reading error {% scale)  {%)  I n i t i a l or final calibration  —0 2  27.679 999.  83.879 20.10 999.  End of f i l e  27.482  84.123 30.10  etc.  2 1 10.OE-10 RUN #1, TEMPERATURE=22 C 7 76.0 3.343 0.4375 .150 3.0 1.8 .175 15.5 11.4 .200 4 1.5 37.7 .225 60.7 57.7 .250 77.3 74.0 .275 88.7 87.4 .300 98.5 97.8 20.0 19 .982 91 . 507 30 . 10 20 . 3 1 9 88 . 557 20 . 10 20 . 6 5 7 87 .641 20 . 10 20 . 9 8 5 87 . 253 20 . 10 21 .314 86 .845 20 . 10 21 . 6 5 5 86 .417 20 . 10 21 . 9 9 0 86 . 173 20 . 10 22 . 331 85 .857 20 . 10 22 . 6 6 5 85 .652 20,. 10 22 . 9 9 9 85 . 387 20,, 10 23 . 331 85 .284 20,, 10 23 .662 85 . 0 3 9 20., 10 23 .994 84 . 8 8 5 2 0 ., 10 24 . 336 84 .773 2 0 . 10 24 . 6 7 5 84 .589 2 0 . 10 25 .007 84 .405 2 0 . 10 2 5 ,. 3 4 0 84 .282 2 0 . 10 25 .672 84,. 169 2 0 . 10 26..012 84 .067 2 0 . 10 26..341 83 ,.995 2 0 . 10 2 6 ..678 83 ,.974 2 0 . 10 2 7 ..008 84 ,,033 2 0 . 10 27 . 346 83 . 931 2 0 . 10 2 7 . 679 8 3 . 879 2 0 . 10 J99. 999. 0 2 27 . 482 84 . 123 3 0 . 10 27 . 821 81 . 407 2 0 . 10 28 . 143 8 0 . 612 2 0 . 10 28 . 481 7 9 . 971 2 0 . 10 28 . 818 7 9 . 349 2 0 . 10 29 . 152 78 . 799 2 0 . 10 29 . 486 78 . 2 7 0 2 0 . 10 2 9 . 826 7 7 . 811 2 0 . 10 3 0 . 155 77 . 434 2 0 . 10 3 0 . 493 77 . 169 2 0 . 10 3 0 . 825 7 6 . 893 2 0 . 10  31 . 154 31 .494 31 . 8 3 3 32 . 164 32 .504 32 .837 33 . 165 33 . 5 0 3 33 .841 34 .171 34 . 5 1 0 34 . 8 4 3 35 . 184 35 . 5 0 9 999  76 .668 76 . 373 76 .098 75 .914 75 . 7 0 0 75 .485 75 .362 75 . 199 74 .822 74 . 8 2 0 74 .718 74 .494 74 . 351 74 . 502 999  20 . 10 20 . 10 20 . 10 20 . 10 20 . 10 20 . 10 20 . 10 20 . 10 20 . 10 20 . 10 20 . 10 20 . 10 20 . 10 20 . 10  35 . 4 9 7 35 .826 36 . 162 36 . 5 0 0 36 . 8 3 3 37 . 172 37 .505 37 .835 38 . 173 38 .512 38 .,835 3 9 . 161 39 . 495 3 9 . 835 4 0 . 168 4 0 . 505 4 0 . 833 41 . 171 41 . 502 41 . 832 4 2 . 174 4 2 . 512 42. 840 4 3 . 175 4 3 . 507 4 3 . 843 4 4 . 176 44 . 510 44 . 843 4 5 . 180 4 5 . 507 4 5 . 842 46 . 177  74 .578 72 . 203 71 . 121 70 . 121 69 . 294 68 .538 67 .874 67 . 230 6.6,. 382 6 5 ..830 6 5 ,, 277 6 4 .,683 64 . 029 6 3 . 721 6 3 . 331 •62 .942 6 2 . 409 6 2 . 071 61 . 589 61 . 189 6 0 . 790 6 0 . 390 5 9 . 868 5 9 . 488 5 9 . 129 58 . 811 5 8 . 421 5 8 . 062 5 7 . 703 5 7 . 486 5 7 . 178 5 6 . 982 5 6 . 714  3 0 .. 10 2 0 .. 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10 2 0 . 10  46 46 47 47 47 48 48 48 49 49 49 50 50 50 51 51 999  0 3  .511 .850 . 175 .509 .841 . 177 .510 .844 . 177 . 508 .842 . 180 .511 .835 . 166 . 507  56 56 56 56 56 55 55 55 54 54 54 54 53 53 53 53 999  .721 .647 .318 .214 .017 .780 .502 . 255 .967 . 567 . 300 .043 .816 .578 .789 .857  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  49 . 701 3 0 . 47 .354 2 0 . 45 .864 2 0 . 44 .882 2 0 . 43 .981 2 0 . 43 . 233 2 0 . 42 . 424 2 0 . 41 .809 2 0 . 41 .223 2 0 . 4 0 . 557 2 0 . 4 0 .022 2 0 . 39 . 599 2 0 . 39 ,. 1 16 2 0 . 38 .592 2 0 . 38 ,. 292 2 0 . 37 .839 2 0 . 37 ,.559 2 0 . 37 ,.207 2 0 . 36 ,.926 2 0 . 36,.657 2 0 . 36,.336 2 0 . 36 ,,066 2 0 . 3 5 ,. 746 2 0 . 35 ,. 445 2 0 . 35 , 175 2 0 . 34 , 844 2 0 . 34 ,,656 2 0 . 34 ,. 376 2 0 . 34 . 167 2 0 . 33 ..856 2 0 . 33 . 730 2 0 .  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  0 4 59 .985 6 0 . 329 6 0 .658 6 0 ,.993 61 , 334 61 .666 , 61 ,.997 6 2 ,, 329 62 ,,667 62 ,.998 6 3 ,. 335 63 ,,674 64 ,,004 64 . 333 6 4 .,668 65 ,,002 6 5 ., 335 6 5 .,672 6 6 .,010 66 ., 343 6 6 .,678 67 .,009 6 7 .,341 67 .,676 68 .,01 1 68 .,344 68 . 676 69 .,01 1 69 ., 346 69 . 682 70. 006  70. ,335 70. ,672 71 .007 . 71 .337 . 71 ,679 , 72.,007 72 ., 349 72 ..678 73. .008 73 ., 350 73 ,.681 74,.022 74..351 74 .690 75 .009 75 .359 75 .684 76 .014 399  33. 410 33. 191 32 . 768 32. 539 32. 279 32 . 142 31 .708 . 31 . 520 31 . 292 31 . 194 30. .873 30. .735 30. ,567 30. .419 30. .212 30. . 103 30 .088 29 .921 999  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  2 1 1.141. 562.462.614.477. 14 10.0E-•10 RUN #2, TEMPERATURE = 22 C 0.4353 8 79.3 3 . 343 3. 6 . 125 2. 1 21 . 7 . 150 20.2 . 175 38 .9 41 .9 57. 4 .200 56.3 69.2 .225 70. 8 82 . 1 .250 80.5 .275 89.7 90. 5 .300 97. 1 96. 9 19.0 18. 977 96. 094 30. 10 93 . 502 20. 10 19 . 312 19. 652 92.,547 20. 10 19 ..986 91 .917 . 20. 10 20. .318 91 ,471 , 20. 10 90. .994 20. 10 20. .653 90. ,680 20. 10 20. .988 21 .321 . 90. .406 20. 10 21 ,653 . 90. . 194 20. 10 89 ..879 20. 10 21 .988 . 89 ..636 20. 10 22.,326 89. .495 20. 10 22..663 89. .293 20. 10 22..996 89, .070 20. 10 23. .332 88. .919 20. 10 23. .664 88 .767 20. 10 23, .999 24 ,. 329 88 .605 20. 10 88 . 373 20. 10 24 .662 24 .999 88 .241 20. 10 25 . 334 88. . 151 20. 10 999 999 0 2 25 . 332 88 .206 30. 10 25 .647 85 .425 20. 10 25 .982 84 .212 20. 10 26 .319 83 . 294 20. 10 26 .652 82 . 599 20. 10 26 .987 82 .068 20. 10 27 .324 81 .587 20. 10 27 .661 80 .862 20. 10 27 .994 80 . 392 20. 10 28 .331 80 .013 20. 10 79 .654 20. 10 28 .667 79 .346 20. 10 28 .999 79 .039 20. 10 29 . 333  29. 30. 30. 30. 31 31 31 32 32 32 33 33 33 999.  669 004 341 668 .007 . 337 .674 . 006 . 339 . 676 . 016 . 340 . 672  78. 833 78 . 515 78. 349 78. 133 77 . 948 77 . 670 77 . 526 77 . 238 77 . 073 76 . 816 76 . 559 76 . 475 76. 300 999.  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20.  10 10 10 10 10 10 10 10 10 10 10 10 10  76. ,702 74 ..686 73. ,666 73. .032 72..409 71 .937 , 7 1 .446 7 1 .087 70 . 738 70 .419 70 . 152 69 . 782 69 . 454 69 .267 69 . 142 68 .813 68 .668 68 .492 68 . 326 68 . 190 68 .024 67 .817 67 .702 67 .608 67 .401 67 . 204 66 .916 66 . 720 66 .503 66 .317 66 .212 66 . 127 66 .083 66 .009  30. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20, 20, 20, 20, 20 20. 20 20 20 20 20 20  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 . 10 , 10 , 10 , 10 , 10 . 10 . 10 . 10 . 10 . 10 . 10 . 10 . 10  0 3 33 ..978 34 .304 34 ..635 34 .954 35 .281 35 .609 35 .936 36 .268 36 .587 36 .912 37 .237 37 . 560 37 .883 38 .214 38 .538 38 .863 39 . 186 39 . 509 39 .839 40 . 170 40 .494 40 .818 41 . 138' 41 .461 41 .786 42 . 109 42 .439 42 . 763 43 .080 43 .409 43 .733 44 .051 44 . 380 44 .704  45..025 45 , .353 45 . .663 999 .  65,.772 20. 10 65 , .616 20. 10 65 .419 20. 10 999 ,  4 45 . 65,.345 30. .650 45..987 63 , .869 20. 46., 322 63 . ,002 20. 46 , ,652 62,.420 20. 46 . ,991 61 .930 , 20. 47 ,326 . 61 . .622 20. 47 ,659 , 61 . , 223 20. 47 . ,994 60,, 834 20. 48.,331 60,.639 20. 48 .663 60,.311 20. 48 .998 59,.993 20. 49,. 3 3 0 59 . 788 20. 49 .668 59 .439 20. 59 .264 20. 50 .004 59 . 140 20. 50 .338 58 .751 20. 50 .669 51 .002 58 .677 20. 51 . 337 58 .482 20. 51 .669 58,.367 20. 52 .001 58,. 223 20. 52 . 334 58 . 108 20. 52 .675 57 .841 20. 53 .003 57 .707 20. 53 . 337 57 . 593 20. 53 .664 57 . 509 20. 54 .000 57 .425 20. 54 .338 57 .219 20. 54 .668 57 . 166 20. 55 .002 57 .021 20. 55 . 335 56 . 785 20. 55 .673 56 .681 20. 56 .005 56 .496 20. 56 .339 56 .402 20. 56 . 267 20. 56 .677 57 .007 56 . 142 20. 57 . 345 56 .079 20. 57 .686 55 .913 20. 58 .013 55 . 779 20. 999 999  5  57 .990 58 .318 58 .653  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  55 .685 30. 10 54 . 444 20. 10 53 .884 20. 10  58. 992 59. 324 59. 657 59. 993 60. 327 60. 6 6 5 60.,993 61 .331 61 . ,664 61 . .998 62. 328 ,664 62 . 62 .9 9 3 63 . ,330 63 , ,670 63 , ,995 64 ,329 , 64 , ,662 64,.994 65 , .330 65,.661 66 .000 66 .336 66 .666 67 .007 67 .336 67 .681 68 .009 68 .340 68 .678 69 .01 1 69 .340 69 .671 70 .006 70 .341 70 .675 71 .012 71 .343 71 .680 7 1.987 72 .325 72 .652 72 .995 73 . 322 73 .660 73 .996 74 .327 74 .662 75 .002 75 .337  53 .365 20. 10 52. 938 20. 10 52. 592 20. 10 52. 347 20. 10 52. 052 20. 10 51 .787 20. 10 51 .482 20. 10 51 .309 20. 10 51 . ,085 20. 10 50.,820 20. 10 50.,617 20. 10 50.,403 20. 10 50.,291 20. 10 50.. 158 20. 10 50.,015 20. 10 49 . .832 20. 10 49..659 20. 10 49,.445 20. 10 49,. 323 20. 10 49,. 109 20. 10 48 .926 20. 10 48,.722 20. 10 48,.498 20. 10 48 .426 20. 10 48 . 355 20. 10 48 . 192 20. 10 48 .161 20. 10 48 .008 20. 10 47 . 784 20. 10 47 . 723 20. 10 47 .631 20. 10 47 .610 20. 10 47 . 549 20. 10 47 .569 20. 10 47 .427 20. 10 47 .345 20. 10 47 .294 20. 10 47 .171 20. 10 47 .059 20. 10 47 .006 30. 10 46 .934 20. 10 46 . 761 20. 10 46 .648 20. 10 46 . 557 20. 10 46 .444 20., 10 46 . 372 20., 10 46 . 240 20.. 10 46 . 239 20., 10 46 . 157 20., 10 46 . 147 20,. 10  75.,504 999 ,  46 .162 20. 10 999.  0 6  46 . , 149 30. 75,,495 75 , 824 45 . , 124 20. 76,, 150 44 . .669 20. 76 , .488 44 , . 152 20. 76,.829 43 , ,929 20. 77,. 161 43.,697 20. 77 , 4 9 3 43 . , 364 20. 77 ,828 , 43 . 253 20. 78 , . 168 ,919 20. 42 . 78 . 4 9 5 42 . .739 20. 78 , .829 ,649 20. 42 . 79,. 166 42 . , 335 20. 79 , . 507 42 , 285 20. 79 . 836 ,094 20. 42 , 41 ,923 , 80,,171 20. 41 . 80,.498 ,825 20. 4 1,653 . 80,.836 20. 81 . , 167 41 .666 , 20. 81 .497 , 41 ,516 . 20. 81 .835 , 41 , . 263 20. 82 , . 165 4 1..306 20. 82 . 501 4 1. . 297 20. .834 82 , 4 1,;198 20. 83 , . 157 4 1,,1 1020. 83 .491 40,,868 20. 83 , .826 40,, 798 20. 84,. 164 40,,667 20. 95 . .499 37 .024 , 20. 95,,835 37 . 168 20. .814 20. 96 , . 165 36 . 96 , 501 36..572 20. 96 , .838 36 . 583 20. 97 , . 178 36 , . 289 20. 97 .514 , 36..393 20. 97 , .857 36 . ,251 20. 999 , 999 .  0 99  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ib 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  2 1 1.141 . 5 6 2 . 4 6 2 . 6 1 4 . 4 7 7 . 14 10.0E-10 RUN #3: TEMPERATURE=22 C 7 9 4 . 0 3.343 0.4760 .150 3.0 12.0 .175 2 6 . 5 35.1 .200 49.2 55.2 .225 6 5 . 8 70.3 .250 7 9 . 0 84.1 .275 89.3 91.9 .300 97.4 9 8 . 6 16.0 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 2 0 .666 9 0 .775 20. 10 21 .001 9 0 .638 20. 10 21 .335 9 0 .471 20. 10 21 .666 9 0 . 365 20. 10 22 .000 90.. 3 3 0 20. 10 999 999 . 0 2 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 .0 0 3 80. 949 20. 10  27 27 28 28 28 29 29 29 30 30 999  .336 .670 .008 .341 .678 .009 .339 .678 .01 1 . 340  80 .683 20. 80 . 305 20. 80 .070 20. 79 .825 20. 79 .569 20. 79 .436 20. 79 . 180 20. 79 .097 20. 78 .781 20. 78 .729 20. 999  10 10 10 10 10 10 10 10 10 10  30 .482 30 .818 31 . 153 31 .486 31 .820 32 . 155 32 .488 32 .822 33 . 158 33 .498 33 .835 34,. 175 34 .501 34 , .838 35 , . 169 35 , .504 35,.839 36 , . 169 36 , .510 36,.849 37 , . 181 37 . ,517 37..846 38., 180 38 , ,515 38 . ,852 39 .. 184 39 .514 39 .,847 40. 180 40..514 40. 847 41 .178 41 . ,513 41 .842 42. 177 42. 524  78 .904 30. 77 .075 20. 76 . 101 20. 75 .382 20. 74 .714 20. 74 . 107 20. 73 .633 20. 73 .046 20. 72 .684 20. 72 .392 20. 71 . .999 20. 71 .646 20. 71 .356 20. 70..993 20. 70,.692 20. 70..390 20. 70,, 130 20. 69 , .777 20. 69.,547 20. 69 ..327 20. 69., 138 20. 68..887 20. 68 . .739 20. 68.,570 20. 68.. 258 20. 68., 120 20. 67 . .982 20. 67 . 782 20. 67 . .583 20. 67 . .414 20. 67 . .418 20. 67 .341 20. 67. 264 20. 67.. 156 20. 66. 947 20. 66. 798 20. 66 .679 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  999.  42.. 494 66 42 . 8 2 2 65 43 ,, 154 64 43 , 4 8 3 63 43,.822 63 44 , 163 62 44 . , 495 61 44 . , 828 61 45 ., 163 60 45 ., 4 9 5 6 0 45 .. 824 59 46,,167 59 46,, 504 59 46,, 8 4 2 58 47 , 174 58 47 , ,505 58 •47 . 8 3 9 58 48 . ,171 58 48 . 504 58 48.. 8 4 0 57 49 .. 173 57 49 .. 507 57 49 . 842 57 50.. 175 57 56 50.. 507 56 50..839 51 , 168 56 51 , 5 0 8 56 ,84 1 51 , 55 , 174 55 52 . 52.,513 55 54 . 5 55 999. 999  0 3  999 .802 30. . 368 20. .289 20. .7 19 20. .006 20. . 507 20. .937 20. . 3 2 6 20. .847 20. .419 20. .910 20. .624 20. .237 20. .890 20. .676 20. .44 1 20. .431 20. .318 20. . 175 20. .910 20. . 746 20. .542 20. . 3 8 9 20. .093 20. .889 20. .675 20. .421 20. .114 20. .961 20. . 778 20. .716 20. . 1 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  55 . 105 30. 54 . 224 20. 53 . 578 20. 52 .972 20. 52 . 376 20. 52 .065 20. 51 .602 20. 51 , . 159 20. 50 .868 20. 50 .476 20. 50 . 164 20. 49 .731 20.  10 10 10 10 10 10 10 10 10 10 10 10  0 5  54 , ,490 54 . ,829 55 . 159 55.. 4 9 9 55.,834 56.. 164 56..496 56.,827 57.. 166 57 . .498 57 . 8 3 5 58 . 175  58 . .508 49 .481 20. 49 . 262 20. 58 . .840 59 . 176 48 .890 20. 59.,506 48 .833 20. 59.,840 48 .604 20. 60., 172 48 .496 20. 48 . 358 20. 60.. 504 60.,837 48 .342 20. 61 . , 174 48 .112 20. 61 . .512 47 .933 20. 61 . .840 47 .917 20. 62 . , 172 47 .952 20. 62., 504 47 .834 20. 62 .829 47 . 564 20. 63 . .171 47 . 365 20. 63 . .501 47 .085 20. 63 . .842 46 .814 20. 64., 173 46 .859 20. 64 . ,503 46 .813 20. 64 . .838 47 .010 20. 65.. 160 47 . 157 20. 65..499 47 . 192 20. 65 .845 47..216 20. 66 . , 173 47 . 169 20. 66. 505 47.. 153 20. 66..840 46 .995 20. 67., 177 46 .857 20. 67.,512 46..851 20. 67.,836 46 .520 20. 68. 176 46 . 503 20. 68., 508 46 .467 20. 68 . ,846 46 .522 20. 69.. 176 46 .567 20. 69.,504 46 . 551 20. 69..842 46 . 525 20. 46 .610 20. 70., 178 46 .675 20. 70..513 46.. 751 20. 70.,846 71 . 172 46 .755 20. 71 . 46,.770 20. .510 71 . ,841 46,.774 20. 72..010 46,.827 20. 999. 999,  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  0 6 71 .984 72. 323 72. 661 72. 9 8 5 73..319  46..979 30. 46,. 106 20. 45..651 20. 45,. 206 20. 45,.056 20.  10 10 10 10 10  73..656 73..995 74,.327 74,.660 74,.991 75,, 332 75 , .667 75,,995 76,.329 76,.668 77 ,005 , 77 .333 , 77,.672 78,.008 78 . 335 78 . .669 79,.008 79..341 79 .672 8 0 .003 80,. 333 80,.674 81 .006 81 . , 337 81 .667 . 82 .007 82 .335 82 .673 83 .001 83 .330 83..662 84 .003 , 84..335 84 .672 85..002 85 .337 85..670 86..002 86 .331 86..674 87 .012 87 ,341 87 .674 88 .013 88 .348 88 .687 89 .016 89 .345 89 .683 9 0 .021  44 . .855 20. 44.,746 20. 44 . .637 20. 44 . .467 20. 44 . 368 20. 44 . 197 20. 44 . ,078 20. 43.,969 20. 43..911 20. 43.,852 20. 43.,712 20. 43.,573 20. 43 . ,453 20. 43., 385 20. 43.. 164 20. 43., 126 20. 43..088 20. 43..060 20. 42.,931 20. 42 . ,913 20. 42 . , 754 20. 42 . , 746 20. 42., 596 20. 42..589 20. 42.,470 20. .441 20. 42 . 42 . , 343 20. 42 , 193 20. 42 , 175 20. 42 , .005 20. 41 .917 , 20. 41 .858 , 20. 41 ,820 , 20. 41 .680 . 20. 41 ,398 , 20. 41 ,320 . 20. 41 , . 241 20. 41 ,020 . 20. 40.,840 20. 40,,761 20. 40.,641 20. 40,.481 20. 40..311 20. 39,.917 20. 39,.767 20. 39,.597 20. 39 .447 20. 39,,419 20. 39,. 188 20. 39 .089 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  90.. 357 90..686 91 .014 91 . 346 91 .688 92 .007 92 . 346 92 .673 93 .014 93 . 346 93 .684 94 .004 999.  0 99  38 .908 20. 38 .799 20. 38. 721 20. 38 . 551 20. 38,,533 20. 38 . 384 20. 38..274 20. 38 , . 186 20. 38.. 137 20. 37..947 20. 37 .909 . 20. 37 .780 . 20. 999.  10 10 10 10 10 10 10 10 10 10 10 10  1 2 1.141. 5 6 2 . 4 6 2 . 6 1 4 . 4 7 7 . 14 10.0E- 10 RUN #4 ; TEMPERATURE=22.0 C 7 9 7 . 0 0 3.8795 0.4150 . 150 2.4 1. 5 . 175 24. 1 22.6 .200 46.7 46 . 3 . 225 64.8 64.2 .250 80. 2 79. 1 . 275 90.8 90. 4 .300 98 .7 98.9 18.0 17 .986 ,317 30. 10 91 . 18.,319 89 . .271 20. 10 88 . 353 20. 10 18.,654 18.,992 87 , .831 20. 10 19., 325 87 , .320 20. 10 19,,660 87 , .052 20. 10 19 .996 , 86,.592 20. 10 20,, 3 3 0 86 . 233 20. 10 20,.662 86,.027 20. 10 21 . ,001 85,.739 20. 10 21 , . 335 85,.563 20. 10 21 . ,667 85,.418 20. 10 22 . ,004 85,. 161 20. 10 22 . ,341 85,.005 20. 10 22,.671 84 .829 20. 10 23 , ,004 84 , .745 20. 10 23,. 342 84 , .589 20. 10 23 , .676 84 .484 20. 10 999 , 999, 0 2 23,.482 84 .481 30. 10 23,.821 82 .830 20. 10 24 , . 147 82 . 185 20. 10 24 .482 81 . 785 20. 10 24 .815 81 .436 20. 10 25 . 151 81 .219 20. 10 25 .483 80 .941 20. 10 25 .818 80 .765 20. 10 26 . 157 80 .498 20. 10 26 .491 80 .291 20. 10 26 .823 80 . 145 20. 10 27 . 161 80 .020 20. 10 27 . 487 79 .802 20. 10 27 .821 79 .809 20. 10 28 . 152 79 .673 20. 10 28 . 491 79 .670 20. 10  28. 824 79.,484 20. 79..429 20. 29., 153 29.,490 79..406 20. 79,,301 2 0 . 29. 826 79,, 175 20. 30. 157 79.,253 20. 30.,495 79,,219 20. 30..829 , 167 79.. 155 20. 31 . 79,. 162 20. 31 , ,508 79,. 159 20. 31 , .840 79,. 145 20: 32 , . 175 78 .999 20. 32 .503 999 999.  10 10 10 10 10 10 10 10 10 10 10 10  44 . 181 44 .511 999.  72 72 999  0 99  0 3  32 .483 3 2 . 829 33. 163 33. 495 33. 826 34. 162 34. 499 34. 838 35. 168 35. 5 0 0 35. 837 36. 167 36. 496 36. 827 37. 163 37 .501 37. 826 38. 166 38.,495 38.,831 39., 175 39 , ,501 39 , ,837 40.. 169 40,.501 40,.842 41 , . 171 41 , .510 41 , .850 42 , 178 42 .514 42 .845 43 . 179 43 .515 43 .846  79. 125 3 0 . 10 78. 369 20. 10 78. 131 20. 10 77.,974 20. 10 77 . ,797 20. 10 77..559 20. 10 77 . ,311 20. 10 77.. 1 142 0 . 10 76.,876 2 0 . 10 76., 790 20. 10 76.,623 20. 10 76..415 20. 10 76,.411 20. 10 76 , . 152 20. 10 76,.077 20. 10 75,.981 20. 10 75 .773 20. 10 75 .668 20. 10 75 .409 20. 10 75 . 334 20. 10 75 .086 20. 10 74 .959 20. 10 74 .803 20. 10 74 .717 20. 10 74 .438 20. 10 74 . 323 20. 10 74 . 155 20. 10 73 .958 20. 10 73 .731 20. 10 73 .594 20. 10 73 .275 20. 10 73 . 189 20. 10 72 .758 20. 10 72 .591 20. 10 72 .271 20., 10  cn O  2 1 1. 141 . 5 6 2 . 4 6 2 . 6 1 4 . 4 7 7 . 14 10.0E-10 RUN #5; TEMPERATURE=22 C 7 9 0 . 0 3.343 0.3994 1 .9 . . 150 3,.7 . 175 24 .0 26 , .3 . 2 0 0 48 . 1 47 , 1 . 225 66 .2 64 ,8 .250 80,.6 79 , 7 . 275 91 , .3 90,, 7 98,.8 98 ,.0 .300 16.0 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 .. 3 6 0 20. 10 66 ,.802 20. 10 20 .002 20 . 333 66..438 20. 10 66 . 20 .666 .053 20. 10 21 .000 65 ..739 20. 10 21 .334 65..283 20. 10 64 ..939 20. 10 21 .668 22 .006 64..778 20. 10 999 999. 0 2 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 . 3 3 0 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  27. 007 27 .349 27 .681 28.,006 28. 341 28.,677 29 .,015 29 .,347 29.,681 30.,018 30. 350 30.,680 999.  48.,663 20. 48 .,351 20. 48. 112 20. 47 .691 20. 47.,320 20. 47 ., 100 20. 46. 912 20. 46.,744 20. ,494 20. 46 , 46 ,,265 20. 45,,985 20. 45 , ,868 20. 999 .  10 10 10 10 10 10 10 10 10 10 10 10  45,.871 30. 43,.077 20. 41 , .647 20. 40,.624 20. 39,,702 20. 38 . .883 20. 38 . 165 20. 37 , .558 20. 36 , .932 20. 36,.469 20. 35,.843 20. 35 .450 20. 34 .997 20. 34 .676 20. 34 . 274 20. 33 .810 20. 33 .571 20. 33 .239 20. 32 .847 20. 32 .628 20. 32 .378 20. 32 .057 20. 31 .716 20. 31 .517 20. 31 .318 20. 30 .957 20. 30 .534 20. 30 .345 20. 30 .014 20. 29 .764 20. 29 .454 20. 29 .204 20. 29 .096 20. 29 .060 20. 28 .871 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  42. 179 42. 512 999.  o 4  0 3  30,,488 30..829 31 . 164 31 . .498 31 , .840 32,,171 32..502 32..846 33 . , 178 33 , ,510 33,,843 34,, 179 34 ,,515 34 ,,847 35,, 177 35,.511 35 .843 36 . 181 36..513 36..849 37 . 178 37 . .514 37..844 38 , . 180 38 .514 38 .842 39 . 176 39 .515 39..842 40,. 178 40,.507 40,.840 41 , . 182 41 , .513 .849 41 ,  28 ..418 20. 10 28 .,341 20. 10 999.  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 . 3 7 0 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 17 .789 20. 10 50,, 181 17 . 747 20. 10 50,,513 17 .634 20. 10 50,,848 51 , 173 17 . 356 20. 10 17 . 152 20. 10 51 , ,513 51 , ,852 17 .040 20. 10 52 ,, 180 16 . 7 9 3 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  0 5  54 .491 54,.825 55 . 166 55 .497 • 55 .828  15 14 13 12 12  . 558 30. .079 20. .239 20. .664 20. .181 20.  10 10 10 10 10  56.. 157 56.,495 56 ..831 57.. 161 57 ..492 57..830 58 . 164 58.,496 58 .,832 59., 164 59,,500 59.,833 60,. 167 60,,495 60..829 61 . 161 61 .504 61 .836 62 . 170 62 .505 62 .837 63.. 174 63 . 509 63 . .832 64 ,. 173 64 ,.515 64 ..838 65 . 175 65..507 65 .843 66 . 176 66 .514 66 .841 67 .171 67 . 509 67 .844 68 . 173 68 .507 68 . 8 4 0 69,. 165 69.. 505 69..835 70 . 177 70 . 506 70 . 838 71 . 180 71 .510 71 .848 72 . 182 72 .514 72 . 849  1 1.627 . 20. 1 1 .245 . 20. 10..974 20. 10..563 20. 10..374 20. 10..083 20. 9..742 20. 9. 502 20. 9. , 273 20. 9.,033 20. 8 .824 . 20. 8..483 20. 8 .314 . 20. 8 . 136 20. 8..008 20. 7..749 20. 7,.792 20. 7 . 583 20. 7 .496 20. 7 . 256 20. 7 . 169 20. 7 . 102 20. 7 .045 20. 6 .888 20. 6 . 769 20. 6..569 20. 6..412 20. 6 . 386 20. 6.. 278 20. 6 .089 20. 5 .982 20. 5 .853 20. 5 .635 20. 5 .609 20. 5 .593 20. 5 .444 20. 5 .378 20. 5 .423 20. 5 .204 20. 5 .220 20. 5 .243 20. 5..096 20. 5 .068 20. 4 .870 20. 4 . 732 20. 4 .715 20. 4 .679 20. 4 . 57 120. 4 .585 20. 4 .620 20. 4 .634 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  73., 178 4 .568 . 20. 73..517 4.,460 20. 73..862 4 .482 . 20. 74 ., 192 4 ,243 . 20. 74 ..523 4 . 197 20. 74 .,851 4 ,212 . 20. 75., 190 4.,216 20. 4, . 138 20. 75., 5 3 0 75.,857 4 .204 . 20. , 187 76 . 4 . 158 20. 76., 5 2 0 4 . 132 20. 76 . 4 .115 . , 860 20. 77 . , 193 4, . 180 20. 77 . ,515 4 . 186 20. 77..856 4.,200 20. 4. , 175 20. 78., 180 78,.517 4,. 169 20. 78 , .855 4 .213 20. 79,. 184 3..964 20. 79,.512 3..786 20. 79..852 3..779 20. 3 .682 20. 80.. 185 3 .646 20. 80..516 80 .848 3 .579 20. 81 . 194 3 . 398 20. 81 .530 3 .463 20. 81 , .855 3.. 378 20. 82.. 191 3 . 392 20. 82 .519 3 .254 20. 82 .858 3 . 146 20. 83 . 191 3 .201 20. 83 . 522 3 .206 20. 83 .863 2 .914 20. 84 . 195 2 .644 20. 84 .534 2 .668 20. 84 .864 2 .653 20. 85 . 202 2 .677 20. 85 .533 2 .752 20. 85 .862 2 .747 20. 86 .204 2 .608 20. 86 .535 2 .714 20. 86 .867 2 .668 20. 87 . 199 2 .540 20. 87 .534 2 .646 20. 87 .867 2 .549 20. 88 . 201 2 .553 20. 88 . 524 2 .325 20. 88 .875 2 .438 20. 89 .210 2 . 158 20. 999 999 0 99  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  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 .5 2.0 17.9 24 .4 150 175 41.8 48. 5 63 . 3 67 .5 200 225 78.3 82. 4 93 .8 2 5 0 90.8 9 8 . 1 99 .9 275 :o.o 93 .365 3 0 . 10 19. 982 20. 310 90. 331 2 0 . 10 88..850 20. 10 20.,642 88 ..027 20. 10 20..984 21 ,317 . 87 .. 339 2 0 . 10 21 .651 , 86 .,671 .20. 10 21 ,980 , 86,,066 20. 10 .319 22 , 85..661 2 0 . 10 22 . .646 85 , ,381 2 0 . 10 22 . .979 84 . ,906 20. 10 84 ., 532 20. 10 23 , .316 23 .655 84 .. 198 20. 10 84 . .018 20. 10 23..989 .697 20. 10 24 . .319 83 . 24..651 83 . .537 20. 10 24 , .987 83 , 337 20. 10 25..315 83..057 20. 10 82 . .967 20. 10 25 .651 9999 9999  )  2 33 33 34 34 34 35 35 35 36 36 36 37 37 37 38 38 38  . 501 .813 . 146 . 480 .813 . 155 .489 .821 . 147 .487 .821 . 149 .482 .817 . 152 .489 .825  80 .961 3 0 . 78 .089 2 0 . 76 .858 2 0 . 76 .075 20. 75 . 475 2 0 . 74 .954 20. 74 . 343 20. 74 .018 20. 73 .593 20. 73 .327 20. 73 .001 20. 72 .788 20. 72 .453 20. 72 . 238 20. 72 .024 20. 71 .942 20. 7 1.829 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  39. 147 71 .750 39 .488 71 .575 39. 825 71 .554 71 .533 4 0 . 159 71 .441 4 0 . 492 71 .523 4 0 . 825 9999. 9999.  20. 20. 20. 20. 20. 20.  10 10 10 10 10 10  i  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 66. 217 20. 10 53 .654 53. 9 9 0 65.,771 20. 10 54 . , 321 65..610 20. 10 54 . 65..369 20. 10 .652 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 1520. 10 64 , 58 ,.321 . 136 20. 10 58 ,.653 64.. 179 20. 10 58 .987 64 . 161 20. 10 64.. 152 20. 10 59 .320 64 .092 , 59 .657 20. 10 59 .993 64 .073 . 20. 10 60 . 323 63 .883 20. 10 63,.700 20. 10 60 .661 63..621 20. 10 60 .993 61 . 329 63 . 592 20. 10 61 .661 63 .604 20. 10 61 . .998 63 .534 20. 10 62 . 329 63 . 556 20. 10 63 .466 20. 10 62 .666 63 .000 63 .518 20. 10 63 .337 63 .418 20. 10 63 .664 63 . 3 7 0 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 . 2 2 2 . 1 5 2 . 9 7 9 . 9 9 9 . 9 9 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 6 5 . 5 60.2 .225 79.1 75.4 .250 91.4 87.8 .275 98.7 95.4 17.0 16,.974 95 .983 3 0 . 10 17,, 309 92 .717 20. 10 17 , .647 91 . 526 2 0 . 10 17,.977 90..500 2 0 . 10 18 , .314 89 .655 2 0 . 10 18,.640 88 .915 2 0 . 10 18,.981 88 . 282 2 0 . 10 19.. 321 87 .801 . 2 0 . 10 19,.660 87 .220 . 2 0 . 10 19..989 86..713 2 0 . 10 86 . 309 2 0 . 10 20,.317 86..004 2 0 . 10 20..649 85.. 768 2 0 . 10 20..989 21 , .323 85 .554 2 0 . 10 21 , .649 85,.364 20. 10 21 .983 85 . 191 20. 10 22,.317 84..906 2 0 . 10 22 ..651 84 , . 764 20. 10 399. 9999. 67 . .994 68..321 68 .,660 68.,993 69..324 69.,656 69 ..988 70., 325 70..653 70,,987 71 . .322 71 . ,659 71 , ,990 72., 326 72. 658 72.,992 73,,320  52 ..901 30. 50..455 20. 49..461 20. 48 ..967 2 0 . 48 ..494 2 0 . 48 ..040 2 0 . 47 .790 . 20. 47 .570 . 20. 47 .269 . 20. 47 .090 . 20. 46 ..890 2 0 . 46,.670 2 0 . 46 ,.451 2 0 . 46,.261 .20. 46.. 133 2 0 . 46 .. 126 2 0 . 46,.070 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  73. 6 5 9 46. 084 2 0 . 73 .993 46 . 148 2 0 . 74 .321 45. 990 2 0 . 45 .841 2 0 . 74 .658 74 .997 45. 692 2 0 . 75..326 45 .646 2 0 . 75 ..665 45 .588 2 0 . 75..996 45. 531 2 0 . 76 .. 329 45., 525 20. 76 .,667. 45.. 355 2 0 . 77 ,001 . 45,, 359 2 0 . 77 ,335 . 45.,363 2 0 . 77 .664 . 45 ,, 276 2 0 . 78 ..000 45 ,, 391 2 0 . 78,.331 45..426 2 0 . 78 .665 45,, 125 2 0 . 78 .994 45,.089 2 0 . 79 . 332 45.. 163 20. 79 .664 45,.096 2 0 . 44 .978 20. 79 .999 44 .890 20. 80 . 329 44 .935 2 0 . 80 .662 45 .011 2 0 . 80 . 9 8 9 44 .964 2 0 . 81 . 322 45 .007 2 0 . 81 .667 81 .986 44 .973 2 0 . 44 .904 2 0 . 82 . 329 82 .661 44 .898 2 0 . 44 .820 2 0 . 82 .996 44 . 742 2 0 . 83 .331 44 . 777 20. 83 .662 84 .002 44 .668 20. 84 .330 44 .653 20. 44 .707 20. 84 .667 44 .577 20. 85 .01 1 44 .463 20. 85 . 322 9999. 9999. 1 99  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  2 1 0.991.293. 799.999.999.99 10.0e-10 RUN #8; TEMPERATURE=29.5 C 7 81.7 3.343 0.4061 .125 2.0 2.1 .150 21.8 23.5 . 175 46.3 46. 1 .200 64.7 64.5 .225 80.1 80.4 .250 91.3 92.0 .275 98.4 98.6 16.5 16 ..502 16,,810 17,. 154 17 .494 17 .824 18 . 154 18 .491 18 .826 19 . 169 19 .503 19 .832 20 . 163 20 .496 2 0 ,.827 21 ,. 171 21 ,.499 21 ,.835 22 .. 170 22,.502 22 ,.837 2 3 .. 165 23 ,.497 2 3 ,.832 24 . 170 24,. 502 24 .836 25 ,. 166 25,.504 25 ,.837 26,. 176 26 ..509 26,.839 27 . 168 27 ,.510 27 ,.844 28 .. 175 28 , 504  91 ,,291 8 3 ., 194 78 ,.823 7 5 ,,856 73,.369 71 ,.563 70,.061 68,.823 67 .940 66,.926 66.. 157 6 5 ,.693 6 5 ,.229 64,.399 64 ,.014 6 3 ,.631 63 ,. 197 62,.865 62 .563 62,.352 61 ,.909 61 ,.475 61 ,. 387 6 0 ,.881 6 0 ,.813 6 0 ,.796 6 0 ,.647 6 0 ,,497 6 0 ., 338 6 0 ,, 188 59 ,.988 5 9 ..839 5 9 ,,640 5 9 .. 387 58..861 58 ,,601 58 ,,218  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  28.,847 2 9 ., 179 2 9 .,513 2 9 .,841 3 0 ., 176 3 0 .,512 3 0 .,845 31 ., 176 31 .,511 31 .,852 32,, 186 32.,514 32 .,844 3 3 ,, 179 3 3 ,,514 3 3 ,,842 34,, 179 34,,512 34 ,.850 35 , 185 35 ,512 3 5 ,.847 36 ,. 180 36,,518 36,,851 3 7 ., 183 37 ,.516 3 7 ,.852 38 ,. 189 38 .525 38 ..858 3 9 ,. 192 3 9 ,.532 3 9 ,.858 4 0 ,. 194 4 0 ,.524 4 0 ,.862 41 .. 193 41 ,,520 4 1.857 , 4 2 ,. 188 42 ,,524 4 2 ,.848 999.  58 ,. 108 58 ,.051 57,.708 57,.610 57 ,.634 57 ,.372 57,.294 57,. 156 57 ,. 169 57,. 150 57 .113 56 .781 56 .633 56 .585 56 .567 56 .500 56 .503 56 .415 56 . 285 56 .207 56 .069 56 .072 56 .055 55,.955 55 .806 55 .667 55 .549 55 .490 55 .585 55 .425 55 .296 55,. 136 55,. 108 55 .021 54 .963 54 .977 54 .877 54 .728 54,.753 54 .603 54 ,.556 54 .376 54 .482 999  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  20. 20. 20. 20.  10 10 10 10  0 2 4 3 ,.005 43 ,.321 43 ,.659 43 ,.995  53 48 46 44  .615 . 528 . 124 .941  44 . 330 44 . 657 4 5 . 001 4 5 . 343 4 5 . 671 4 6 . 004 46 .,329 46 .,671 47 .,004 47 ., 340 47 ..673 48 ..003 48 ,.336 48 ..670 4 9 ,.006 49 ., 348 49 ..679 5 0 ,,012 5 0 .,347 5 0 .,666 51 .,005 51 ., 338 51 ,,670 52 ,,014 52 ,, 333 52,,667 53 ,.003 53 ,. 332 53 ,.667 54,.004 54,.335 54 ..670 55 ..004 5 5 ,.340 55 ,.668 56 ,.009 56 ,. 343 56 .678 57 ,.005 5 7 ,.338 57 ,.674 58 .009 58,.341 58 .671 59 .012 5 9 ,. 343 59 .684 6 0 .008 6 0 . 344 6 0 .675  4 3 .,758 4 2 .,923 42 ., 227 41 ,. 399 4 0 ,, 787 4 0 ,.358 39 ,,654 39 , 152 38,.814 38 ,639 38 .565 38 . 553 38 .449 38 . 345 38 .27 1 38 . 104 38 .01 1 37 ,.825 3 7 ,.599 3 7 ,.588 37 . 280 37 . 186 37 . 123 36 .956 37 .007 36 .953 36 . 9 0 0 36 .837 36 .855 36 .943 36 .951 36 . 867 36 .865 36 .923 36 .932 36 .979 37 . 109 36 .995 37 .044 37 .031 36 .978 36 .914 36 . 8 1 0 36 .849 36 .815 36 .833 36 .626 36 . 737 36 .714 36 .681  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20.  10 10 10 10 1.0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  61 . ,009 61 .346 61 .677 62. 0 0 9 6 2 . 341 62. 678 63. 008 63. 345 63. 678 64 .017 64 .344 64 .678 65 .0 0 9 65.,342 999.  36,.689 36,,605 36,.725 36,,611 36..629 36..636 36..573 36 . .560 36.,548 36 . ,453 36 . ,462 36 .296 36..356 36 , .201 999 ,  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10  3I 65 .510 65,.825 66,. 167 66,.503 66 ..846 67,. 175 67 , 501 67 , ,841 68 . 170 68 . .516 69,.4 73 .299 73,.620 73,.958 74 . 293 74 .624 74 .956 75 .292 75 .624 75 .960 76 .291 76 .629 76 .956 77 . 291 77 .626 77 .954 78 . 286 78 . 631 78 .960 79 . 296 79 .632 79 .965. 8 0 . 301  35 .546 20. 10 31 .776 20. 10 30 .222 20. 10 29 .443 20. 10 28 .672 20. 10 28 .352 20. 10 27 .911 20. 10 27 .406 20. 10 26 .862 20. 10 26 .366 20. 10 25 .8 0. 20 24 . 165 30. 10 23 .997 20. 10 24 . 142 20. 10 24 .247 20. 10 24 . 281 20. 10 24 .295 20. 10 24 .257 20. 10 24 .433 20. 10 24 . 182 20. 10 .24 .216 20. 10 24 .076 20. 10 23 .999 20. 10 23 .920 20. 10 23 .628 20. 10 23 .408 20. 10 23 . 167 20. 10 22 .996 20. 10 22 . 837 20. 10 22 .870 20. 10 22 .679 20. 10 22 .825 20. 10 23 .052 20. 10  23., 290 20. 80,,627 23,,344 20. 80,,959 .297 81 , 23 ,214 20. 81 , .628 23,, 157 2 0 . .981 81 , 23 , 147 2 0 . 82 .306 22,,978 20. 82..634 22,, 759 2 0 . 82..971 22,.771 20. 83 .295 22 .705 20. 83,.632 22 .657 20. 83 .966 22 .721 20. 84 .299 22 .643 20. 84 ,640 22 .482 20. 84 .969 22 .476 20. 85 .299 22 .479 2 0 . 85 .632 22 .554 2 0 . 85 .970 22 .505 2 0 . 86 .303 22 .417 2 0 . 86 .632 22 .034 20. 86 .971 21 .975 20. 87 . 299 21 .888 20. 87 .642 21 .971 20. 87 .969 21 .934 20. 88 .317 21 .833 20. 999 999 0 99i  16 .480 42 .988 65 .490  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  93 . 176 30. 10 54 .940 30. 10 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 6 6 . 6 69.1 .225 8 0 . 5 82.8 .250 9 2 . 0 9 3 . 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 83 . 593 20. 10 19., 3 0 9 19.,650 82.,602 20. 10 81 . .826 20. 10 19.,980 81 . 20,,316 , 1 1020. 10 20.,657 80.. 505 20. 10 79 , 840 20. 10 20,.990 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 77 , .868 20. 10 22 .660 77 , 22 , 9 9 2 .651 20. 10 77 , 23 , .361 20. 10 . 330 .041 20. 10 23 , .672 77 , 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,. 3 4 2 75,.852 20. 10 25 .668 75 . 564 20. 10 26 .000 75 . 347 20. 10 26 . 3 3 9 74 .946 20. 10 74 . 709 20. 10 26 .669 74 .593 20. 10 27 .004 27 .335 74 .467 20. 10 27 .673 74 .402 20. 10 74 . 277 20. 10 28 .OOO 28 . 3 3 3 73 . 988 20. 10 28 .663 73 .924 20. 10 28 .997 73 .676 20. 10 29 . 3 3 3 73 .539 20. 10 73 .321 20. 10 29 .669 73 . 195 20. 10 30 .004  73 . ,049 20. 10 30., 3 4 0 73.,005 20. 10 30..670 72 . .848 20. 10 31 ,001 . 31 . 339 72.,854 20. 10 31 . ,671 72..789 20. 10 32 . 72.,603 20. 10 ,003 32.,341 72 .639 . 20. 10 32..675 72.,401 20. 10 33.,01 1 72..417 20. 10 33 . 344 72., 352 20. 10 33 . ,674 72,.237 20. 10 34 . ,012 72.,273 20. 10 34., 347 72.. 147 20. 10 34 ,676 . 72 , ,083 20. 10 35 . 7 1.906 , .012 20. 10 35..346 71 .871 . 20. 10 35,.679 71 .776 . 20. 10 36..01 1 71 .589 , 20. 10 36 . 344 71 .575 20. 10 36 .679 71 .480 , 20. 10 37 .012 71 . 364 20. 10 37 . 3 5 0 71 . 187 20. 10 37,.687 71 .213 20. 10 71 .078 20. 10 38 .012 38 .350 70 .972 20. 10 38 .685 , 70 .795 20. 10 39 .015 70 .649 20. 10 39 . 3 5 0 70 .584 20. 10 39,.681 70 .458 20. 10 4 0 .016 70 .373 20. 10 4 0 .347 70 . 186 20. 10 999 999 4 0 .500 4 0 .814 41 . 161 41 .495 41 .830 42 . 163 42 . 505 42 .833 43 . 165 43 .503 . 43 .834 44 . 174 44 .512 44 .838 45 . 176 45 .514  69 . 340 30. 64 .257 20. 62 . 104 20. 6 0 .799 20. 59 .820 20. 58 .973 20. 58 . 399 20. 57 .920 20. 57 .267 20. 56 .847 20. 56 . 407 20. 56 .007 20. 55 .505 20. 55 . 108 20. 54 .616 20. 54 .327 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  45. 837 53. 962 20. 10 57. O05 48. 445 20. 10 57. 319 48. 365 20. 10 48. 258 20. 10 57. 654 57. 995 48. 130 20. 10 58. 322 48. 157 20. 10 47 .957 20. 10 58 .666 58.,996 47..821 20. 10 47 . .735 20. 10 59 . .330 47 . .527 20. 10 59..663 47 . .582 20. 10 60..003 47 .445 . 20. 10 60.. 335 47 .288 , 20. 10 60.,671 47 , 244 20. 10 60.,998 47,.086 20. 10 61 .334 , 47 , 143 20. 10 61 .667 , 62 . 47,,098 20. 10 .000 62 . 46,.881 20. 10 .330 62 .671 46,.884 20. 10 63..005 46 .951 20. 10 63,. 337 46,.926 20. 10 46 .901 20. 10 63..671 46 .644 20. 10 63 .997 64 .331 46 .772 20. 10 64 .677 46 .683 20. 10 46 . 538 20. 10 65 .001 999 999  0  3  73 .012 73 .314 73 .649 73 .998 74 . 329 74 .661 75 .002 75 .334 75 .670 76 .002 76 .332 76 .667 77 .002 77 .338 77 .661 77 .999 78 .336 78 .671 78 .998 79 .333 79 .661  43 .653 20. 10 40 .637 20. 10 39 .403 20. 10 38 .632 20. 10 38 .295 20. 10 37 . 754 20. 10 37 .464 20. 10 37 .442 20. 10 37 .388 20. 10 37 . 192 20. 10 36 .987 20. 10 36 .832 20. 10 36 .646 20. 10 36 . 378 20. 10 35 .992 20. 10 35 .479 20., 10 35 .323 20.. 10 35 .219 20., 10 34 .963 20., 10 34 .859 20.. 10 34 .655 20.. 10  0 99  79 .997 80. 325 8 0 . 662 80. 9 9 5 81 .328 81 .6 6 0 81 .9 9 0 82 .329 82 .6 6 5 82 .991 83 .334 83 .6 5 9 84 .001 84 . .331 84 .661 . ,993 84 . 85.,325 85 . .668 86.,001 86 . 338 86 . .663 .994 86 . 87 . 326 87 .667 87 .994 88 . 326 88 . 661 88 .997 89 . 329 89 . 651 89 .995 90 . 334 9 0 .657 9 0 . 994 91 . 326 91 .674 92 .010 95 .004 999  34 .672 20. 10 34 .488 20. 10 34 .393 20. 10 34 .299 20. 10 34 .184 20. 10 34 .172 20. 10 33 .937 20. 10 34 .0 7 5 20. 10 33 .818 20. 10 33 .736 20. 10 33. 6 8 0 20. 10 33..649 20. 10 33. 543 20. 10 33 . ,541 20. 10 33 . .611 20. 10 33 . 507 20., 10 33 . .444 20., 10 33 , ,429 20.. 10 33 , 477 20., 10 33,.413 20., 10 33 . 2 4 0 20.. 10 33 . 126 20,, 10 33 .114 20,. 10 33 .089 20,. 10 33 .017 20,. 10 33 .066 20.. 10 33 . 124 20.. 10 33 .080 20 . 10 33 . 139 20 . 10 33 .211 20 . 10 33 .084 20 . 10 33 . 120 20 . 10 33 .111 20 . 10 32 .985 20 . 10 33 .044 20 . 10 33 .007 20 . 10 32 .862 20 . 10 32 .862 20 . 10 999  17 .995 4 0 .487 72 .980  97 . 100 30 . 10 70 .219 30 . 10 44 .771 30 ,10  2 1 0.991 .,293.799.999.999. 99 10.0E-•10 RUN #10; TEMPERATURE=29.5 C 7 95.8 3 . 343 0.4325 1 .7 . 125 0,.3 24 , . 150 27.2 .7 47 ,.7 . 175 48.8 67.2 65,.6 .200 81.3 .225 80.,5 .250 91.5 91 , .2 . 275 98.7 98.,0 16.0 15.,999 97,. 108 20. 10 16 . ,316 91 , .441 20. 10 88 .422 20., 10 16 , ,649 .977 16 . 85,.952 20., 10 17 . .312 84,.012 20., 10 17 .647 82,. 347 20., 10 17 . .967 81 , .039 20., 10 18.. 302 79 .781 20., 10 18 .620 78 .829 20.. 10 18 , .957 77 .887 20., 10 19,. 292 77 .037 20.. 10 19 , .623 76 .370 20., 10 19 .946 75 .621 20.,10 74 .863 20., 10 20 . 271 74 . 399 20., 10 20 .600 20 . 939 73 .936 20., 10 73 .656 20.. 10 21 , .259 21 .579 73 . 335 20., 10 72 . 943 20.. 10 21'..923 22 .246 72 .622 20.. 10 2 2 ,.570 72 . 190 20., 10 71 .909 20., 10 22,.904 23,. 2 4 0 71 .578 20., 10 23 .570 71 . 196 20., 10 23 , .896 70 .916 20., 10 24 ,. 224 70 .514 20., 10 24,. 552 70 .204 20., 10 24 .884 69 .862 20.. 10 25 . 204 69 .583 20., 10 25 . 538 69 .506 20,, 10 25 .867 69 .369 20.. 10 26 . 196 69 .089 20,, 10 26 . 528 68 .900 20,. 10 26 .853 68 .630 20,. 10 27 . 179 68 .401 20.. 10 27 . 509 68 . 142 20,. 10 27 .842 67 .973 20.. 10  28. 169 67. 734 20. 28. 506 67. 505 20. 28. 824 67. 266 20. 29. 159 67. 200 20. 29. 489 67 .031 20. 29 .803 66 .782 20. 66. 594 20. 30. 140 66. 6 7 0 20. 30. 466 66. 563 20. 30. 794 31 . , 129 66 .,273 20. 31 .453 66. 186 20. 31 .777 66 .0 9 0 20. 32., 1 10 65.,728 20. 32..441 65. 652 20. 32 .,773 65. 504 20. 65..316 20. 33..092 65.. 209 20. 33.,431 33.,756 65..051 20. 34.,086 65.,036 20. 34.,420 64 ..837 20. 34 . , 744 64., 7 2 0 20. 64 .. 562 20. 35,,077 35.,411 64., 506 20. 64 .,318 20. 35 .,727 64,,425 20. 36,,062 36,.399 64 ..318 20. 64,. 190 20. 36,.730 37,.060 64 ,. 124 20. 37..382 63..987 20. 37 ..714 63 , .880 20. 38 ..037 63,.722 20. 38 ,.363 63,.635 20. 38,.697 63..569 20. 39 ,.029 63,.442 20. 39 .354 63..447 20. 63,. 248 20. 39,.687 63 .284 20. 40,.012 63,.086 20. 40,.336 63,.030 20. 40,.665 62,.943 20. 40,.999 999, 999, 0  2  41 41 41 42 42 42 43  . 345 , .656 .993 .320 .656 .990 .324  61 57 55 53 52 51 50  , .553 30. . 151 20. .041 20. .603 20. .461 20. . 797 20. .981 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  10 10 10 10 10 10 10  4 3 . 655 44 .0 0 2 44 .333 44 .657 44 .9 9 5 4 5 . 334 45 .6 6 5 45 .997 46. 329 46 .6 7 0 47 .0 0 5 47 .325 47 .659 47 .996 48 .333 48 .666 48 .,993 49 .,321 49 ,,657 49..991 50,. 322 50,.653 50 .984 51 .316 51 .649 51 .982 52 .320 52 .652 52 .982 53 .312 53 .653 53 .989 54 .319 54 .645 54 .981 55 .311 55 .657 55 .984 56 .312 56 .649 56 .977 57 .314 57 .657 57 .980 58 .314 58 .646 58 .977 59 . 307 59 .644 59 .973  50. 378 20. 10 49 .653 20. 10 49 . 1 12 20. 10 4 8 . 591 20. 10 48 .202 20. 10 47 .691 20. 10 47 .446 20. 10 47 . 159 20. 10 4 6 . 903 20. 10 46 .626 20. 10 46 .462 20. 10 45 .982 20. 10 4 5 . 757 20. 10 45 .4 8 0 20. 10 45 .469 20. 10 45 .253 20. 10 45 ., 161 20. 10 45.,037 20. 10 44 .,924 20. 10 44 ,, 566 20. 10 44 ,.412 20. 10 44 , 339 20. 10 44 .033 20. 10 43 .970 20. 10 43 .847 20. 10 43 .672 20. 10 43 .620 20. 10 43 .588 20. 10 43 .485 20. 10 43 .412 20. 10 43 . 339 20. 10 43 . 287 20. 10 43 . 245 20., 10 43 .071 20. 10 43 .008 20., 10 42 .997 20., 10 42 .944 20,. 10 42 .882 20 . 10 42 . 779 20 . 10 42 . 757 20 . 10 42 . 532 20 . 10 42 .479 20 . 10 42 .416 20 . 10 42 .324 20 . 10 42 .312 20 . 10 42 . 2 3 0 20 . 10 42 . 147 20 . 10 41 .911 20 . 10 41 .859 20 . 10 41 .838 20 . 10  60 60 60 61 61 61 62 62 62 63 63 63 64 64 999  31 1 64 1 971 303 64 1 973 300 640 971 305 640 970 301 641  64 65 65 65 66 66 66 67 67 67 68 68 68 69 69 69 70 70 70 71 71 71 72 72 72 73 73 73 74 74 74 75 75  840 149 480 821 161 487 829 151 487 828 164 493 821 155 501 829 163 491 820 157 487 820 163 503 830 163 496 832 160 492 836 165 496  41 .734 41 539 41 447 4 1 374 41 219 41 188 41 014 40 951 40 827 4 0 714 40 417 4 0 375 40 191 40 190 999  20 20 20 20 20 20 20 20 20 20 20 20 20 20  10 10 10 10 10 10 10 10 10 10 10 10 10 10  3 19 17 17 16 16 16 15 15 15 15 14 14 14 14 14 14 14 13 13 13 13 13 14 14 13 13 13 13 13 13 12 12 12  723 971 291 672 317 034 654 493 378 120 964 757 652 455 360 148 124 933 813 855 887 879 017 105 777 610 332 313 071 012 805 684 706  30 10 20 10 20 10 20 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10  75 76 76 76 77 77 77 78 78 78 79 79 79 80 80 80 81 81 81 82 82 82 83 83 83 84 84 84 85 85 85 86 86 86 87 87 87 88 88 88 89 89 89 90 90 90 91 91 91 92  830 164 488 838 168 495 826 1 19 509 830 170 492 821 162 497 825 156 496 833 164 496 831 166 496 845 172 499 830 169 500 835 176 504 840 176 499 825 164 493 832 162 503 832 162 497 839 163 501 830 165  12 632 12 4 2 0 12 351 12 235 12 074 12 0 7 0 12 042 12 0 5 0 12 334 12 275 12 282 12 238 12 184 12 0 3 8 1 1 928 1 1 797 1 1 773 1 1 541 1 1 568 1 1 376 1 1 480 1 1 334 1 1 346 1 1 312 1 1 318 1 1 360 1 1 286 1 1 303 1 1 299 1 1 393 1 1 272 1 1 258 1 1 296 1 1 175 1 1 223 1 1 174 1 1 150 1 1 080 1 1 092 1 1 099 1 1 075 1 1 168 1 1 089 1 1 029 1 1 1 17 1 1 088 1 1 070 1 1 066 1 1 068 1 1 024  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20 20 20. 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  92 92 93 93 93 94 94 94 95 95 95 999  496 824 157 486 831 166 507 833 170 486 836  1 1 143 1 1 170 1 1 304 1 1 295 1 1 271 1 1 278 1 1 162 1 1 093 1 1 094 1 1 005 10 971 999  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20.  10 10 10 10 10 10 10 10 10 10 10  0 99 15 9 8 0 4 1 319 64 823  98 799 30 10 63 0 3 2 3 0 10 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 81 . .225 .2 81 .2 . 250 92 .3 91 .8 .275 99.. 1 99.. 1 22.5 22 . .497 85 .959 20. 10 22 , 8 0 3 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 . 64 , .816 . 254 20. 10 25 . 154 63,.420 20. 10 25..485 62 .701 20. 10 25 , .815 62 , .033 20. 10 .464 20. 10 26 . .151 61 , 26 . .487 61 , .048 20. 10 26 . .824 6 0 .600 20. 10 27.. 157 6 0 .307 20. 10 27,.491 59 .790 20. 10 27 , .821 59 .590 20. 10 28.. 159 59 .315 20. 10 28,, 4 9 0 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 58 .121 20. 10 30 . 165 57 .850 20. 10 30,.494 57 .793 20. 10 30,.821 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  34 .813 56. 320 20. 10 35 .160 56. 509 20. 10 56. 357 20. 10 35. 494 56. 415 20. 10 35. 814 56. 145 20. 10 36. 165 55 .977 20. 10 36. 490 36. 835 55. 678 20. 10 37 .150 55. 474 20. 10 37. 500 55. 0 9 3 20. 10 54 .818 20. 10 37. 837 38. 162 55., 199 20. 10 55 .,232 20. 10 38. 494 38. 823 55.,255 20. 10 39. 164 55.,050 20. 10 39..498 55.,051 20. 10 54.,807 20. 10 39..836 ,474 20. 10 54 , 40.. 167 .557 20. 10 40., 500 54 , 54,.304 20. 10 40..834 41 . , 174 54 , .201 20. 10 .507 54 .040 20. 10 41 , 54 .075 20. 10 41 , .833 . 174 42 , 53 .992 20. 10 54 .074 20. 10 42,.509 53 .972 20. 10 42 , .846 43,. 168 53 .917 20. 10 43 .502 53 .786 20. 10 53 .707 20. 10 43 .834 44 . 167 53 .668 20. 10 44 .503 53 .495 20. 10 44 .832 53 .519 20. 10 53 .510 20. 10 45 . 166 53 .315 20. 10 45 .507 45 .832 53 .381 20. 10 46 . 176 53 .378 20. 10 53 . 301 20. 10 46 .502 46 .835 53 . 242 20. 10 47 . 173 53 .201 20. 10 47 .506 53 .202 20. 10 999 999 0 2  47 .854 48 . 148 48 .486 48 .823 49 .151 49 . 499 49 .836 5 0 . 166  51 47 45 44 43 42 41 41  .496 .438 .503 .403 .226 .506 .812 .345  20. 10 20. 10 20. 10 20., 10 20., 10 20., 10 20., 10 20., 10  50. 501 50. 821 51 . 164 51 .4 9 4 51 .8 2 6 52 .156 52 .5 0 0 52. 828 5 3 . 158 53 .4 9 0 5 3 . 827 54. 161 54. 4 9 6 54 .8 2 9 55 . 160 55. 4 9 3 55 .8 2 8 56. 164 56 .5 0 0 56..826 57 . , 159 57 . , 495 57 . ,833 . 163 58 , ,495 58 , 58 .829 59 . 170 59 . 4 9 9 59 . 8 3 5 6 0 . 165 60 . 503 6 0 .835 61 . 173 61 . 5 0 2 61 .837 62 . 168 62 .504 62 .832 63 . 172 63 . 5 0 2 63 .836 64 . 174 64 .510 64 .835 65 . 173 65 . 498 65 .840 66 . 178 66 .508 66 .838  41 .048 20. 10 40. 647 20. 10 40. 347 20. 10 40. 165 20. 10 39 .748 20. 10 39 .494 20. 10 39. 285 20. 10 39 .0 5 2 20. 10 38 .901 20. 10 38 .555 20. 10 38 .4 3 0 20. 10 38.,408 20. 10 38.,458 20. 10 37 . ,979 20. 10 37 , 735 20. 10 37 , ,785 20. 10 37 .499 , 20. 10 37 . , 344 20. 10 37 . 190 20. 10 37 . 182 20. 10 36 . 958 20. 10 36 .731 20. 10 36 .840 20. 10 36 . 7 5 0 20. 10 36 .627 20. 10 36 .575 20. 10 36 . 377 20. 10 36 .277 20. 10 36 . 295 20. 10 36 . 123 20. 10 36 . 150 20. 10 36 . 150 20. 10 35 .953 20. 10 35 .965 20. 10 35 .638 20. 10 35 .669 20. 10 35 . 544 20. 10 35 .698 20. 10 35 .552 20.. 10 35 .430 20., 10 35 . 389 20., 10 35 .477 20., 10 35 . 393 20., 10 35 . 488 20,, 10 35 . 403 20,. 10 35 . 264 20,. 10 35 . 147 20 . 10 35 . 185 20 . 10 35 .094 20 . 10 35 .034 20 . 10  G7 . 182 34 .916 67 .518 34 .944 67 .853 34 .800 68 . 177 34 .803 68 .514 34 .699 68 .850 34 .687 69 . 180 34 .830 69 .512 34 .657 69 .848 34 .502 7 0 . 179 34 . 563 34 .422 70 . 508 70 .837 34 .322 7 1. 167 34 .332 71 . 524 34 . 269 999 999  20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20. 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10  I  71 . 508 71 .818 72 . 153 72 .490 72 .813 73 . 144 73 . 476 73 .819 74 . 152 74 .479 . 74 .805 , 75 . 138 75 . .476 75..804 76... 137 76 .474 76,. 796 77 . , 125 77..453 77 . , 790 78., 123 78.,452 78. 788 79 .104 79. 446 79 .773 80. 114 80. 428 80. 755 81 .081 81 .4 1 0 81 .739 82 .0 6 5  33 .453 30. 10 30 .482 20. 10 29 . 239 20. 10 28 .260 20. 10 27 .555 20. 10 27 .095 20. 10 26 .746 20. 10 26 .012 20. 10 25..521 20. 10 25,. 172 20. 10 24..986 20. 10 24 .668 , 20. 10 24..493 20. 10 24,.083 20. 10 23..938 20. 10 23,.712 20. 10 23..576 20. 10 23,. 309 20. 10 23.. 123 20. 10 22..846 20. 10 22 . , 579 20. 10 22.,555 20. 10 22 . , 156 20. 10 21 . .848 20. 10 21 .703 20. 10 21 .466 20. 10 21 .382 20. 10 20. 789 20. 10 20. 807 20. 10 20. 448 20. 10 20. 425 20. 10 20. 493 20. 10 20. 398 20. 10  82 .407 82 .732 83..067 83..390 83..724 84..045 84 .390 . 84..707 85,.042 85,.385 85,.711 86 .045 86..379 86.. 705 87 .029 87 .367 87 .686 88 .034 88 .359 88 .684 89 .017 89 . 351 89 .680 90,.010 90 .346 9 0 .684 90 .996 91 . 346 91 .667 . 91 .994 92 . 324 92 .655 92 .978 93..311 93..645 93 .964 94 . 294 94 .631 94 .964 95 . 295 95 .635 95 .958 96 .289 96 .628 96 .942 97 . 277 97 .610 97,.949 98 .269 98 .598  20,.213 20. 19..884 20. 19..597 20. 19..268 20. 18 .961 . 20. 18,.836 20. 19,.006 20. 18,.952 20. 18 .807 20. 18 .672 20. 18 . 587 20. 18 .310 20. 18 . 206 20. 18 .010 20. 17 .681 20. 17 .556 20. 17 .543 20. 17 .571 20. 17 .283 20. 17 . 230 20. 17 .318 20. 17 . 122 20. 17 .048 20. 16 .964 20. 16 .880 20. 16 .592 20. 16 .518 20. 16 .078 20. 16 . 157 20. 15 .981 20. 16 .029 20. 15 .639 20. 15 .616 20. 15 .512 20. 15 . 356 20. 15 .312 20. 15 .076 20. 15 .012 20. 15 .273 20. 15 . 199 20. 15 .502 20. 15 .427 20. 15 .221 20. 15 . 198 20. 14 .94 1 20. 14 .968 2 0 . 14 .783 20. 14 .810 20. 14 .695 20. 14 .581 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  o 99  98. 927 14 .547 20. 14 .463 20. 99 .273 14 .582 . 99. 5 8 0 20. 14 .406 . 99 . ,925 20. 14 , . 393 20. 100.. 249 14., 3 7 0 20. 100..588 14 ,316 . 100.,921 20. 14 . 273 20. 101 ,261 , 14 . 321 20. 101 , 5 8 0 14 . 409 20. 101 .913 , 14 . 234 20. 102 . 237 14,.200 20. 102 .572 , 14 .024 20. 102 .892 14 .001 , 103 . 226 20. 13 .988 20. 103 . 555 103 .889 13,.934 20. 104 .217 . 13 . 728 20. 104 . , 540 13 . 735 20. 104 .877 13 .631 . 20. 105 . 209 13 .404 20. 105 . 536 13 .513 20. 106 . 200 13 . 761 20. 106 . 538 13 . 738 20. 106 . 863 13 . 593 20. 107 . 198 13 .692 20. 107 .519 13 .252 20. 107 .855 13 .046 20. 108 . 180 13 .083 20. 108 .517 12 .918 20. 999 999  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  2 1 0.951.222.152.97 10.0E-10 RUN 12; TEMPERATURE=29.5 C 7 1G8.0 3.343 0.3793 7 .3 . 125 2.0 . 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 84 ,227 30. 10 19. 477 78. 732 20. 10 19. 817 ,767 20. 10 20.. 144 76 . 75 , ,369 20. 10 20.,479 74 . ,327 20. 10 20.,816 21 , 155 73.,467 20. 10 21 . .488 72 . ,740 20. 10 21 . 72.,217 20. 10 ,820 .734 20. 10 22., 155 71 . . 191 20. 10 22 , 484 71 , 22 . .816 70,.891 20. 10 23,. 155 70,.550 20. 10 23 , .488 70,.291 20. 10 69 , 23,.825 .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 9999 0 2 67 .609 30. 10 31 . 178 63 .349 20. 10 31 .514 31 .846 61 .812 20. 10 32 . 175 60 .845 20. 10 59 .998 20. 10 32 .513 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 37 37 37 38 38 999  .857 . 183 .510 .850 . 180 .515  68 .990 69 . 328 69 .663 69 .993 70 . 330 70 .663 70,.992 71 .321 71 .664 71 .995 . 327 72,.664 72 .994 73,. 326 73 .664 73 , .993 74 , .330 74 , .666 74 , .993 75,.330 75,.663 75,.999 76,.338 76,,667 77,.003 77.,336 77.,672 78.,007 78.,338 78. 672 79.,009 79., 338 79 . ,676 80. 007 80. 340 80. 669 81 .005 81 .341 81 .675 82. 006 8 2 . 342  72;  55 55 55 55 55 55 9999  .978 .865 .609 .555 .390 .255  20. 20. 20. 20. 20. 20.  10 10 10 10 10 10  4 0 .857 30. 10 38 .456 20. 10 37 .805 20. 10 37 . 551 20. 10 37 . 265 20. 10 36,.970 20. 10 36,.848 20. 10 36,. 279 20. 10 35 , .942 20. 10 35,.688 20. 10 35,.495 20. 10 35,.230 20. 10 35,.006 20. 10 34 , . 762 20. 10 34 , .558 20. 10 34 , .508 20. 10 34 , .456 20. 10 34 . .364 20. 10 34 . .222 20. 10 34..039 20. 10 33,.937 20. 10 33.,845 20. 10 33.,814 20. 10 33.,722 20. 10 33.,651 20. 10 33.,671 20. 10 33.,447 20. 10 33 . .334 20. 10 33., 192 20. 10 33 .121 20. 10 33. 140 20. 10 32. 998 20. 10 32 .886 20. 10 32. 825 20. 10 32 .774 20. 10 32. 734 20. 10 32 .5 7 0 20. 10 32 .489 20. 10 32. 549 20. 10 32. 5 9 0 20. 10 32. 519 20. 10  82 .669 32.,570 20. 83 .004 32 .692 . 20. 83 . 332 32,,702 20. 83,.669 32 , ,631 20. 84 .008 32.,650 20. 84 . 339 32 . .599 20. 84 .669 32 , .508 20. 85 .006 32 , 507 20. 85 . 342 32 . 334 20. 85 .672 32 . .212 20. 86 .016 31 .977 , 20. 86,.347 31 .916 . 20. 86 . .684 31 . 722 20. 9999. 9999. 0 99  10 10 10 10 10 10 10 10 10 10 10 10 10  2 1 10.0E-•10 RUN #13; TEMPERATURE=29.5 C 7 9 3 . 0 3.343 0.4230 2 .1 . 125. 2. 1 . 150 27 . 5 27. 5 49. 7 . 175 49.7 . 2 0 0 67 .0 67 .0 .225 79.7 79. 7 89. 5 . 2 5 0 89.5 97, 9 .275 97.9 19.0 84 .153 20. 10 19. 908 73. 823 20. 10 20. 193 69. 641 20. 10 20. 514 67. 404 20. 10 20. 833 21 . 153 66. 072 20. 10 .467 64.,936 20. 10 21 . ,786 64., 124 20. 10 21 . 22., 105 63 .,515 20. 10 22 . .430 62..711 20. 10 22.,733 62,,321 20. 10 61 , 23 . ,051 . 764 20. 10 23. 366 61 . .431 20. 10 23 ..687 61 . ,413 20. 10 ,316 20. 10 23.,999 61 , 24 . 61 , 4 8 0 20. 10 ,320 24..634 60..843 20. 10 24 .951 60,.428 20. 10 25 .257 6 0 .017 20. 10 25 .576 59 .785 20. 10 25 .895 59 .604 20. 10 26 .217 59 .361 20. 10 26 . 529 59 . 152 20. 10 26 .839 59 . 137 20. 10 58 .972 20. 10 27 . 171 27 .482 58 .814 20. 10 58 .991 20. 10 27 .796 28 . 108 58 .802 20. 10 28 .420 58 .898 20. 10 28 . 744 58 .756 20. 10 58 .700 20. 10 29 .054 29 .376 58 .650 20. 10 29 .678 58 .648 20. 10 29 .999 58 .670 20. 10 30 . 3 2 0 58 .518 20. 10 58 .533 20. 10 3 0 .633 58 .424 20. 10 30 .949 31 . 264 58 .580 20. 10 58 .829 20. 10 31 .575  58. 821 20. 10 31 .894 32. 215 58. 853 20. 10 32. 523 58 .839 20. 10 58 .812 20. 10 32. 837 33. 165 58. 852 20. 10 59. 0 0 0 20. 10 33. 474 33. 791 59.,064 20. 10 34., 118 59., 125 20. 10 34,,428 59,, 171 20. 10 34.,740 59 . , 124 20. 10 35.,060 59., 106 20. 10 35.,371 59,,090 20. 10 35.,697 59,. 192 20. 10 59,, 146 20. 10 36..009 36 ..327 59 . 189 20. 10 36..645 59,, 201 20. 10 36,,959 59 . 144 20. 10 37,.276 59 .218 20. 10 37 . 593 59 .221 20. 10 37 .906 59 .164 20. 10 38 .227 59 . 176 20. 10 38 .541 59 .119 20. 10 38 .864 59 . 161 20. 10 39 . 178 59 . 154 20. 10 39 .486 59 . 129 20. 10 59 . 170 20. 10 39 .811 59 .066 20. 10 40 . 113 59 .087 20. 10 4 0 .439 59 . 101 20. 10 4 0 .750 41 .064 59 .085 20. 10 41 .380 59 .057 20. 10 41 .703 58 .845 20. 10 42 .015 58 .920 20. 10 999 999 0 99 19 .886  86 .277 30., 10  2 1 0 . 9 5 1 . 222 . 1 5 2 . 9 7 9 . 9 9 9 . 99 10.OE- 10 RUN 14; TEMPERATURE=29.5 7 117.0^ 3 . 343 0.4590 . 125 2 . 1 O.C . 150 27 . 7 4 .C 31 .6 . 175 49.5 6 8 . 1 51 .8 .200 69 .0 . 225 8 1 . 0 89 . 7 81 .9 .250 . 275 98 . 9 90. 0 21.0 92 .175 30. 10 20. 9 9 0 89 .813 20. 10 21 .329 8 9 . 155 20. 10 21 .661 88 .499 20. 10 21 .988 88 .0 7 5 20. 10 22 .324 87 .751 20. 10 22 .666 87 .431 20. 10 22 .993 23 .329 87 .312 20. 10 23. 664 86. 919 20. 10 86 .709 20. 10 23. 996 86 .521 20. 10 24 .327 24 .663 86 .351 20. 10 24 , 86 .203 20. 10 ,996 86 .0 4 3 20. 10 25,,332 85. 833 20. 10 25 ,.666 25,.992 85. 718 20. 10 85. 638 20. 10 26,.332 85. 459 20. 10 26..667 9999 . 9999, 0 2 85 .,046 30.. 10 27 . 306 27 .649 82 . ,853 20., 10 27 .983 81 . ,852 20.. 10 81 . , 198 20., 10 28 .316 28 .645 80,,7 17 20,. 10 28 .977 80,,215 20 . 10 .784 20 . 10 79 . 29 .311 79,.524 20 . 10 29 .648 29 . 979 79.. 328 20,. 10 78 .888 20,. 10 30 . 309 78 .691 20 . 10 3 0 .640 78 .532 20 . 10 30 .982 31 .316 78 .324 20 . 10 31 .650 78 . 107 20 . 10 77 .911 20 . 10 31 . 977 77 .723 20 . 10 32 .315 77 .515 20 . 10 32 . 648  1 1  32..990 77 . 285 20. 33 . 324 77 . 149 20. 33 .653 76 .973 20. 33 .991 76.. 754 20. 34 . 328 76 .698 20. 34 . .663 76 , .541 20. 9999 . 9999 ,  10 10 10 10 10 10  0 3  35.,998 75.,957 30. 36.,325 73.,290 20. 36..660 72.,379 20. 36..992 71 . .652 20. 37 . .325 70.,924 20. 37..660 70,.277 20. 37..992 69,.712 20. 38..331 69..247 20. 38 .663 68,.906 20. 38,.997 68 .463 20. 39 . 328 68 . 153 20. 39..660 67 , .882 20. 39 , .993 67 . .531 20. 40., 324 67 . 363 20. 40,.658 67., 103 20. 40.,995 66 . , 7 3 0 20. 4 1 ,.3 3 0 66 . .510 20. 41 . ,665 66.,218 20. 41 . ,994 66..020 20. 42., 331 65.,790 20. 42 . ,667 65..529 20. 43,.002 65..360 20. 43,,335 65,.089 20. 43,.668 64 . .870 20. 44 . .005 64 , .609 20. 44..335 64..319 20. 44 , .669 64 . .099 20. 44 , .999 64 . 247 20. 45..339 64 . , 107 20. 45 .675 63..886 20. 46. 0 0 5 63. 647 20. 46 .344 63. 284 20. 46. 672 62. 9 2 3 20. 47 . .010 62.,723 20. 47..347 62. 533 20. 47 . .674 62 .163 20. 48..010 62. 156 20. 9999. 9999 . 0 99  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  2 1 0.951 .2 2 2 . 1 5 2 . 9 7 9 . 9 9 9 . 9 9 10.0E--10 RUN #15; TEMPERATURE=29.5 C 0.4083 7 146.0 3.343 . 125 1 .9 2, . 1 26.,0 . 150 26.3 . 175 49.2 49.,0 , 1 .200 66. 1 67 . .225 81 .3 81 . .0 .250 92.3 91 . .9 .275 99.4 99.. 1 26.5 26. 50 87.,653 3 0 . 1 0 26 .83 81 . .507 20. 10 79.,511 2 0 . 1 0 27. 16 27. 50 78..014 20. 10 27..83 76 . .936 20. 10 28 .16 76..313 2 0 . 1 0 28..50 75..715 2 0 . 1 0 28. 83 75..256 2 0 . 1 0 29 .16 74 . .811 2 0 . 1 0 74 . 29 .50 .499 2 0 . 1 0 29 .83 74 . .191 2 0 . 1 0 73..924 20. 10 30. 16 73..691 2 0 . 1 0 30. 5 0 30. 83 73..478 2 0 . 1 0 31 . 16 73..296 2 0 . 1 0 31 . 73,.186 2 0 . 1 0 .50 31 .83 73 .035 2 0 . 10 32.. 16 72,.802 2 0 . 1 0 999. 999 0 2 36. 989 *71 . .538 3 0 . 1 0 37 . 321 66 .931 2 0 . 1 0 37 . ,658 65,.367 2 0 . 1 0 37.,997 64,.374 2 0 . 1 0 38. 337 63 .471 2 0 . 1 0 38..669 62 .793 2 0 . 1 0 39.,001 62 .297 2 0 . 1 0 39.. 333 61 .710 2 0 . 1 0 39..668 61 .326 2 0 . 1 0 40.,002 60 .963 2 0 . 1 0 40.. 335 60 .529 2 0 . 1 0 40.,667 60 .379 20. 10 41 . ,007 60 .006 2 0 . 1 0 41 , 336 59 .663 2 0 . 1 0 41 . .669 59 .422 2 0 . 1 0 42.,002 59 .181 2 0 . 1 0 58 .899 2 0 . 1 0 42,. 337  42 .668 58 . ,648 20. 43 . .457 20. .002 58 . 43 . .333 58 , ,2 16 20. 43 . .663 58 . .015 20. 44..000 57.,785 20. 44 . 332 57 . 554 20. 999. 999 . 0  10 10 10 10 10 10  3 50 51 51 51 52 52 52 53 53 53 54 54 54 55 55 56 56 56 56 57 57 58 58 58 59 59 59 60 60 60 61 61 61 62 62 62 63 63 63 999  0 99  .985 .319 .654 .989 .320 .659 .989 .323 .658 .988 . 323 .659 .993 . 329 .665 .002 .337 .667 .993 .331 .662 .000 . 338 .671 .004 .338 .670 .001 . 334 .665 .002 . 337 .676 .001 .330 .672 .001 . 331 .668  54 . .712 30. 10 50..988 20. 10 50,,047 20. 10 49 , . 299 20. 10 48 . .621 20. 10 48.. 1 1720. 10 47 . .521 20. 10 47..006 20. 10 46 . 654 20. 10 46 , .250 20. 10 46 . .010 .20. 10 45 , .648 20. 10 45 . 377 20. 10 45 . 126 20. 10 44 . .804 20. 10 44 . .655 20. 10 44 . .364 20. 10 44 , . 1 1320. 10 43 . .801 20. 10 43 , 6 7 3 20. 10 43 . .361 20. 10 43 . 202 20. 10 42 . .870 20. 10 42 . 74 120. 10 42 . .572 20. 10 42 .341 20. 10 42..090 20. 10 4 1 .840 , 20. 10 41 , .609 20. 10 41 , .419 20. 10 41 , .230 20. 10 40,.938 20. 10 40,, 708 20. 10 40,.630 20. 10 40,, 4 4 0 20. 10 40,. 301 20. 10 40,,071 20. 10 39 , .891 20. 10 39,, 691 20. 10 999 ,  2 1 0.752.584 . 4 9 9 . 9 9 9 . 9 9 9 . 9 9 10.0E-10 RUN #16; TEMPERATURE=35 C 7 8 5 . 0 3.8795 0.4262 1 .. 8 1 .8 . 125 . 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 , 154 78 . .889 20. 10 19 . 19 . 76 . , 426 20. 10 ,490 19..825 74 . .939 20. 10 20.. 165 73..798 20. 10 73..063 20. 10 20..504 72,.227 20. 10 20..836 21 . 164 71 .726 , 20. 10 21 . 71 .276 . .502 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 . 64 .764 20. 10 .988 35 , . 322 64 .426 20. 10 64 . 169 20. 10 35..657 64 .014 20. 10 35 , .986 36 . 321 63 .839 20. 10  36 .651 63. 6 2 3 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 .6 5 0 62 . .571 20. 10 38. 9 9 0 . 62.,507 20. 10 39. 321 62 . .281 20. 10 39 .658 62 . , 167 20. 10 39 .988 61 . .900 20. 10 61 . ,796 20. 10 40.,334 ,549 20. 10 61 . 40.,660 61 . ,506 20. 10 40.,997 41 . 61 , ,341 20. 10 ,330 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 . 59,.774 20. 10 .340 44.,676 59 .578 20. 10 45..008 59 .433 20. 10 45 . .341 59 .258 20. 10 59 . 113 20. 10 45,.671 46..001 58 .887 22 .0 0  999I . 0 2 45,.979 46,.320 46 ,657 46 .991 47 .324 47 .665 48 .005 48 .328 48 .664 48 .993 49 .328 49 .668 49 .997 50 .329 50 .663 50 .999 51 .328 51 .664  58 49 47 46 45 44 43 42 42 41 41 40 40 39 39 39 38 38  .825 30. 10 .728 20. 10 .693 20. 10 . 228 20. 10 . 242 20. 10 . 396 20. 10 .693 20. 10 .974 20. 10 .364 20. 10 .725 20. 10 . 186 20. 10 .625 20., 10 .444 20., 10 .804 20.. 10 .489 20., 10 . 143 20.. 10 .636 20., 10 .270 20., 10  52 .0 0 0 52 .334 52 .669 5 2 . 998 53 .336 5 3 . 672 54 .005 54 .337 54 .673 55 .007 55 .333 55 .666 55. 998 56 . 334 56 .,675 57..001 57 .. 339 57 .,679 58 . ,000 58 , 337 58..660 .996 58 , 59 . 344 59 .672 6 0 .001 60 . 339 60 .666 61 .009 61 . 334 61 .671 62 .010 62 . 343 62 .679 63 .012 63 . 342 63 .682 64 .015 64 . 345 64 .676 65 .017 65 . 351 65 .685 66 .017 66 . 343 66 .678 67 .020 67 . 343 67 .680 68 .014 68 . 347  37. 985 20. 10 37 .6 1 0 20. 10 37 .325 20. 10 37 .103 20. 10 36 .746 20. 10 36. 390 20. 10 36 . 167 20. 10 35 .7 0 0 20. 10 35 .405 20. 10 35 .0 4 0 20. 10 35 .022 20. 10 34 .738 20. 10 34. 342 20. 10 33 .793 20. 10 33. 171 20. 10 32 .777 20. 10 32 .258 20. 10 31 .717 20. 10 31 .273 20. 10 30. 734 20. 10 30. 402 20. 10 29. 862 20. 10 29 . ,483 20. 10 29..088 20. 10 28.,643 20. 10 , 144 20. 10 28 . 27 . .800 20. 10 27 . .503 20. 10 27 , . 160 20. 10 26..621 20. 10 26 . 305 20. 10 25.. 776 20. 10 25 .420 20. 10 25 . 157 20. 10 24 .853 20. 10 24 .425 20. 10 24 . 120 20.. 10 23 .918 20.. 10 23 .441 20.. 10 23 . 125 20.. 10 22 .851 20.. 10 22 . 536 20.. 10 22 .313 20, 10 21 .868 20.. 10 21 .482 20 . 10 2 1. 185 20.. 10 20 .883 20 . 10 20 .670 20 . 10 20 .283 20 . 10 19 .939 20 . 10  68 .677 69..009 69 , . 354 69 .685 70..023 85,.0 999. 0 99  19 .686 19 .300 19 .390 19 .513 19 .604 14 .7  i  20. 10 20. 10 20., 10 20. 10 20. 10 22. 0 0  1 2 2.582. 584..4 9 9 . 9 9 9 . 9 9 9 . 9 9 10.0E-•10 RUN #18; TEMPERATURE=35 C 7 114.5 3.343 0.4054 . 125 2.0 9.,8 . 150 24.8 31 .8 . 175 46 .6 52 . ,2 .3 .200 64 .9 69 . .225 78 .8 81 .9 .4 .250 89.7 92 . .275 96 . 7 98 .8 40.5 79 . 168 3 0 . 10 40. 499 79,.270 3 0 . 1 0 40. 489 77 , 40. 518 .434 3 0 . 1 0 72 .991 2 0 . 1 0 40. 822 41 .163 70 .875 2 0 . 1 0 41 .497 69 .509 2 0 . 1 0 41 .829 68 .620 2 0 . 1 0 67 .873 2 0 . 1 0 42 .164 42 .502 67 .236 2 0 . 1 0 42 .828 66 .773 2 0 . 1 0 43 .168 66 .359 2 0 . 1 0 65 .935 2 0 . 1 0 43. 512 43 .,844 65 .542 2 0 . 1 0 44., 172 65 .231 2 0 . 1 0 64 .848 2 0 . 1 0 44 . ,505 44 . 64 .607 2 0 . 1 0 ,839 , 177 64 .264 2 0 . 1 0 45 . 64 .105 2 0 . 1 0 45.,509 ,841 45 . 63 .712 2 0 . 1 0 46 . , 181 63 .460 2 0 . 1 0 46.,51 1 63 .392 2 0 . 1 0 63 .060 2 0 . 1 0 46,,842 47 , . 180 62 .900 2 0 . 1 0 47 , .514 62 .902 2 0 . 1 0 47 , .852 62 .802 2 0 . 1 0 48,. 178 62 .653 2 0 . 1 0 48 .517 62 .493 2 0 . 1 0 48 , .851 62 .363 2 0 . 1 0 49 , . 181 62 .244 2 0 . 1 0 49 , .515 62 .115 2 0 . 1 0 49 .835 61 .905 2 0 . 1 0 50,. 176 61 .755 2 0 . 1 0 61 .686 2 0 . 1 0 50 .507 61 .679 2 0 . 1 0 50,.838 51 . 170 61 .590 2 0 . 1 0 51 .500 61 .430 2 0 . 1 0 51 .832 61 .281 2 0 . 1 0  61 .222 20. 52. 164 52 .502 61 . 153 20. 52. 835 61 .064 20. 53 . 168 60. 935 20. 53 .506 60. 815 20. 53 .836 60. 828 20. 54 .170 60. 688 20. 54 . ,501 60. 599 20. 54.,835 60.,703 20. 55 . , 165 60.,685 20. 55,, 505 60..606 20. 55,.839 60.,658 20. 56,, 172 60.. 5 8 0 20. 56..507 60. 592 20. 56, 838 60.,503 20. 57 . , 174 60.,404 20. 57 . 5 0 3 60., 376 20. 57 . ,845 60., 337 20. 58 . 175 60., 279 20. , 504 60., 342 20. 58 . .841 58 . 60., 293 20. 59,, 174 60., 255 20. 59.,512 60., 206 20. 59 , ,835 60,,088 20. 60..171 60. 029 20. 60..507 60,,01 1 20. ,922 20. 60.. 84 1 59 . 61 . 175 59 . ,853 20. 61 , ,504 59 . ,805 20. ,837 ,696 20. 61 . 59 , 62 . 166 59 , 708 20. 62 . 504 59 . , 599 20. 62 , 831 59 , 551 20. 63 , . 169 59 , 472 20. 59 .433 20. 63 .. 501 63 ,. 842 59., 506 20. . 179 64 , 59 . , 396 20. 64 , . 502 59 . 491 20. 64 , .837 59 . 179 20. 59 , 65 . 178 . 180 20. 65,.510 59 . 132 20. 65 .844 59 . .073 20. 66 . 176 58 . 944 20. 66 . .513 58 . 824 20. 999 , 999 . 1 3 66 , .490 66 .513 66 .830  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  59..022 30. 10 57 , ,911 30. 10 .524 20. 10 54 .  G7 . 164 G7 .491 G7 .827 68 . 159 68 .501 68 .8 4 0 69 . 172 69 .5 0 0 69 .8 3 3 70. 170 70. 503 70. 836 7 1 .161 71 . ,504 71 . ,838 72., 165 72.,495 72 . ,829 73,, 166 73 , .503 73,.836 74 . 173 74,. 505 74 , .834 75 , . 162 75 , .506 75 , .834 76 , . 172 76 , .507 .834 76 , 77,. 169 77 .504 77 .841 78 . 172 78 .493 78 .843 79 . 177 79 .505 79 .834 8 0 . 168 80 . 503 8 0 .833 81 . 163 81 .493 81 .831 82 .171 82 . 499 82 .837 83 . 172 83 .507  53. 369 20. 10 52 .662 20. 10 52 .128 20. 10 51 .615 20. 10 51 .245 20. 10 50. 997 20. 10 50. 718 20. 10 50. 388 20. 10 50. 109 20. 10 49. 8 1 0 20. 10 49. 664 20. 10 49. 466 20. 10 49 .228 20. 10 49. 072 20. 10 48. 915 20. 10 48.,789 20. 10 48.,572 20. 10 48.,456 20. 10 48.,442 20. 10 48 . .062 20. 10 47 . .864 20. 10 47,,514 20. 10 47 , ,317 20. 10 47 , 160 20. 10 46 . .861 20. 10 46 . 766 20. 10 46 . ,660 20. 10 46 , . 4 7 3 20. 10 46 . 195 20. 10 46,, 130 20. 10 45,.851 20. 10 45 . 735 20. 10 45 . 579 20. 10 45 . 494 20. 10 45 .235 20. 10 45 .079 20. 10 44 .933 20. 10 44 .735 20. 10 44 . 568 20. 10 44 .310 20. 10 44 . 178 20. 10 44 .002 20. 10 43 .825 20. 10 43 . 668 20. 10 43 .471 20. 10 43 . 294 20. 10 43 . 189 20. 10 43 . 104 20. 10 42 .906 20. 10 42 .668 20. 10  1 99  8 3 . 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 41 .716 20. 10 85. 843 41 .519 20. 10 86 .180 41 .433 20. 10 86. 513 41 . ,226 20. 10 86. 844 41 . ,151 20. 10 87 .175 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 39 .718 20. 10 90..502 39 .592 20. 10 90,.843 91 , . 172 39 .558 20. 10 91 , .507 39 .340 20. 10 .841 39 .052 20. 10 91 , 92,. 167 39 .048 20. 10 38 .952 20. 10 92 .506 92 .835 38 .887 20. 10 93 . 168 38 .721 20. 10 38 .513 20. 10 93 .508 93 .842 38 .398 20. 10 94 . 174 38 .394 20. 10 94 .505 38 .329 20. 10 94 .841 38 .284 20. 10 38 . 2 5 0 20. 10 95 . 171 95 .510 38 .226 20. 10 38 .151 20. 10 95 .843 96 . 183 38 .076 20. 10 96 .505 38 .062 20. 10 1 14.5 37 .2 20., 10 999 999  2 1 1.202.302.403.209.999.99 10.0E-10 RUN 19; TEMPERATURE=35 7 7 6 . 5 3.343 0.4041 .150 5.7 5.7 .175 30.4 30.4 .200 5 1 . 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 89 .777 30. 10 23 .486 86 .4 1 0 20. 10 23. 827 24. 169 85. 569 20. 10 24 .486 84 .823 20. 10 84 .399 20. 10 24 .827 25. 163 84 .017 20. 10 83 .604 20. 10 25 .497 25 .838 83 .364 20. 10 26.. 166 83 . 125 20. 10 82 .785 20. 10 26.,493 26 . ,825 82 .628 20. 10 ,407 20. 10 27 . 166 82 . 82 . , 138 20. 10 27 . ,495 27 , 82 .0 0 0 20. 10 .830 28 . 166 81 . ,873 20. 10 81 ,694 . 28 . 502 20. 10 28 . 8 2 9 81 ,659 , 20. 10 81 , 29,. 162 .430 20. 10 29,.497 81 , 3 4 3 20. 10 81 , .3 17 20. 10 29 .835 81 .118 20. 10 30 . 168 30 .510 8 0 .928 20. 10 80 . 751 20. 10 30 .839 999l. 0 2 34 . 996 79 . 479 30. 10 35 . 326 76 . 123 20. 10 74 . 799 20. 10 35 .658 73 .628 20. 10 35 . 9 9 0 72 .629 20. 10 36 . 328 71 .864 20. 10 36 .660 71 . 181 20. 10 36 .990 37 .326 70 .609 20. 10 37 .656 70 .058 20. 10 37 .990 69 .608 20. 10 69 . 109 20. 10 38 .315  38 .6 4 9 38. 987 39 .322 39. 6 6 3 39 .997 40. 334 40. 661 40. 997 41 .336 41 .6 6 9 41 .998 42 .333 42 .6 7 3 4 3 . 01 1 4 3 . 348 43. 673 44 .0 0 2 44 .337 44 .6 7 5 45 . .008 45 .337 45 . ,678 46 .0 1 0 , 343 46 . 46.,673 47 , 338 47 .679 . 48 .016 48 . 342 48 .682 999. 0 3 6 0 .535 6 0 .83 61 . 17 61 .50 61 .83 62 . 17 62 .50 62 .83 63 . 17 63 .50 63 .83 64 . 17 64 .50 64 . 83 65 . 17 65 .50 65 .83  68. 7 3 0 20. 10 68 .381 20. 10 68 .002 20. 10 67. 6 7 3 20. 10 67 .365 20. 10 67. 087 20. 10 66. 7 5 0 20. 10 66 .493 20. 10 66 .286 20. 10 66 .0 0 9 20. 10 6 5 . 763 20. 10 6 5 . 536 20. 10 65 .380 20. 10 65. 163 20. 10 65. 007 20. 10 64 .793 20. 10 64 .628 20. 10 64 .381 20. 10 64 . ,337 20. 10 64 . ,111 20. 10 64 . ,007 20. 10 63.,901 20. 10 63 . .868 20. 10 63 , ,652 20. 10 . 549 20. 10 63 , 63 . 391 20. 10 63 . ,285 20. 10 63,. 160 20. 10 63 . 1 1820. 10 62 .921 20. 10  6 0 .267 57 .527 56 .68 1 56 .070 55 . 397 54 .674 54 .215 53 .827 53 .521 53 . 134 52 .747 52 .523 52 .319 52 .024 51 .780 51 .616 51 .402  30. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20., 10 20., 10 20,, 10 20., 10 20,, 10 20., 10 20.. 10  66 . 17 66 .50 66,.87 67 . , 17 67 .50 , 67..83 68 . 17 68 . .50 68 .83 69,. 17 69,.50 69..83 70,. 17 70 .50 70,.83 71 . , 17 71 .50 71 .83 72 . 17 72 .50 72 .83 73 . 17 73 .50 73 .83 74,. 17 74 .50 , 74 .83 999. 0 4 76 .995 77 . , 328 77 .666 77 .999 78 . 328 78 .666 79 .001 79 .339 79 .672 8 0 .014 8 0 .348 . 80.677 81 .016 81 . 344 81 .677 82 .015 82 .347 82 .680 83 .082 83 .344  51 . , 157 20. 50..933 20. 50. 801 20. 50.,627 20. 50.. 341 20. 50., 199 20. 49..985 20. 49.,781 20. 49..668 20. 49 . ,628 20: 49.,393 20. 49..311 20. 49.,301 20. 49., 199 20. 48..903 20. 48 . .720 20. 48 . ,546 20. 48 , ,373 20. 48 , 230 20. 48 , ,067 20. 47 .904 , 20. 47 , . 781 20. 47 , . 740 20. 47 ,648 . 20. 47 . 506 20. 47 . ,485 20. 47 . .444 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10. 10 10 10 10 10 10 10 10 10  47,, 144 30. 44 ,402 , 20. 43 , ,432 20. 42 , ,879 20. 42 , 327 20. 41 ,805 , 20. 41 , 293 20. 40. 923 20. 40,,696 20. 40..438 20. 40,,008 20. 39 . .619 20. 39 . ,422 20. 39,. 145 20. 39.,050 20. 38 .935 . 20. 38,.770 20. 38 .533 20. 38 .424 20. 38,.375 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  83 , .685 84 .016 . 84 . , 352 84 , 676 85 , ,013 85,.346 85,.684 86,.016 . 354 86 , 86..679 87 .004 87 . 3 5 0 87 .684 88 .01 1 88 . 346 88 . 6 7 5 89 .009 89 . 348 89 .676 9 0 .025 9 0 . 349 9 0 .684 91 .018 91 . 354 91 .687 92 .016 92 .352 92 .686 93 .014 93 . 348 94 .020 94 . 349 94 .687 95 .009 95 . 348 95 .682 96 .008 999 . 0 99  38 . , 260 20. 38 . ,064 20. 37 . 796 20. 37 . .682 20. 37 . .618 20. 37 . 401 20. 37 .245 , 20. 37 . , 141 20. 36 , .812 20. 36 , . 708 20. 36,.818 2 0 . 36,,631 20. 36., 445 20. 36 , 341 20. 36 , . 257 20. 36 , . 193 20. 36 .119 20. 35 .994 20. 35 .889 20. 35 .672 20. 35 . 578 20. 35 .361 20. 35 . 308 20. 35 . 172 20. 35 .210 20. 34 . 984 20. 34 .961 20. 34 .938 20. 34 . 874 20. 34 . 8 2 0 20. 34 .540 20. 34 . 456 20. 34 . 504 20. 34 . 593 20. 34 . 356 20. 34 . 343 20. 34 . 147 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 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 4 7 . 6 50.9 .200 6 3 . 9 68.5 .225 77.5 82.0 .250 8 9 . 6 92.2 .276 9 6 . 6 98.5 20.5 96. 563 30. 10 20. 476 93. 566 20. 10 20. 798 21 . 123 92 .429 20. 10 21 . .45291 .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 . 89.,302 20. 10 .691 24..015 89. 161 20. 10 24.,328 88. 9 3 0 20. 10 24..638 88.,739 20. 10 24 . ,957 88. 568 20. 10 88..488 20. 10 25..288 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 87 . 32 . 5 .0 20. 10 I.  .473 32 . 32 , 804 33,. 143 33 , ,477 33 , .810 34 , . 145 34 , .478 34 .816 35 .151 35 .477 35 .810 36 . 147 36 . .488  86.,994 30. 82 . .650 20. 81 . 193 20. 80.. 103 20. 79.. 308 20. 78..777 20. 78,. 1 1420. 77 .541 20. 77 . , 203 20. 76 . 806 20. 76 . 539 20. 76 . 303 20. 75 .995 20.  10 10 10 10 10 10 10 10 10 10 10 10 10  36 .825 37 . 155 37 .488' 37 .827 38 . 163 38 .492 38 .832 39 . 165 39 .504 39 .836 40 . 167 40 .500 40 .840 41 . 173 41 .509 41 .840 42 . 180 42 .507 42 .847 44 .519  999). 0 3 44 .479 44..816 45.. 145 45..482 45 . .817 46 , . 151 46..485 46..822 47., 162 47.,490 47.,826 48., 158 48. 499 48. 837 49. 174 49. 501 49. 839 50. 181 50. 515 50. 849 51 . 179 51 .510 51 .843 5 2 . 180 52. 51 1 52. 845 53. 179  75 .727 20.. 10 75 .563 20.. 10 75 .276 20., 10 75 . 182 20.. 10 75 . 108 20., 10 74 .832 20.. 10 74 .727 20., 10 74 .542 20., 10 74 .427 20.. 10 74 .303 20. 10 74 . 2 3 0 20. 10 73 .873 20. 10 73 .808 20. 10 73 .572 20. 10 73 .631 20. 10 73 .477 20. 10 73 . 352 20. 10 73 .340 20. 10 73 .113 20. 10 73 .071 20. 0 0  73 . 2 8 0 30. 10 69 .612 20. 10 68 .356 20. 10 67 .526 20. 10 66 .951 20. 10 66 .224 20. 10 65 .811 20. 10 65..358 20. 10 65,.067 20. 10 64,.473 20. 10 64 , .091 20. 10 63., 729 20. 10 63 . ,459 20. 10 63., 168 20. 10 63..030 20. 10 62.,741 20. 10 62 . .674 20. 10 62..606 20. 10 62 .469 20. 10 62. 209 20. 10 62. 103 20. 10 62 .017 20. 10 61 .819 20. 10 61 .732 2 0 . 10 61 .737 20. 10 61 .559 20. 10 61 .482 20. 10  53 . ,515 53.,849 54 . , 181 54 . .517 54 . .850 55., 183 55..517 55.,853 56 . 180 56 . ,511 56 . .846 57 . 180 57 . .516 999I . 0 4 57 .478 57,.809 58 , . 149 58 . .490 58 , ,831 59 , . 160 59 , 4 8 8 59 , .8 17 60.. 160 60,,495 60..830 61 , . 165 .497 61 , 61 . .834 62 . 160 , 499 62 . 62..830 63.. 168 63.,500 63 . ,837 64 . 167 64 . ,500 64 . .833 65.. 173 65 . ,512 65 . .836 66 . , 172 66., 507 66 .,841 67.. 169 67.,503 67 . .833 68 . 177 68 . .513  61 . ,568 20. 10 61 , .482 20. 10 61 . .497 20. 10 61 . 3 7 0 20. 10 61 . .385 20. 10 61 , ,421 20. 10 61 , . 2 5 3 20. 10 61 , 227 20. 10 61 , . 182 20. 10 61 , . 198 20. 10 61 . 131 20. 10 61 , . 1 16 20. 10 60..998 20. 0 0  61 .023 30. 58 . 193 20. 57 .427 20. 56 . .895 20. 56 .445 20. 56 . .047 20. 55..751 20. 55..455 20. 55.. 208 20. 55..023 20. 54 . .817 20. 54 . .500 20. .489 20. 54 . 54 . 232 20. 54 . .079 20. 53..914 20. 53.,872 20. 53 . , 778 20. 53., 7 0 5 20. 53 . .510 20. 53 , 407 20. 53,.222 20. 53 . 241 20. 53 , .228 20. 53,, 175 20. 53 . .043 20. 53 . 244 20. 53 . .090 20. 52 . .895 20. . 894 20. 52 , 52 . 7 2 9 20. 52 . ,627 20. 52 , 4 4 0 20. 52 , 306 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  68. 846 6 9 . 179 69 .513 6 9 . 851 70. 186 70. 524 70. 858 74. 0 999 . 0 99 73 .9 8 3 74 .312 74 .6 5 0 74 .991 75. 334 75 .6 6 6 75 . ,996 76 . , 338 .667 76 . 77 . .003 77 . 337 77..676 78 . .015 78 , .338 78..675 79 .010 79 .349 79 .678 8 0 .010 8 0 . 357 8 0 .688 81 .023 8 0 .992 81 .322 81 .658 . 81 .661 , 81 .995 , 82 . 322 82 .660 82 . 991 83 .321 83 .669 84 .001 84 . 322 84 .664 84 .994 85 . 333 85 .669 85 .996  52. 406 52 .283 52. 098 51 .831 51 .758 .644 51 . 51 . ,510 51 . ,3  20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 10 20. 0 0  51 . ,358 30. 10 49..477 20. 10 48..941 20. 10 48 . ,497 20. 10 48., 297 20. 10 48 . .046 20. 10 47 ,773 , 20. 10 47 .675 20. 10 47 .494 20. 10 47 . 365 20. 10 47 . 307 20. 10 47 . 178 20. 10 46 .998 20. 10 47 .081 20. 10 46 .952 20. 10 46 .894 20. 10 46 .846 20. 10 46 .899 20. 10 46 .647 20. 10 46 .448 20. 10 46 . 359 20,. 10 46 . 403 20.. 10 46 .825 20, 10 46 .596 20, 10 46 .542 20. 10 46 .644 20. 10 46 .609 20. 10 46 . 553 20. 10 46 .662 20., 10 46 .607 20.. 10 46 . 551 20.. 10 46 . 529 20.. 10 46 .565 20.. 10 46 .488 20.. 10 46 .618 20.. 10 46 .562 20.. 10 46 .640 20,. 10 46 .576 20,. 10 46 .540 20.. 10  86..334 86..669 86 . .999 87 .331 87 . ,672 88 . ,017 88 . ,343 88 . ,671 89..015 ,341 89 . 89.,687 90..013 90..347 90..681 91 .018 . 91 .353 , 91 , .680 92..012 92 .343 92 .680 93 , ,007 93 .352 93 .682 94 .017 , 94..351 94 .682 , 95 .01 1 95,. 344 95 .687 96 .020 96 . 358 96 .687 97 .028 97 .357 97 .692 98 .029 98 , .513 999. 0 6 98.,478 98 .807 99 . 147 99 .478 99 .806 100 . 141 100 .473 100 .809 101 . 139 101 ,478 .  46.,628 20. 10 46.,757 20. 10 46. 722 20. 10 46. 667 20. 10 46.,531 20. 10 46.,631 20. 10 46..442 20. 10 46.,509 20. 10 46 . , 394 20. 10 46,, 379 20. 10 46., 305 20. 10 46,. 188 20. 10 46,,256 20. 10 46,.221 20. 10 45,.912 20. 10 45,.878 20. 10 45,.873 20. 10 45,.848 20. 10 45,.721 20. 10 45 .494 20. 10 45 .479 20. 10 45 .456 20. 10 45,.258 20. 10 45 . 285 20. 10 45,. 199 20. 10 45 .062 20. 10 45 . 1 1920. 10 45 ,074 20. 10 44 .878 20. 10 44,.813 20. 10 44 .718 20. 10 44 .713 20. 10 44 .455 20. 10 44 . 563 20. 10 44 .386 20. 10 44 . 382 20. 10 44 .389 20. 0 0  44 .515 30. 42 .597 20. 42 . 294 20. 41 .850 20. 41 .650 20. 41 .491 20. 41 .423 20. 41 . 182 20. 41 .002 20. 4 0 .964 20.  10 10 10 10 10 10 10 10 10 10  101 ,808 , 102 . ,14 1 102,,475 102.,818 103., 149 103.,476 103.,806 104 , 149 104 , 477 104 ,812 , 105,, 151 105 , 491 105,.815 106,. 147 106 , .484 106,.813 107,. 156 107 .492 107,.818 108,. 158 108 .497 108 .826 109 . 170 109 . 496 109 .823 1 10 . 153 1 10,.492 1 10.838 111 . 158 111 . 486 111 . 828 112 . 183 112 . 482 112 .818 113 . 173 113 . 507 113 . 838 1 14.171 114 . 5 0 5 1 14. 844 115 . 174 1 15.504 115 .831 1 16. 175 1 16.505 1 16.847 117 . 179 117 . 507 117 .850 118 . 179  40. 805 20. 40. 859 20. 40. 811 20. 40. 824 20. 40. 654 2 0 . 40. 688 20. 40. 661 2 0 . 40. 593 20. 40.,494 20. 40. 518 20. 40. 409 20. 40. 544 20. 40.,466 20. 40.,489 20. 40., 370 20. 40.,435 20. 40..468 20. 40.,400 20. 40.. 332 20. 40., 355 20. 40.. 378 20. 40., 361 20. 40..242 20. 40., 367 20. 40.,117 20. 40., 191 20. 40.,235 2 0 . 40.. 288 20. 40.. 353 2 0 . 40., 244 20. 40.. 328 20. 40..361 20. 40.. 203 2 0 . 40.. 298 20. 40.. 289 20. 40,, 394 2 0 . 40..326 20. 40,.441 2 0 . 40..394 20. 40..417 20. 40,.318 20. 40,.312 20. 40,. 305 2 0 . 40,. 389 20. 40,, 34 12 0 . 40,. 364 20. 40,, 164 20. 39 , .761 20. 39,,672 20. 39 , .492 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  118,.516 118 , ,857 119,. 190 ,518 1 19, 1 19 .848 , 120,. 184 120,.519 120,.853 121 . , 189 121 . ,532 ,861 121 , 122,. 188 122,.522 122 , .850 123 , . 188 123 , .517 123 .848 124 . 178 124 .520 124 . 872 125 . 185 125 .529 125 .865 126 .195 126 . 528 126,.866 127,. 196 127 , .527 127 , .863 128 , . 198 128 , .525 128 , .862 129,.222 129,.531 129,.864 130,. 2 2 0 130 .531 130 .869 131 . 206 131 . 5 3 0 131 .855 132 . 174 132 .515 132 . 844 133 . 174 133 .504 133 .845 134 . 175 134 .522 134 .847  ,434 20. 39 , 39.,061 20. 38 . ,993 20. ,894 20. 38 . ,877 20. 38 . 38 . .555 20. 38 . ,690 20. 38 . ,531 20. 38 . ,513 20. 38.,445 20. 38 . .316 20. 38,, 147 20. 38..343 20. 38 . ,031 20. 38..003 20. 37 . .895 20. 37 .827 20. 37 .861 20. 37 .701 20. 37 .632 20. 37 .565 20. 37 .537 20. 37 .438 20. 37 .350 20. 37 . 180 20. 37 .092 20. 37 . 176 20. 37 . 302 20. 37 .111 20. 37 .247 20. 37 .077 20. 36 . 796 20. 36 .950 20. 37 .046 20. 36 .856 20. 36 . 766 20. 36 .638 20. 36 .489 20. 36 .461 20. 36 .668 20. 36 .417 20. 36 .279 20. 36 .353 20. 36 .285 20. 36 . 105 20. 35 .865 20. 35 .776 20. 35 .667 20. 35 .710 20. 35 . 368 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  135.196 135.520 135.851 136. 183 136.513 999. 0 50  35.289 35.425 35.316 34.994 34.977  20.10 20.10 20.10 20.10 20.00  2 1 1.202.302.403.209.999.99 10.0E-10 RUN #21; TEMPERATURE=35 C 7 6.5 3.343 0.3838 . 125 9.6 16. 1 .150 30.9 37.0 .175 50.9 57.2 .200 68.5 72.7 .225 82.0 85.1 .250 92.2 94.7 .285 99.9 99.9 19 . 5 19..518 99.,899 30. 10 97., 292 20. 10 19..828 96 ., 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.488 49 .820 50 . 155 50 .494 50 .826 51 . 169 51 .499 51 .831 52 . 170 52 .508 52 .843 53 . 176 53 .516 53 .854 54 . 188 54 .518 54 .856  72 .203 20. 10 72 .027 20. 10 71 .617 20. 10 71 .309 20. 10 70. 981 20. 10 70. 836 20. 10 70. 569 20. 10 70. 322 20. 10 70.,004 20. 10 69 .,787 20. 10 69 .,500 20. 10 69.,294 20. 10 69., 128 20. 10 68 . .922 20. 10 .655 20. 10 68 . 68 . 479 20. 10 68 .222 20. 10 68 . .067 20. 10 67 .911 20. 10 67 .664 20. 10 67 . 397 20. 10 67 .211 20. 10 67 .015 20. 10 66 .840 20. 10 66 .847 20. 10 66 .639 20. 10 66 .606 20. 10 66 .348 20. 10 66 . 305 20. 10 66 . 130 20. 10  64 . 478 30., 10 61 .094 20. 10 6 0 .221 20., 10 59 . 227 20.. 10 58 . 537 20.. 10 58 .062 20.. 10 57 .483 20., 10 57 . 170 20,, 10 56 . 796 20.. 10 56 . 401 20 . 10 56 .057 20 . 10 55 .693 20 . 10 55 .400 2 0 . 10 55 .046 2 0 . 10 54 .865 2 0 . 10 54 .500 20 . 10 54 .258 20 . 10  55 .186 55. 524 63..4  53 . ,913 20. 10 53,,763 20. 10 49 , ,5 20. 10  i.  75..489 45 , 269 30. 10 75 .8 2 5 42 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501 33 .666 20. 10 89 .831 33 .454 20. 10  90. 160 90. 502 90. 833 91 .169 91 .507 91 .837 92 .168 92 .844 93. 177 93. 503 93. 839 94. 177 94. 511 94. 848 999. 0 99 123 . ,498 123. 839 124., 166 124 ,499 . 124.,842 125. 180 125.,511 125.,842 126., 174 126.,503 126. 839 127.. 174 127.,496 127..838 128 , 176 128 .499 , 128,,840 129,. 172 129,.510 129,.836 130.. 168 130,. 505 130..836 131 . 171 131 . , 507 131 .839 132,. 178 132 .509 132 .843 133 . 185 133 .513 133 .842 134 . 173  33. 181 20. 10 33. 001 20. 10 33. 0 0 3 20. 10 32. 832 20. •10 32 .824 20. 10 32 . .613 20. 10 32 . .665 20. 10 32..650 20. 10 32.,652 20. 10 32..490 20. 10 32.,442 20. 10 32., 342 20. 10 31 . ,958 20. 10 31 ,991 , 20. 10  20..997 30. 10 18 .726 , 20. 10 18 . 245 20. 10 18 .019 , 20. 10 17..824 20. 10 17 .720 20. 10 17 .352 20. 10 16 .902 20. 10 16 .645 20. 10 16 .318 20. 10 16 . 163 20. 10 15 .937 20. 10 15 .894 20. 10 15 .566 20. 10 15 .656 20. 10 15 .542 20. 10 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  134 .508 134 .832 135. 176 135 .512 135 .8 4 5 136 .177 136 .506 136 . .836 137 ,17 , 1 137 , 503 137 .838 , 138 . , 168 138 . 504 138 .830 139 . 166 139 .507 139 .84 1 140 . 167 140 .510 140 . 8 4 0 141 . 177 141 .506 141 .843 142 . 178 142 .519 142 .853 143 . 187 143 . 507 143 .847 167 .5 999 . 0 99  14 .0 0 9 20. 10 13 .946 20. 10 13. 812 20. 10 13 .8 4 0 20. 10 13. 614 20. 10 13. 622 20. 10 13. 569 20. 10 13 .547 . 20. 10 13,,494 20. 10 13 . 248 20. 10 13,,073 20. 10 13 .091 . 20. 10 12 .977 20. 10 12 .863 20. 10 12 .861 20. 10 12 .676 20. 10 12 .816 20. 10 12 . 5 8 0 20. 10 12 . 72 1 20. 10 12 .647 20. 10 12 . 503 20. 10 12 .552 20. 10 12 .560 20. 10 12 . 466 20. 10 12 . 484 20. 10 12 . 452 20. 10 12 .399 20. 10 12 . 397 20., 10 12 .151 20. 10 9 .0 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 4 5 . 0 4 5 . 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 . 3 2 3 77 , 168 20. 10 28 .657 76,.387 20. 10 28 .995 75,, 788 20. 10 29,. 3 3 0 75 , 2 5 0 20. 10 29,.673 74 , .660 20. 10 74 . , 174 20. 10 30,.006 30,.341 73,.809 20. 10 73 , 30,.674 .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 71 ,571 , 33,.351 20. 10 33,.663 71 . , 301 20. 10 71 , . 129 20. 10 33.,997 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 . 3 3 3 70.,546 20. 10 36,.666 70. 323 20. 10 37 , .005 70.,415 20. 10 37 , . 3 3 3 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  38 . ,995 69 .853 20. 39.,330 69. 722 20. 69. 794 20. 39.,658 39.,997 69. 733 20. 40., 337 69 .693 20. 69. 603 20. 40.,667 41 . 69.,594 20. ,000 41 . , 337 69.,482 20. 41 . .659 69.,495 20. 42 . ,004 69.,301 20. 42.,329 69.,364 20. 42 , .669 69.. 242 20. 69 .223 20. 43,,000 43 , .338 69., 183 20. 43 , .675 69.. 163 20. 43,.999 69 , ,003 20. 44 , .327 68 , ,872 20. 44 , .674 68 . ,902 20. 44,.998 68,,874 20. 45,. 3 4 0 68..680 20. 68 , 45,.670 .631 20. 46,.000 68 . .612 20. 46 .343 68 , .581 20. 46 .668 68 . .542 20. 47 .005 68,.472 20. .493 20. 47 . 337 68 , 47 .674 68,.311 20. 47,.995 68 . 151 20. 48,. 339 68,.079 20. 48 .666 68,.071 20. 68 . 143 20. 48 .998 49 .332 68 , .063 20. 49 .661 68 .085 20. 49 .995 68 .004 20. 67 .943 20. 50 .333 68 .005 20. 50 .670 51 .010 67 .964 20. 51 . 336 68 .007 20. 67 .998 20. 51 .667 52 .013 67 .875 20. 52 .343. 67 .897 20. 52 .677 67 .959 20. 53 .003 67 .940 20. 999 999  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  0 2  53 53 53 53  .050 .325 .656 .991  66 62 60 58  . 192 30. .620 30. .633 30. .921 30.  10 10 10 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. 0 6 0 30. 10 56 . ,012 54 .576 30. 10 56 . , 334 54 .305 30. 10 56..668 53.,751 30. 10 ,997 56 . 53 .,429 30. 10 57 . 332 53. 179 30. 10 57 , ,705 30. 10 ,670 52 . 57 , ,999 52. 404 30. 10 58 . 336 52 . 266 30. 10 ,671 58 . 51 . ,894 30. 10 59 . , 735 30. 10 .001 51 . ,464 30. 10 59 , 51 . ,330 59,.670 51 . ,468 30. 10 51 . ,045 30. 10 60,.003 ,008 30. 10 60,. 34 1 51 . 6 0 .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 . 3 3 3 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 49 . 534 30. 10 66 .664 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 48 . 255 30. 10 70 . 334 48 . 228 30. 10 70 .664  •71 .000 48 . 282 30. 71 . 331 48 . 266 30. 7 1.669 48 .229 30. 72 .003 48 .314 30. 72 . 335 48 . 155 30. 72 .666 48 .118 30. 73 .009 48 . 152 30. 73 . 347 48 . 176 30. 73 .675 48 .048 30. 74 .007 47 .919 30. 74 .337 47 .923 30. 74 .668 47 .795 30. 74 .999 47,.646 30. 75 .336 47,.477 30. 75 .671 47 .542 30. 76 .007 47..494 30. 76 .338 47 . 386 30. 76 .672 47 .400 . 30. 76 .999 47 .241 30. 77 . 335 47 . 143 30. 77 .672 46 .995 30. 78 .005 46 .968 30. 78 . 327 46 .819 30. 78 .666 46,.762 30. 78 .999 46 . 725 30. 79 .327 46..790 30. 79 .661 46 , .722 30. 79 .997 46..675 30. 46 . .516 30. 8 0 . 336 46 .459 30. 8 0 .667 46,.473 30. 80,.997 81 .331 46 . , 385 30. 81 .664 46 . 501 30. 82 .002 46,,484 30. 82 . 335 46 , . 366 30. 999 999 .  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  45 , ,037 30. 41 . , 149 30. 39,.682 30. 38 , 573 30. 38 . 138 30. 37 . , 377 30. 36 . .799 30. 36. 221 30. 35.,929 30. 35.. 393 30. 35 .131 30. 34.,574 30.  10 10 10 10 10 10 10 10 10 10 10 10  82 .518 82 .829 83,. 153 83 , 485 83,,819 84 . 154 84,.484 84 . .811 85 , . 146 85..481 85.,811 86.. 136  86.,455 86., 795 87 , 123 87 , ,441 87 . , 774 88.,116 88.. 440 88 . , 765 89 . .087 89 . .430 89..761 90..092 90..425 90,.749 91 .085 , 91 .407 , 91 . 736 92,.070 92,. 398 92 , . 737 . 93,.060 93,. 374 93..717 94 .040 . 94 . 375 94..700 95..031 95,. 359 95 .688 96 .022 96 . 337 96,.681 97,.012 97 . 336 97 .668 97 . 996 98 . 321 98 .650 98 .983 99 .313 99 .645 99 .975 100 .305 100 .630 100 .970 101 .297 101 .629 101 .961 102 . 284 102 .623  34 . ,261 20. 33 . .929 20. 33 .586 20. 33 .375 20. 33 . 155 20. 32 . .700 20. 32 . .449 20. 32 . , 136 20. 31 . ,987 20. 31 ,941 . 20. 31 ,435 . 20. 31 ,541 , 20. 31 ,311 , 20. 31 ,550 , 20. 31 .034 , 20. 31 ,068 , 20. 31 ,052 , 20. 30,,546 20. 30,.581 20. 30..617 20. 30.. 570 20. 30..635 20. 30..313 20. 30..419 20. 30 .444 20. 30 .530 20. 30 .401 20. 30..395 20. 30..287 20. 30..455 20. 30..418 20. 30..474 20. 30..223 20. 29..921 20. 29..783 20. 29 .491 20. 29..474 20. 29 .121 20. 29 . 177 20. 28 .895 20. 28 . 787 20. 28 .475 20. 28 .500 20. 28 .218 . 20. 28 .019 20. 27..972 20. 28 .007 20. 27 .899 2 0 . 27 .975 20. 27 .714 20.  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  0 99  102 .9 5 0 103 .283 103 .604 103 .937 104 .267 104 .596 104 .928 105. 255 105..587 105 . .909 106.. 244 106 . ,573 106,.898 107 ,242 , 107 ,560 , 107..893 108 , 229 108 .554 , 108 .878 109 . 205 109 .539 109 .867 1 10 .200 1 10 . 524 1 10 .848 111 . 197 111 .516 1 1 1.850 1 12. 180 1 12.507 999  27 .616 20. 10 27 .283 20. 10 27 .267 20. 10 27 .2 2 0 20. 10 27. 163 20. 10 27 . .035 20. 10 27., 101 20. 10 26.,901 20. 10 26.,752 20. 10 26 , .858 20. 10 26 . .944 20. 10 26..847 20. 10 26.. 749 20. 10 26 .672 20. 10 26 . 574 20. 10 26 . 323 20. 10 26 .327 20. 10 26 . 158 20. 10 26 . 152 20. 10 26 .085 20. 10 25 .946 20. 10 25 . 705 20. 10 25 .689 20. 10 25 .632 20. 10 25 . 534 20. 10 25 . 376 20. 10 25 . 3 9 0 20. 10 25 . 364 20. 10 25 .042 20. 10 25 .036 20. 10 999  26 .988 52 .996 82 . 504  91 .823 30. 10 68 . 172 30. 10 46 . 334 30. 10  2 1 0.759.999.999.999.999.99 10.0E-10 RUN 2 6 ; TEMPERATURE=35 C 8 6 9 . 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 . 2 5 0 69 .2 69.2 .275 76 .4 76 . 4 .300 86 .5 86 . 5 .325 97 .9 97 .9 42.5 73. 763 30. 10 42. 492 42 .517 71 .431 30. 10 64 .538 30. 10 42 .823 43. 166 60. 552 30. 10 58 . 43 .502 ,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 . , 4 9 3 47 , . 198 30. 10 47 ;8 3 0 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 44 .861 20. 10 49,.841 50,. 171 44 .458 20. 10 44 . 369 20. 10 50,.514 44 . 149 20. 10 50,.839 . 171 44 .000 20. 10 51 , 51 , . 504 43 .800 20. 10 .834 51 . 43 .519 20. 10 52 . 179 43 . 298 20. 10 52 .508 43 . 109 20. 10 42 .847 20. 10 52 ,844 53 . 183 42 .698 20. 10 53 . 5 0 9 42 .702 20. 10 53 .839 42 . 3 7 0 20. 10  54,. 172 42 .251 20. 42 . 194 20. 54,.508 54 , .839 42 , . 136 20. 55,. 166 41 .815 20. 41 .828 20. 55,.509 41 .883 20. 55,.835 67,.514 36 .042 20. 67 .837 35 .833 20. 68 . 168 35 .644 20. 35 .677 20. 68 .512 68 .836 35 .518 20. 35 . 237 20. 69 . 171 34 .925 20. 69 .505 34 .868 20. 69 .831 999. 999. 0 99  10 10 10 10 10 10 10 10 10 10 10 10 10 10  

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