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Studies on physical properties of egg shells Tung, Marvin Arthur 1967

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STUDIES ON PHYSICAL PROPERTIES OF EGG SHELLS  by MARVIN ARTHUR TUNG B.S.A.,  University  of  British  Columbia,  i960  A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE I N AGRICULTURE I n the  Department of  Agricultural  We a c c e p t t h i s required  Mechanics  t h e s i s as conforming t o  standard  THE UNIVERSITY OF BRITISH COLUMBIA APRIL,  1967  the  In p r e s e n t i n g for  thesis  an a d v a n c e d d e g r e e  that  the- L i b r a r y  study thesis  for  make  agree  University  it  that  freely  of  permission  for  representatives.  by h i s of  of  this  thesis  for  It  financial  permi ssion ,  A g r i c u l t u r a l Mechanics  A p r i l , 1967  Columbia  of  British  available  or  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada Date  the  fulfilment  p u r p o s e s may be g r a n t e d  my w r i t t e n  Department  at  in p a r t i a l  scholarly  publication  v/i t h o u t  shall  I further  Department or  this  for  the  requirements  Columbia,  I  reference  and  extensive  copying of  agree  this  by t h e Head o f my  is understood gain  shall  that not  be  copying allowed  ii ABSTRACT P h y s i c a l c h a r a c t e r i s t i c s of egg s h e l l s and t h e i r r e l a t i o n s h i p s to s h e l l strength were studied I n 2 , 7 3 3 eggs c o l l e c t e d over t h i r t y - t w o weeks from a f l o c k of. s i x t y S i n g l e Comb White Leghorn p u l l e t s . S h e l l strength under q u a s i - s t a t i c l o a d i n g was measured as maximum f o r c e a t f a i l u r e and as energy absorbed a t f a i l u r e when load was a p p l i e d a t the equator of the egg. Area under the force-deformation  curve was taken as energy absorbed  by the s h e l l up t o f a i l u r e and the slope of the curve as s h e l l stiffness. Egg s i z e was measured as egg weight, width and length.  S h e l l weight, thickness a t the equator, percent egg  as s h e l l , and s h e l l weight per u n i t surface area were studied as measures of s h e l l quantity.  Shape index, roundness, and  three concepts of s p h e r i c i t y were used to describe egg shape. Hardness i n r a d i a l sections of ^ 2 5 s h e l l s was tested w i t h a micro-indentation technique.  V a r i a t i o n i n hardness across the  thickness o f egg s h e l l s was examined i n r a d i a l and t a n g e n t i a l sections of nine s h e l l s . Force a t f a i l u r e as a measure of s h e l l  strength  showed high m u l t i p l e c o r r e l a t i o n s w i t h combinations of p h y s i c a l p r o p e r t i e s , whereas energy absorbed a t f a i l u r e had r e l a t i v e l y small m u l t i p l e c o r r e l a t i o n s with p h y s i c a l c h a r a c t e r i s t i c s . S h e l l s t i f f n e s s was found to be the most Important  ill i n d i r e c t measure of s h e l l strength along with l e s s e r  effects  of egg weight, s h e l l width, shape index, and hardness. S h e l l q u a n t i t y c h a r a c t e r i s t i c s , along with egg s i z e and shape, were shown by means of t h e o r e t i c a l and  statistical  analyses to be l a r g e l y responsible f o r s h e l l s t i f f n e s s . Shape index proved to be the most s a t i s f a c t o r y measure of egg shape w i t h respect to reducing r e s i d u a l variance of force at f a i l u r e a f t e r s t i f f n e s s was considered and was  Judged  to be the most accurate of the shape measurements studied. S h e l l hardness was found to vary i n a p a r a b o l i c manner across the s h e l l thickness, reaching minimum values near the midpoint of the s h e l l .  Comparable hardness gradients were  observed i n both r a d i a l and t a n g e n t i a l s h e l l s e c t i o n s .  No  appreciable change i n hardness or I t s gradient r e s u l t e d from removal of s h e l l membranes w i t h sodium hydroxide  solution.  The proportions of v a r i a t i o n i n f o r c e at f a i l u r e exp l a i n e d by the non-destructive v a r i a b l e s s h e l l s t i f f n e s s , egg s i z e , and shape were 60.5,  77.7,  and 86.3  percent i n pooled-egg,  b i r d average per p e r i o d , and o v e r a l l b i r d average analyses respectively.  iv TABLE OF CONTENTS Page  INTRODUCTION  1  REVIEW OF THE LITERATURE  2  EXPERIMENTAL METHODS  6  Sampling Procedures  6  Egg and S h e l l P h y s i c a l P r o p e r t i e s  6  Egg S i z e  6  Egg Shape  6  S h e l l Strength  10  S h e l l Quantity  13  S h e l l Hardness  14  Tests o f . R a d i a l Sections  14  Tests of Tangential Sections  1?  A n a l y t i c a l Procedures RESULTS AND DISCUSSION Egg and S h e l l P h y s i c a l P r o p e r t i e s  20 21 21  S h e l l Strength  21  Shell Stiffness  23  Egg S i z e  27  Egg Shape  27  S h e l l Quantity  29  S h e l l Hardness  30  Page Importance to S h e l l Strength  30  Hardness Gradient  31  Non-Destructive E s t i m a t i o n of S h e l l Strength  38  SUMMARY  39  LIST OF REFERENCES  41  APPENDIX A  44  APPENDIX  B  5^  APPENDIX  C  6?  vi LIST OF TABLES Table 1  Page C o e f f i c i e n t s of M u l t i p l e Determination (x 1 0 0 ) f o r Regression of a l l S h e l l P r o p e r t i e s on S h e l l Strength Expressed as Force and Energy at F a i l u r e .  2  Group 1 ,  22  Simple C o r r e l a t i o n s of S h e l l S t i f f n e s s w i t h S h e l l Quantity Measurements.  3  Group 1  24  C o e f f i c i e n t s of M u l t i p l e Determination (x 1 0 0 ) f o r Regressions of S h e l l Quantity, Egg S i z e , and Shape on S t i f f n e s s .  4  Group 1 .  25  Percent Reduction In Residual Variance by Adding Egg Shape Measurements to the Regression of S t i f f n e s s on Force a t F a i l u r e .  5  Group 1  28  Comparison of Non-Destructive S h e l l P r o p e r t i e s w i t h a l l S h e l l Measurements i n Regression Group 1  38  Al  Testing Periods and Sample Size  k$  A2  Eggs Tested by B i r d and P e r i o d  k6  A3  Means and Standard Deviations. Group 1  4-9  Ak  Means and Standard Deviations. Group 2  50  A5  Means and Standard Deviations by P e r i o d  51  on Force a t F a i l u r e .  vii Table BI  Page Simple C o r r e l a t i o n C o e f f i c i e n t s .  Group  1.  Pooled-Egg Basis B2  55  Simple C o r r e l a t i o n C o e f f i c i e n t s .  Group  1.  B i r d Average Per P e r i o d Basis B3  56  Simple C o r r e l a t i o n C o e f f i c i e n t s .  Group  1.  O v e r a l l B i r d Average Basis B4  57  Simple C o r r e l a t i o n C o e f f i c i e n t s .  Group  2.  Pooled-Egg Basis B5  58  Simple C o r r e l a t i o n C o e f f i c i e n t s .  Group  2.  B i r d Average Per P e r i o d B a s i s B6  Simple C o r r e l a t i o n s  59  Between Load and  Selected  V a r i a b l e s P o r Each T e s t P e r i o d B7  Squares o f  Simple and P a r t i a l  B e t w e e n Load and S e l e c t e d  60  Correlations  Variables.  Group 1 B8  Squares o f  6l S i m p l e and P a r t i a l  B e t w e e n E n e r g y and S e l e c t e d  Correlations Variables.  Group 1 B9  Squares o f  62 Simple and P a r t i a l  Between S t i f f n e s s Group 1  Correlations  and S e l e c t e d  Variables. 63  viil Table BIO  Page Squares of Simple and P a r t i a l Between Load and Selected  Correlations  Variables.  Group 2 Bll  64  Squares of Simple and P a r t i a l  Correlations  Between Energy and Selected  Variables.  Group 2 B12  65  Squares of Simple and P a r t i a l  Correlations  Between S t i f f n e s s and Selected  Variables.  Group 2 Cl  66  Stepwise M u l t i p l e Regression With Load as the Dependent V a r i a b l e .  Group 1.  Pooled-Egg  Basis C2  68  Stepwise M u l t i p l e Regression With Energy as the Dependent V a r i a b l e .  Group 1.  Pooled-  Egg B a s i s C3  69  Stepwise M u l t i p l e Regression With S t i f f n e s s as the Dependent V a r i a b l e .  Group 1.  Pooled-Egg Basis C4  70  Stepwise M u l t i p l e Regression With Load as the Dependent V a r i a b l e . Average per Period B a s i s  Group 1.  Bird 71  ix Table C5  Page Stepwise M u l t i p l e Regression With Energy as the Dependent V a r i a b l e .  Group 1 .  Bird  Average Per Period B a s i s C6  72  Stepwise M u l t i p l e Regression With S t i f f n e s s as the Dependent Variable.  Group 1 .  Bird  Average Per P e r i o d Basis C7  73  Stepwise M u l t i p l e Regression With Load as the Dependent V a r i a b l e .  Group 1 .  Overall  B i r d Average B a s i s C8  74  Stepwise M u l t i p l e Regression With Energy as the Dependent V a r i a b l e .  Group 1 .  Overall  B i r d Average B a s i s Q9  75  Stepwise M u l t i p l e Regression With S t i f f n e s s as the Dependent V a r i a b l e .  Group 1 .  O v e r a l l B i r d Average Basis CIO  Stepwise M u l t i p l e Regression With Load as the Dependent V a r i a b l e .  Group 2 . Pooled-  Egg B a s i s Cll  76  77  Stepwise M u l t i p l e Regression With Energy as the Dependent V a r i a b l e . Egg B a s i s  Group 2 . Pooled78  X  Table C12  Page Stepwise M u l t i p l e Regression with S t i f f n e s s as the Dependent Variable.  Group 2. 79  Pooled-Egg Basis C13  Stepwise M u l t i p l e Regression With Load as the Dependent V a r i a b l e .  Group 2.  Bird  Average Per Period Basis Cl4  80  Stepwise M u l t i p l e Regression with Energy as the Dependent V a r i a b l e .  Group 2.  Bird  Average Per Period Basis C15  81  Stepwise M u l t i p l e Regression With S t i f f n e s s as the Dependent V a r i a b l e .  Group 2.  Bird  Average Per Period Basis Cl6  Selected  82  Non-Destructive C h a r a c t e r i s t i c s i n  M u l t i p l e Regression on Load.  Group 1.  Pooled-Egg Basis C17  Selected  83  Non-Destructive C h a r a c t e r i s t i c s i n  M u l t i p l e Regression on Load.  Group 1.  B i r d Average Per Period Basis C18  Selected  84  Non-Destructive C h a r a c t e r i s t i c s i n  M u l t i p l e Regression on Load. O v e r a l l B i r d Average Basis  Group 1. 85  Selected Non-Destructive C h a r a c t e r i s t i c s i n M u l t i p l e Regression on Load f o r Each Test Period  LIST OF FIGURES Figure 1.  Shadow Photography Method  2.  Bellows V a l v a i r Hydrocheck Compression Unit  3.  Bellows V a l v a i r Hydrocheck Compression Unit Showing Load C e l l (A) and L.V.D.T. (B)  4.  T y p i c a l Force-Deformation Curves f o r Egg S h e l l s  5.  Tukon Micro-Indentation Hardness Tester  6.  S h e l l s Mounted i n Epoxy f o r Hardness Testing A - R a d i a l Tests, (Mag.  7.  B - Tangential Tests,  x 2)  Photomicrograph of a R a d i a l S e c t i o n of Egg S h e l l Showing Indentation a t S h e l l Level .25 (Mag.  8.  x 210)  Schematic Diagram of an Egg S h e l l i n the Plane of i t s Equator  9.  Hardness Gradient of S h e l l No. 19a.  Tests  Made on a Tangential S e c t i o n 10.  Average Hardness Gradient of S h e l l s of B i r d s No. 5, 9, 19. Sections  Tests Made on Tangential  ziii Figure 11.  Page Comparison of R a d i a l (upper) and Tangential (lower) Hardness Gradients of S h e l l s 19a,  .... 35  b, c. 12.  Comparison of Radial (upper) and Tangential (lower) Hardness Gradients of S h e l l s of  36  B i r d s No. 5. 9, 19.  13.  Photomicrograph of a Radial S e c t i o n of Egg S h e l l Showing Indentations a t S h e l l Levels  .25  (A), and  .75  (B).  (Mag. x  210).  37  xiv L I S T OF ABBREVIATIONS D.P.H., Diamond p y r a m i d  AND D E F I N I T I O N S  hardness.  - Load p e r u n i t a r e a o f  s u r f a c e c o n t a c t i n kgm./sq.mm. Eggwt, E g g w e i g h t .  - Fresh weight  Energy, Energy absorbed absorbed  o f t h e e g g I n gm.  at failure.  - Amount  by t h e egg on b e i n g crushed  o f energy calculated as  t h e a r e a u n d e r t h e f o r c e - d e f o r m a t i o n c u r v e i n gm.-cm. Length,  E g g l e n g t h i n cm.  Load, Force a t f a i l u r e .  - The f o r c e i n grams a p p l i e d t o t h e  e q u a t o r o f t h e egg t h a t r e s u l t s i n s h e l l  failure,  i n gm. Mgmcm2,, S h e l l w e i g h t Persh, Percent  shell.  egg w e i g h t  perunit  s u r f a c e a r e a - i n mgm./sq.cm.  - The r a t i o o f s h e l l w e i g h t  i n percent.  P o l s s o n ' s R a t i o - The r a t i o o f u n i t l a t e r a l unit longitudinal Prasph,  Practical  to fresh  extension f o r a solid  sphericity.  the diameter  contraction to material.  - The r a t i o f o r m e d by d i v i d i n g  of a c i r c l e  equal i n area t o t h e pro-  j e c t e d a r e a o f a p a r t i c l e by t h e d i a m e t e r smallest circumscribing c i r c l e ,  of the  i n percent.  XV  P 3 d s p h , P r a c t i c a l three-dimensional s p h e r i c i t y . - The r a t i o  formed by d i v i d i n g the diameter of a sphere of volume equal to that of the p a r t i c l e by the diameter of the smallest c i r c u m s c r i b i n g sphere, i n percent. Q u a s i - S t a t i c Loading - The a p p l i c a t i o n of f o r c e to a specimen at r e l a t i v e l y low r a t e s . Round, Roundness. - The maximum projected area of the egg d i v i d e d by the area of the smallest c i r c u m s c r i b i n g c i r c l e , i n percent. S h e l l Level - P o s i t i o n across the thickness of the egg s h e l l from the outer edge as a f r a c t i o n of s h e l l thickness at that l o c a t i o n . Shelw.t, S h e l l weight. - Weight of the d r i e d s h e l l without membranes, i n gm. Shindx, Shape index. - The r a t i o formed by d i v i d i n g egg width by egg length, i n percent. S t i f f , S h e l l s t i f f n e s s . - The r a t i o formed by d i v i d i n g f o r c e a p p l i e d to the s h e l l by deformation i n the d i r e c t i o n of a p p l i e d f o r c e , i n gm./micron. Thick, S h e l l thickness. - Thickness of the s h e l l taken a t the egg's equator, i n microns.  zvi Totdef, T o t a l deformation. - The o v e r a l l dimensional change In the d i r e c t i o n of applied f o r c e , I n microns. Trusph, True s p h e r i c i t y . - The r a t i o formed by d i v i d i n g the surface area of a sphere of volume equal to that of the p a r t i c l e by the surface area of the p a r t i c l e , i n percent. Width, Egg width. - The diameter of the egg a t i t s equator, i n cm. Young's Modulus - The p r o p o r t i o n a l i t y constant between s t r e s s and s t r a i n i n an e l a s t i c m a t e r i a l .  xvli  ACKNOWLEDGEMENTS  The w r i t e r wishes t o express h i s a p p r e c i a t i o n f o r a s s i s t a n c e i n t h i s study bys Professor L.M. S t a l e y who d i r e c t e d t h i s research, provided encouragement, and advice, Dr. J.F. Richards, Department of P o u l t r y Science, f o r counsel on aspects of egg s h e l l strength and the supply of some m a t e r i a l s and f a c i l i t i e s , Dr. C.W. Roberts and Professor E.L. Watson f o r serving on the research committee and reviewing t h i s paper, Dr. E. Teghtsoonlan and the Department of Metallurgy f o r advice and f a c i l i t i e s i n the study of hardness, Mr. M. Hudson, foreman, and other s t a f f members of the P o u l t r y Farm who c o l l e c t e d and recorded eggs used i n t h i s study, Mr. W. Gleave f o r suggestions which l e d to c o n s t r u c t i o n of shadow photography equipment.  INTRODUCTION  The p r o p o r t i o n of cracked eggs reported by r e g i s t e r e d grading s t a t i o n s i n Canada has increased by 140 percent since  1953  according to the P o u l t r y Market Review  Cray  (1953) found  that grading s t a t i o n s  (1964. and 1965). detected only about 48  percent of a l l eggs cracked up to the time of grading because the remaining 5 2 percent were removed on the 'farm.  Assuming  comparable breakage i n f l o c k s whose eggs were not shipped to grading s t a t i o n s and a decrement of 10 cents per dozen, weak s h e l l s cost the Canadian egg i n d u s t r y approximately dollars i n  1965.  I n B.C., where Raffa  (1967)  4.2 m i l l i o n  estimates.that  65 percent of a l l eggs pass through r e g i s t e r e d grading s t a t i o n s , the l o s s was about 5 9 0 thousand d o l l a r s i n 1 9 6 5 . have been shown by Brown et a l .  (1966)  Cracked eggs  to be more s u s c e p t i b l e  to b a c t e r i a l spoilage than sound eggs under c e r t a i n adverse c o n d i t i o n s , thereby presenting a p o t e n t i a l h e a l t h hazard. Reduction of damage to egg s h e l l s i n mechanical handl i n g r e q u i r e s a knowledge of s t r e s s l e v e l s which r e s u l t i n shell failure.  O v e r a l l improvement of egg s h e l l strength by  e i t h e r genetic or n u t r i t i o n a l means i s contingent upon s e l e c t i o n of an appropriate measure of s h e l l strength and i d e n t i f i c a t i o n of s h e l l c h a r a c t e r i s t i c s that contribute to i t s strength. This study was designed to examine a number of p h y s i c a l and mechanical p r o p e r t i e s of egg s h e l l s and t h e i r i n f l u e n c e on two measures of egg s h e l l strength.  2 REVIEW OF THE LITERATURE E a r l y studies on egg s h e l l strength have been reviewed by T y l e r (196l).  The concept of strength has been described as  r e s i s t a n c e of the s h e l l to crushing, Impact and puncturing. Rehkugler (1964) studied Impact strength of s h e l l s using various types of cushioning m a t e r i a l s .  He observed that  s h e l l s have a greater capacity to absorb energy under Impact l o a d i n g than s t a t i c l o a d i n g .  Sluka et a l . (1965) reported the  development of an h y d r o s t a t i c s h e l l strength t e s t e r that i s claimed to simulate dynamic s i t u a t i o n s involving, impact d e c e l e r a t i o n of the egg.  In a l a t e r paper, Sluka et a l . (1966)  presented an a n a l y s i s of s h e l l stresses under Impact decelerat i o n which was used to c a l c u l a t e u l t i m a t e s h e l l s t r e s s . Voisey and Hunt (1967c)described a device used f o r measuring the maximum f o r c e imposed on egg s h e l l s by the impact of a f a l l i n g s t e e l rod. In general, r e s i s t a n c e of...the s h e l l to crushing i s measured by q u a s i - s t a t i c l o a d i n g of the s h e l l between two surfaces.  Brooks and Hale (1955) used load a t f a i l u r e and a l s o  l o a d a t f a i l u r e d i v i d e d by s h e l l thickness as measures of r e sistance to crushing.  Presumably the l a t t e r concept was an  attempt to evaluate the i n t r i n s i c strength of the s h e l l mater i a l by c o r r e c t i n g f o r v a r i a t i o n s i n s h e l l thickness.  Rehkug-  l e r (1964) introduced the degree of energy absorption by the egg under q u a s i - s t a t i c l o a d i n g as a measure of s h e l l strength. Energy absorbed by the s h e l l was taken as the area under the  3 l o a d - d e f o r m a t i o n c u r v e up t o t h e p o i n t o f f a i l u r e . and Boersma (1962) s u g g e s t e d t h e u s e o f s h e l l  Schoorl  deformation  caused b y a g i v e n l o a d a s a n i n d e x o f s t r e n g t h b e c a u s e t h i c k n e s s a n d p e r c e n t a g e s h e l l a r e more h i g h l y deformation than breaking strength. R i c h a r d s and S t a l e y  Shell  that  with  (1966) a n d  Hunt and V o i s e y  failure  strength.  s t r e n g t h measurements by p u n c t u r i n g a r e d e -  s c r i b e d b y L u n d e t al.(1938), and T y l e r  correlated  (1967) have u s e d maximum f o r c e a t  as a measure o f c r u s h i n g  shell  (I96I).  Novlkoff  and G u t t e r l d g e  (19^9),  The m a i n a d v a n t a g e o f p u n c t u r i n g methods  is  s e v e r a l m e a s u r e m e n t s may be made o n a s i n g l e e g g . Romanoff  (19^9), B r o o k s a n d H a l e (1955), B r o o k s  (1958). a n d G a i s f o r d (1965) r e p o r t e d no s i g n i f i c a n t b e t w e e n egg s i z e a n d c r u s h i n g s t r e n g t h .  correlation  I n a study of  300 e g g s , S t e w a r t (1936) f o u n d a h i g h l y s i g n i f i c a n t  correlation  ( r = +.260) b e t w e e n egg w e i g h t a n d c r u s h i n g s t r e n g t h .  (1967) r e p o r t e d a s m a l l b u t s i g n i f i c a n t  and S t a l e y  Richards  simple  correlation  ( r = +.11,  egg w e i g h t .  Egg s i z e a s m e a s u r e d b y egg w i d t h a n d egg l e n g t h  was shown t o be h i g h l y  n = 531)  over  between s h e l l  correlated with shell  work o f R i c h a r d s and S t a l e y  s t r e n g t h and  strength i n the  (1967).  S h e l l q u a n t i t y measured as s h e l l w e i g h t , as s h e l l ,  and s h e l l  correlated with are Shuster Staley  p e r c e n t egg  t h i c k n e s s have been shown t o be v e r y  shell  highly  s t r e n g t h by s e v e r a l w o r k e r s , among whom,  (1959), Hunt a n d V o i s e y (1966) a n d R i c h a r d s a n d  (1967).  An I n d i r e c t  method u s i n g s p e c i f i c  gravity  of  4  the whole egg as a measure of s h e l l quantity has been used by Novlkoff and Gutteridge Prank et Grimlnger  al.(1964).  (1949),  Marks and Kinney  T y l e r and Geake  (1961)  (1964)  and  and Hurwitz and  suggest the use of s h e l l weight per u n i t  (1962)  surface area as a more accurate measure of s h e l l q u a n t i t y . Stewart  (1936)  studied egg shape and curvature i n  r e l a t i o n to s h e l l strength and found small but s i g n i f i c a n t relations  between strength and shape measurements.  cor-  Frank et a l .  ( 1 9 6 4 and 1 9 6 5 ) recognized the need to consider s h e l l geometry i n r e l a t i o n to strength.  Richards and Swanson  (1965)  reported  egg shape expressed as shape index to be independent of s h e l l thickness and to account f o r 1 5 to 35 percent of the v a r i a b i l i t y i n crushing strength a f t e r s h e l l thickness was considered. Hunt and Volsey  (1966)  found egg shape t o be the most important  s h e l l strength p r e d i c t o r a f t e r s h e l l s t i f f n e s s was considered. Richards and S t a l e y  (1967)  point out that shape index, when  ;  included w i t h deformation per u n i t l o a d increased the c o e f f i c i e n t of determination of crushing strength by 1 5 and 2 0 percent i n t h e i r pooled-egg and b i r d average analyses r e s p e c t i v e l y . Mechanical p r o p e r t i e s of egg s h e l l m a t e r i a l were f i r s t studied w i t h micro-Indentation hardness t e s t i n g by Brooks. and Hale  (1955).  They reported the average hardness of t e n  strong s h e l l s to be s i g n i f i c a n t l y higher than that of ten weak .. shells.  A gradient of hardness was found t o e x i s t across the  thickness o f the s h e l l which increased almost l i n e a r l y toward the outer edge.  Rehkugler  (1963)  developed a technique whereby  5 the modulus of e l a s t i c i t y and u l t i m a t e strength of s h e l l m a t e r i a l were measured. The behavior of the egg s h e l l under q u a s i - s t a t i c l o a d i n g has been studied by Brooks and Hale and Boersma and Voisey  (1962), (1966)  Rehkugler  (1964),  (1955)»  Gaisford  and Richards and Staley  Schoorl  (1965),  (I967)  Hunt  with simul-  taneous measurement of a p p l i e d load and r e s u l t a n t deformation of the s h e l l .  Each of these i n v e s t i g a t o r s has observed that  the load-deformation curve i s approximately l i n e a r and that the slope of the curve, or i t s Inverse, i s h i g h l y c o r r e l a t e d w i t h load a t f a i l u r e .  Richards and Staley p o i n t out the v a l i d i t y  of c a l c u l a t i n g the slope of the curve d i r e c t l y as the r a t i o of maximum load and deformation. The l i t e r a t u r e reveals that several p h y s i c a l charact e r i s t i c s of the hen's egg s h e l l are important to i t s strength! however,, the roles, of egg s i z e , egg shape and s h e l l hardness i n r e l a t i o n to other p h y s i c a l p r o p e r t i e s and to s h e l l strength are not w e l l understood.  This i n v e s t i g a t i o n was designed to  c l a r i f y r e l a t i o n s between egg s i z e , egg shape, s h e l l q u a n t i t y , s h e l l hardness measurements and s h e l l strength and to i n v e s t i gate the f e a s i b i l i t y of non-destructive strength.  e v a l u a t i o n of egg s h e l l  6  EXPERIMENTAL METHODS Sampling Procedures A t o t a l of  2,733  eggs were c o l l e c t e d during the  second and t h i r d weeks of eight four-week periods  beginning  January the second, 1 9 6 6 , from a f l o c k of s i x t y Single-Comb White Leghorn p u l l e t s i n t h e i r f i r s t year of production.  The  f l o c k , which consisted of equal numbers of b i r d s from the two r e s u l t a n t crosses of a r e c i p r o c a l mating program, was fed a commercial r a t i o n containing f o u r percent calcium.  Individual  wire cages allowed i d e n t i f i c a t i o n of eggs produced by each hen. For the purpose of a n a l y s i s , Group One was made up of the e n t i r e sample of  2,733  eggs, whereas a subsample of  425  eggs  from ten a r b i t r a r i l y selected b i r d s of one cross was d e s i g nated as Group Two f o r the a d d i t i o n a l t e s t i n g of s h e l l hardness. Egg and S h e l l P h y s i c a l P r o p e r t i e s Egg S i z e P h y s i c a l c h a r a c t e r i s t i c s representing egg s i z e were assumed to be egg weight, width, and length.  The f r e s h weight  of each egg was measured to the nearest centigram a f t e r which egg width and length were determined w i t h a p r e c i s i o n of + . 0 0 5 cm. using a v e r n i e r c a l i p e r . Egg Shape Shape index was c a l c u l a t e d i n the usual manner as the quotient of egg width and l e n g t h m u l t i p l i e d by one hundred. Roundness i n a plane p a r a l l e l t o the major a x i s of  F i g . 1 . Shadow Photography Method. the egg was measured with the a i d of a shadow photograph taken as shown I n F i g . 1 and the formulas Roundness = 127 A D  where  (1)  2  A = area of the shadow cast by the egg, and D = maximum diameter of the shadow.  This formula defines roundness as one hundred times the maximum projected area of the egg d i v i d e d by the area of the smallest circumscribing c i r c l e .  A roundness of 1G0 i s approached as the  shadow approaches c i r c u l a r i t y .  Area of the shadow photograph  was measured with a p o l a r compensating planlmeter and shadow length w i t h d i v i d e r s and a scale to p r e c i s i o n l i m i t s of + . 0 1  8 square i n c h and + .01 i n c h r e s p e c t i v e l y . The concepts of roundness and s p h e r i c i t y as a p p l i e d to geology and petrography were c l a r i f i e d by Wadell  (1933)  from which three measures of s p h e r i c i t y were adapted f o r use i n t h i s study to describe egg shape. Wadell defined true s p h e r i c i t y ass l/j-s S where  • •  (2)  s = surface area of a sphere of volume equal to that of the p a r t i c l e , and S = surface area of the p a r t i c l e .  The formula of T y l e r and Geake ( 1 9 6 l ) was used to represent the volume of an egg V = .512LB  that i s ,  8  -  2  .06  (3) 3  where  V = volume of the egg i n cm.% L = egg l e n g t h i n cm., and B = egg width i n cm.  Por a sphere, surface area and volume are r e l a t e d by s = 4 . 836V  where  2  /  (4)  3  s = surface area I n cm. , and 2  V = volume i n cm.  3 0  By s u b s t i t u t i o n of equation ( 3 ) I n ( 4 ) , the surface area of a sphere w i t h a volume equal to that of an egg was given by s = 4.836(.512LB -.06) 2  2 /  3.  (5)  Surface area of the egg was taken from the formula of Mueller and Scott ( 1 9 ^ 0 ) ,  9 S = 4.67W  (6)  2/3  2 where  S = surface area of the egg I n cm. , and W = f r e s h weight of the egg i n gm.,  which gave true s p h e r i c i t y based on an index of one hundred as \jj = 100s = 483.6(.512LB ~.06) 2  4.67W  S  2  /  3  .  (7)  2 / 3  That I s , True s p h e r i c i t y =  103.6^. 5 1 2 L B - . 0 6 J 2  2 / / 3  (8)  I t i s noteworthy that t h i s expression of egg shape was derived from three measures of egg slze--egg weight, width, and length. Wadell defined p r a c t i c a l s p h e r i c i t y a s :  d> where  (9)  = d D  d = diameter of a c i r c l e equal i n area t o the area of the p a r t i c l e p r o j e c t i o n , and D = diameter of the smallest c i r c l e c i r c u m s c r i b i n g the p a r t i c l e .  The r e l a t i o n of the diameter of a c i r c l e t o i t s area, d = (l.Z7A) ,  (10)  1/2  was s u b s t i t u t e d i n t o equation (9) which r e s u l t e d i n Cfj> = ^1'27A j  1  /  2  (11)  as the formula f o r p r a c t i c a l s p h e r i c i t y based on an index of one hundred.  I t was noted that p r a c t i c a l s p h e r i c i t y was the  square root of the roundness measurement p r e v i o u s l y discussed; t h e r e f o r e , p r a c t i c a l s p h e r i c i t y of each egg was c a l c u l a t e d from  10 (Roundness )  (12)  1 / / 2  P r a c t i c a l three-dimensional  s p h e r i c i t y was  suggested  by Wadell to be; (13)  y=dj_  P' where  d  = diameter of the sphere of volume equal to that  ?  of the p a r t i c l e , D' = diameter of smallest c i r c u m s c r i b i n g sphere. Using the r e l a t i o n , diameter = 1.24(volumeJ ^ 1  3  ,  (14)  f o r a sphere along with the formula of T y l e r and Geake f o r the volume of an egg and s u b s t i t u t i n g the length of the egg f o r the equation becomes; V = 124(.512LB - . 0 6 ) L 2  (15)  1 / 3  f o r the p r a c t i c a l three-dimensional  D',  s p h e r i c i t y of an egg.  It  was noted that t h i s measure of egg shape was a f u n c t i o n of egg width and length and was therefore s i m i l a r to shape index i n that respect. Shell  Strength Two  concepts of s h e l l strength under q u a s i - s t a t i c  l o a d i n g were studied--force at f a i l u r e , and energy absorbed up to f a i l u r e .  The t e s t i n g machine (Figs. 2 and 3) was a Bellows  V a l v a l r Hydrocheck Compression Unit i n which the p i s t o n was moved by compressed a i r at a r a t e c o n t r o l l e d by h y d r a u l i c checking valves. Mohsenin (1963).  This equipment was described i n d e t a i l by  11  F i g . 3.  Bellows V a l v a i r Hydrocheck Compression Unit Showing Load C e l l (A) and L.V..D.T. (B).  12 A f o r c e was a p p l i e d to the egg p a r a l l e l t o i t s minor a x i s by two f l a t brass p l a t e s .  The lower p l a t e was adjustable  v e r t i c a l l y to accommodate eggs of varying s i z e and was ridged near the outer edge to prevent eggs from r o l l i n g o f f the p l a t e . Load a p p l i e d to the egg was measured by supporting the lower p l a t e on a s t r a i n gauge l o a d c e l l and feeding the a m p l i f i e d s i g n a l to the pen d r i v e (Y-axis) of the XY recorder.  Deforma-  t i o n of the egg while being crushed was measured by a l i n e a r v a r i a b l e d i f f e r e n t i a l transformer  (L.V.D.T.) whose a m p l i f i e d  s i g n a l was f e d to the carriage d r i v e (X-axis) of the XY recorder.  S e n s i t i v i t i e s of 600 + 10 grams per inch on the Y-axls  and 4 2 + 2 microns per inch on the X-axis were used and the deformation r a t e was c o n t r o l l e d a t 44 + 2 microns p e r second. T y p i c a l force-deformation eggs appear i n F i g . 4.  curves f o r two d i f f e r e n t  The curves were l i n e a r , o r nearly so,  and the p o i n t of s h e l l f r a c t u r e was i n d i c a t e d by the sharp peak on the graph.  Four data were obtained from each graph:  at f a i l u r e (max. Y v a l u e ) , energy absorbed up to f a i l u r e  force (area  under the curve up to the point of f a i l u r e ) , t o t a l deformation of the s h e l l (max. X v a l u e ) , and s h e l l s t i f f n e s s curve).  (slope of the  The graphs were analyzed q u i c k l y by means of a modi-  f i e d d r a f t i n g set square to which scales were glued that allowed reading f o r c e and t o t a l deformation a t f a i l u r e d i r e c t l y from the graph.  Energy absorbed up to f a i l u r e was taken as one-half  the product of maximum force and t o t a l deformation,  and s h e l l  s t i f f n e s s was c a l c u l a t e d as the quotient of maximum f o r c e and t o t a l deformation.  13  3.0  2.4  E g  1.8  73 ft 0  12  .6  0 - — —  •- — —  l major division : 4 2 microns Deformation F i g . 4.  Typical Force-Deformation Curves f o r Egg S h e l l s .  S h e l l Quantity S h e l l weight, s h e l l thickness, percent egg as s h e l l , and s h e l l weight per u n i t surface area were used to express s h e l l quantity.  A l i n e was drawn around each egg a t i t s equa-  t o r a f t e r which the egg contents were discarded and the s h e l l s b o i l e d i n . 6 2 5 Molar aqueous sodium hydroxide f o r ten minutes to remove s h e l l membranes and c u t i c l e .  The s h e l l s were rinsed  thoroughly i n tap water and d r i e d i n an oven a t 80°C. f o r  14 twenty-four hours.  Dried s h e l l s were weighed to the nearest  centigram, and s h e l l thickness to the nearest micron was  taken  as the average of three measurements at the equator using an anvil-jawed d i a l  micrometer.  Percent egg as s h e l l was c a l c u l a t e d as the quotient of d r i e d s h e l l weight and f r e s h egg weight expressed i n percent. Egg surface area was estimated using the formula of Mueller and Scott (Equation 6 ) .  S h e l l weight was d i v i d e d by egg surface  area and converted to m i l l i g r a m s per square centimeter. S h e l l Hardness Tests of R a d i a l Sections Hardness of s h e l l s produced by 10 b i r d s was measured by a m i c r o - i n d e n t a t i o n technique using the Tukon hardness t e s t e r shown i n P i g . 5. and described by Mott (1956).  After  the s h e l l membranes and c u t i c l e had been removed, a small s t r i p of s h e l l taken from near the equator of each egg was mounted i n epoxy r e s i n as shown In F i g . 6,A.  Each t e s t block contained  sections of s h e l l from s e v e r a l eggs i n order to minimize the number of blocks made. The epoxy blocks were p o l i s h e d w i t h a s e r i e s of i n c r e a s i n g l y f i n e emery papers and two aluminum oxide l a p i d a r y wheels to r e v e a l a r a d i a l s e c t i o n of each s h e l l approximately i n the plane of the equator (see F i g . 7 ) .  Diamond pyramid  hardness was measured along a l i n e at one-quarter the t h i c k ness of the s h e l l from the outer edge ( s h e l l l e v e l .25)  by  P i g . 5.  Tukon Micro-Indentation Hardness Tester.  Fig. 6.  S h e l l s Mounted i n Epoxy f o r Hardness Testing. A - Radial Tests. B - Tangential Tests. (Mag. x 2 )  16  F i g . 7.  Photomicrograph of a R a d i a l Section of Egg S h e l l Showing Indentation a t S h e l l Level , 2 5 . (Mag. x 210)  f o r c i n g a square-based diamond pyramid i n t o the s h e l l and measuring the diagonals of the recovered indentations with an ocular micrometer on the Tukon t e s t e r .  The diamond pyramid  hardness i s defined as the load per u n i t area of surface cont a c t i n kilograms per square m i l l i m e t e r c a l c u l a t e d from the average diagonal length and the formula: D.P.H. =  1.8544L  d where  (16)  2  D.P.H. • diamond pyramid hardness L  = load i n kilograms  d  - average diagonal l e n g t h i n m i l l i m e t e r s .  The average of the diagonal lengths of s i x indentations was used to c a l c u l a t e the hardness of each s h e l l a t i t s .25 s h e l l  17  level. .25  A load of 1 0 0 grams on the lndenter was used and the  s h e l l l e v e l was chosen because Brooks and Hale  (1955)  re-  ported greater d i f f e r e n c e s i n hardness near the outer edge of the egg s h e l l .  B r i t t l e n e s s of the s h e l l m a t e r i a l precluded  t e s t i n g nearer the outer edge i n r a d i a l sections. Nine s h e l l s , produced by three d i f f e r e n t b i r d s , were selected to measure the hardness across the s h e l l from l e v e l s . 2 5 to . 7 5 . Forty indentations per s h e l l were made a t randomly selected s h e l l l e v e l s which were a l s o recorded.  The hardness  data of each s h e l l were separated i n t o s i x groups f o r which the average hardness and s h e l l l e v e l were c a l c u l a t e d .  These  data were p l o t t e d i n order to I d e n t i f y p o s s i b l e v a r i a t i o n s i n hardness across the s h e l l . Tests of Tangential Sections A method was developed whereby a t a n g e n t i a l s e c t i o n of s h e l l could be exposed to a l l o w t e s t i n g f o r hardness near the edges of the egg s h e l l .  The major d i f f i c u l t y presented  was that of l o c a t i n g p o s i t i o n s of s h e l l l e v e l s on a t a n g e n t i a l s e c t i o n as shown i n F i g . 8. The p r i n c i p l e used was that of the i n t e r s e c t i o n of an a r c (the s h e l l l e v e l ) and a chord (representing, the exposed surface).  Symbols used i n the d e r i v a t i o n  are; B = egg width a t the equator, T = s h e l l thickness a t the equator, C - chord length, P = distance along chord from e i t h e r end,  18  F i g . 8.  Schematic Diagram of an Egg S h e l l i n the Plane of i t s Equator.  j = s h e l l l e v e l from outer edge (a decimal number).and x, y = coordinate d i r e c t i o n s . I n t e r s e c t i o n of the chord and the arcs w i l l be at p o i n t s , P = C - x. 2  (17)  From the t r i a n g l e , (V)  B  2  2  - C  (18)  2  and f o r the arcs a t various s h e l l l e v e l s x  2  + y  2  = 'B - JT!  (19)  At the i n t e r s e c t i o n s of the arcs w i t h the chord, y = y equation (18) may be s u b s t i t u t e d  and  i n t o equation (19) to give  19  x  2  + p £ - c£ = (B r  - jTl  12  r  (20)  2  j  w h i c h may b e s o l v e d f o r x. x = (.25C  - jBT + j T 2  2  )  2  1  /  (21)  2  and P = .5C -  (.25c  2  - jBT + j T 2  2  )  1  /  The u n i t s o f B a n d T w e r e c e n t i m e t e r s a n d i n c h e s The l e n g t h o f t h e c h o r d ,  o t h e r u n i t s were c o n v e r t e d  to give the working P - .50  -  (.25C  respectively.  C, was m e a s u r e d w i t h t h e M i c r o t o n  s t a g e o f t h e T u k o n t e s t e r i n u n i t s o f 10 m i c r o n s ; all  (22)  2  therefore  t o those o f the M i c r o t o n  stage  equation: 2  - 2.54 x 1 0  6  jBT + 6.452 x 1 0  6  A c o m p u t e r p r o g r a m was w r i t t e n t o c a l c u l a t e t h e t e s t  j T ) (23) 2  2  1  2  location  P f o r v a r i o u s v a l u e s o f j when C, B, a n d T w e r e p r o v i d e d . p r e c i s i o n e r r o r l i m i t s u s i n g t h i s method t o l o c a t e s h e l l on a t a n g e n t i a l s u r f a c e were e s t i m a t e d t o be + 1 . 2  /  The levels  percent.  N i n e s h e l l s whose h a r d n e s s g r a d i e n t s w e r e m e a s u r e d In r a d i a l  s e c t i o n s were a l s o t e s t e d t a n g e n t l a l l y a t s h e l l  .02,  .20, . . . .  .10,  corresponding  .90.  levels  A piece of shell bearing a l i n e  t o the equator  o f t h e s h e l l was m o u n t e d i n a n  epoxy b l o c k such t h a t a t a n g e n t i a l s e c t i o n a t t h e e q u a t o r  could  be e x p o s e d f r o m t h e o u t s i d e ( s e e F i g . 6 , B ) . T h r e e i n d e n t a t i o n s w e r e made a t e a c h d e s i g n a t e d  shell level  s t a r t i n g f r o m one edge  of t h e exposed s e c t i o n a l o n g a narrow s t r i p on e i t h e r s i d e o f the equator.  A d u p l i c a t e s e t o f i n d e n t a t i o n s was t h e n made  s t a r t i n g a t t h e o p p o s i t e edge o f t h e e x p o s e d a r e a s o t h a t t h e  20  average, of s i x indentations was used to c a l c u l a t e hardness a t each s h e l l l e v e l .  A f t e r t e s t s were made from l e v e l . 0 2 to . 5 0 ,  the t e s t block was cast i n epoxy so that the o r i g i n a l block could be ground away to expose a s i m i l a r s h e l l s e c t i o n from the i n s i d e on which l e v e l s . 5 0 to . 9 0 were t e s t e d .  The d u p l i c a t e  t e s t i n g of l e v e l . 5 0 provided a t o t a l of twelve  Indentations  from which the hardness a t that l e v e l was c a l c u l a t e d , A t e s t was conducted to determine whether the hardness gradient was a f f e c t e d by removing s h e l l membranes and c u t i c l e w i t h b o i l i n g sodium hydroxide s o l u t i o n .  Membranes were  s t r i p p e d mechanically from pieces of three s h e l l s that were then t e s t e d f o r hardness t a n g e n t i a l l y and compared w i t h other samples of the same s h e l l s that had been t r e a t e d with sodium hydroxide. A n a l y t i c a l Methods F a c i l i t i e s of the U n i v e r s i t y of B r i t i s h Columbia Computing Center, which include an I.B.M.  7040  d i g i t a l computer  were used to c a l c u l a t e data derived from o r i g i n a l measurements and to analyze the r e s u l t s of t h i s study.  Means, standard de-  v i a t i o n s , simple and p a r t i a l c o r r e l a t i o n s , simple and m u l t i p l e l i n e a r regressions, and stepwise m u l t i p l e regressions were c a l c u l a t e d w i t h a method s i m i l a r to that of Ralston and W l l f (I960).  Snedecor  (1956)  and E z e k l e l and Fox  (1959)  were used  as references In the I n t e r p r e t a t i o n of s t a t i s t i c a l analyses. A p l o t t i n g program was a l s o employed to f i t polynomial  curves  21 by the method of l e a s t squares to the hardness gradient  data.  A l l eggs tested i n t h i s study formed Group One which was studied on a pooled b a s i s w i t h each egg c o n t r i b u t i n g a set of v a r i a b l e s t o the a n a l y s i s .  Data of i n d i v i d u a l b i r d s f o r  each t e s t period were then averaged and analyzed on a b i r d average per period b a s i s .  O v e r a l l averages were c a l c u l a t e d f o r  those b i r d s having complete records over a l l eight t e s t periods to form the basis of the t h i r d , a n a l y s i s .  Eggs tested f o r hard-  ness c o n s t i t u t e d Group Two which was examined on both pooledegg and b i r d average per period bases.  RESULTS AND DISCUSSION Appendix A contains general sample data, means and standard d e v i a t i o n s f o r a l l analyses.  Results of simple and  p a r t i a l c o r r e l a t i o n analyses appear i n Appendix B.  Stepwise  m u l t i p l e regressions which successively eliminated n o n - s i g n i f i cant independent v a r i a b l e s were tabulated i n Appendix C along w i t h selected m u l t i p l e l i n e a r regressions using only non-des t r u c t i v e s h e l l measurements i n r e l a t i o n to f o r c e a t f a i l u r e . EKK and S h e l l P h y s i c a l P r o p e r t i e s Shell  Strength The mean strength of eggs i n t h i s study was  3557 + 578  grams when measured as f o r c e a t f a i l u r e , and  27.5 + 6.1 gm.-cm. when taken as energy absorbed while  being  crushed by a q u a s i - s t a t i c f o r c e a p p l i e d a t the s h e l l equator.  22  V a r i a t i o n i n f o r c e a t f a i l u r e was more  completely  accounted f o r by p h y s i c a l c h a r a c t e r i s t i c s of the s h e l l than was v a r i a t i o n i n energy absorbed a t f a i l u r e .  (Table 1 and  Appendix C). TABLE 1 COEFFICIENTS OF MULTIPLE DETERMINATION (x.100) FOR REGRESSION OF ALL SHELL PROPERTIES ON SHELL STRENGTH EXPRESSED AS FORCE AND ENERGY AT FAILURE. GROUP 1. Pooled-Egg Basis  B i r d Av. Per Period  Overall Bird Av.  Force  62.2  79.6  89.0  Energy  20.2  41.1  61.8  I f p h y s i c a l p r o p e r t i e s were assumed t o be capable of e x p l a i n i n g v a r i a b i l i t y i n s h e l l strength measured as energy absorption, the r e l a t i v e l y l a r g e r e s i d u a l variance i n the r e gressions on energy i n d i c a t e d that, important f a c t o r s had been overlooked  or that the present method of a n a l y s i s was unsuitable.  R e l a t i o n s h i p s among v a r i a b l e s may d i f f e r from b i r d to b i r d such that strong r e l a t i o n s h i p s w i t h i n b i r d s were masked by analyzing samples composed of eggs from several b i r d s .  This  contention  was supported by the f a c t that Richards and Staley (1967)found i n c o n s i s t e n t r e l a t i o n s h i p s between s h e l l c h a r a c t e r i s t i c s f o r different birds. C o e f f i c i e n t s of m u l t i p l e determination were found to be c o n s i s t e n t l y higher f o r regressions using averages rather than i n d i v i d u a l egg data (Table 1 ) . To a c e r t a i n extent t h i s r e s u l t was to be expected because the averaging process tends  23  to reduce the e f f e c t s of random e r r o r s due to p r e c i s i o n l i m i t s of measurement.  Another major source of random v a r i a t i o n could  have been that of the measured strength of the s h e l l which was composed p r i m a r i l y of the ceramic m a t e r i a l , c a l c l t e .  Ceramics  c h a r a c t e r i s t i c a l l y show considerable v a r i a t i o n i n strength (Hayden et a l .  1965s  Rehkugler,  1963)  which could r e s u l t i n an  appreciable range of strengths measured f o r o s t e n s i b l y i d e n t i c a l egg s h e l l s .  For t h i s reason, strength of i n d i v i d u a l  egg  s h e l l s may w e l l defy complete explanation i n terms of p h y s i c a l properties.  Average values f o r s h e l l strength and p h y s i c a l  p r o p e r t i e s of a small sample of eggs are therefore recommended when e v a l u a t i n g the strength of s h e l l s produced by i n d i v i d u a l birds. Shell Stiffness Egg s h e l l s t i f f n e s s was found to be the most important s i n g l e p r e d i c t o r of s h e l l strength measured as f o r c e at failure.  C o e f f i c i e n t s of determination were  57..1.  and  72.9,  7 8 . 5 percent f o r Group One pooled-egg, b i r d average per period and o v e r a l l b i r d average analyses r e s p e c t i v e l y . These r e s u l t s are s l i g h t l y higher than those of Richards and Staley who  (1967)  reported corresponding values of 4 9 . 0 and 62.4 percent f o r  pooled=egg and b i r d average samples. S t i f f n e s s alone explained only 8 . 4 , 2 0 . 4 , and  25.1  percent of the v a r i a t i o n i n energy absorbed at f a i l u r e i n pooled-egg,, b i r d average per period and o v e r a l l b i r d average data r e s p e c t i v e l y .  24 Egg s h e l l s t i f f n e s s was h i g h l y c o r r e l a t e d with measures of s h e l l q u a n t i t y (Table 2).  The f a c t that each of  the s h e l l quantity c h a r a c t e r i s t i c s was h i g h l y c o r r e l a t e d w i t h s t i f f n e s s was not s u r p r i s i n g i n view of t h e i r strong i n t e r — correlation. TABLE 2 SIMPLE CORRELATIONS OF SHELL STIFFNESS WITH SHELL QUANTITY MEASUREMENTS. GROUP 1. Pooled-Egg Basis S h e l l weight Thlckness Percent s h e l l S h e l l wt./area  B i r d Av. Per Period  .701 .836  .755 .914  .849 .846  .921 .918  Overall Bird Av.  .853 .956 .944 .958  R e l a t i o n s h i p s between s h e l l s t i f f n e s s and other p h y s i c a l p r o p e r t i e s were examined f u r t h e r by stepwise m u l t i p l e r e g r e s s i o n of egg s i z e , shape, and s h e l l quantity measurements on s t i f f n e s s (Tables C3, C 6 , and C9). I n the pooled-egg sample, egg width and roundness were important i n a d d i t i o n to s h e l l quantity w i t h a c o e f f i c i e n t of m u l t i p l e determination of 76.1 percent.  B i r d average per period analyses revealed the  importance of egg shape as roundness and true s p h e r i c i t y i n a d d i t i o n to s h e l l quantity w i t h an R  of 90.2 percent.  Width  was included w i t h s h e l l quantity i n the o v e r a l l b i r d average a n a l y s i s to give R  2  = 95.2 percent.  A d d i t i o n of a l l egg s i z e  and shape v a r i a b l e s t o the r e g r e s s i o n of s h e l l quantity measures on s t i f f n e s s reduced the r e s i d u a l v a r i a t i o n i n s t i f f n e s s by  25 5.9, 20.5,  and 34.9 percent i n pooled-egg, b i r d average per  p e r i o d , and o v e r a l l b i r d average analyses respectively.. (Table 3).  These analyses show the existence of a strong  relationship  between s h e l l s t i f f n e s s and s h e l l quantity along with minor c o n t r i b u t i o n s by egg s i z e and shape. TABLE 3 COEFFICIENTS OF MULTIPLE DETERMINATION (x 100) FOR REGRESSIONS OF SHELL QUANTITY, EGG SIZE, AND SHAPE ON STIFFNESS. GROUP 1. Pooled-Egg Basis ,  B i r d Av. Per Period  Overall Bird Av.  Shell quantity*  74.6  87.8 ,  93.7  Shell quantity, egg s i z e * * and shape***  76.1  90.3  95.9  * S h e l l weight, thickness, percent s h e l l , and s h e l l weight/area ** Egg weight, width, and length *** Shape index, roundness, true s p h e r i c i t y , p r a c t i c a l s p h e r i c i t y , and p r a c t i c a l three-dimensional s p h e r i c i t y .  Voisey and Hunt  (1967,b) developed a t h e o r e t i c a l  a n a l y s i s of stresses i n the egg s h e l l under external loads. They showed that when f o r c e i s a p p l i e d to the poles of the egg, deformation of the s h e l l I s given by: ^UVSq-V^PR  2ET where  (24)  2  § = deformation i n the d i r e c t i o n of a p p l i e d load, V = Poisson's r a t i o f o r s h e l l m a t e r i a l , P = load a p p l i e d ,  26 R = one-half of egg width, E = Young's modulus f o r s h e l l m a t e r i a l , and T = thickness of s h e l l . S t i f f n e s s of the s h e l l i s defined as the r a t i o of force to deformation which i s P = 2ET 8  (.25)  2  /3(1-V*)R  I f Polsson'.s r a t i o and Young's modulus f o r s h e l l m a t e r i a l a r e assumed to be constant and the s u b s t i t u t i o n , .5B = R where B - egg width i s made, a l l constants may be combined to give: S t i f f n e s s = k_T_ B where  k =  (26)  4E  In the present study, f o r c e was a p p l i e d a t the equator of the egg; t h e r e f o r e , a s i m i l a r a n a l y s i s of f a c t o r s involved i n s h e l l s t i f f n e s s would be complicated  by the l a c k of  symmetry i n a plane normal to the d i r e c t i o n of a p p l i e d f o r c e . Egg shape would undoubtedly be an Important f a c t o r i n the a n a l y s i s of s t i f f n e s s when f o r c e i s a p p l i e d to the equator. From the previous d i s c u s s i o n s i t may be concluded that t h e o r e t i c a l and s t a t i s t i c a l analyses i n d i c a t e that egg s h e l l s t i f f n e s s i s l a r g e l y a r e f l e c t i o n of s h e l l q u a n t i t y along with probable e f f e c t s of egg s i z e and shape.  27 Egg Size Egg s i z e measured e i t h e r as egg weight or width r e mained as a s i g n i f i c a n t Independent v a r i a b l e i n the stepwise m u l t i p l e regressions on f o r c e and energy absorbed at f a i l u r e f o r Group One  (Appendix C).  I n s i m i l a r analyses of Group Two:  both egg weight and l e n g t h remained i n the regressions.  After  s h e l l s t i f f n e s s had been considered, the three measures of egg: s i z e In combination explained 7.7.  17.0,  and 3^.9  percent of  the r e s i d u a l v a r i a t i o n i n f o r c e at f a i l u r e f o r Group One  pooled-  egg, b i r d average per p e r i o d , and o v e r a l l b i r d average analyses respectively. Egg width was found to be the most important measure of egg s i z e i n m u l t i p l e r e g r e s s i o n w i t h s t i f f n e s s on f o r c e at failure.  Decreases of 4.4,  5.5.  and 24.2 percent i n the r e -  s i d u a l variance of f o r c e at f a i l u r e r e s u l t e d from i n c l u d i n g egg width w i t h s t i f f n e s s i n the three Group One analyses. Egg Shape Egg shape measured as shape index, roundness, pract i c a l s p h e r i c i t y , and p r a c t i c a l three-dimensional s p h e r i c i t y had h i g h l y s i g n i f i c a n t p o s i t i v e simple c o r r e l a t i o n s w i t h f o r c e and energy absorbed at f a i l u r e i n Group One pooled-egg and b i r d average per period analyses.  True s p h e r i c i t y showed h i g h l y  s i g n i f i c a n t negative simple c o r r e l a t i o n s w i t h both measures of s h e l l strength i n these analyses.  28 Table 4 was used to compare the f i v e egg shape measurements on the b a s i s of t h e i r reduction of the r e s i d u a l variance i n f o r c e a t f a i l u r e a f t e r s h e l l s t i f f n e s s had been considered.  Shape index and p r a c t i c a l three-dimensional  s p h e r i c i t y showed c o n s i s t e n t l y greater contributions  to the  regressions i n each a n a l y s i s than d i d the other measures of egg shape. TABLE  V  PERCENT REDUCTION IN RESIDUAL VARIANCE BY. ADDING EGG SHAPE MEASUREMENTS TO THE REGRESSION OF STIFFNESS ON FORCE AT FAILURE. GROUP 1. Pooled-Egg Basis  B i r d Av. Per Period  Overall B i r d Av.  Shape index  5.3  13.3  19.5  Roundness  3.5  11.1  14.4  True s p h e r i c i t y  3.0  6.6  15.8  Practical sphericity  3.5  10.7  14.0  P r a c t i c a l three dimensional sphericity  5.3  13.3  19.5  P r a c t i c a l three-dimensional s p h e r i c i t y was highly c o r r e l a t e d w i t h shape index ( r =  therefore, comparable  .999)>  r e s u l t s f o r these shape measurements were expected.  This s i m i -  l a r i t y can be examined In the formula by which p r a c t i c a l threedimensional s p h e r i c i t y was  calculated:  P3dsph = 124C512LB  2  -  .06)  1  /  3  .  (15)  29 When cubed, (P3dsph)  3  =  976,190 B_ 2  - 114.400  L  L  3  (27)  S u b s t i t u t i n g shape Index, Shindx = 100B  and noting that the  L  second term may be omitted because i t I s very small compared w i t h the f i r s t (about .1$), gives; P 3 d s p h = 4.6(Shindx) ^ 2  3  (approximately).  (28)  Roundness proved to be the most important measure of egg shape i n the stepwise m u l t i p l e regressions on f o r c e and energy absorbed a t f a i l u r e i n b i r d average per period and overa l l b i r d average analyses of Group One; however, i n regressions of egg shape w i t h s t i f f n e s s on f o r c e a t f a i l u r e , shape index was s l i g h t l y superior to roundness i n e x p l a i n i n g r e s i d u a l variation.  I t i s noteworthy that'measurement of roundness and  p r a c t i c a l s p h e r i c i t y was of r e l a t i v e l y low accuracy because a planimeter was used to f i n d the projected area of the egg. A p p l i c a t i o n of average geometrical r e l a t i o n s h i p s of eggs i n the d e r i v a t i o n of true s p h e r i c i t y and p r a c t i c a l three-dimens i o n a l s p h e r i c i t y detracted from t h e i r accuracy as measures of egg shape.  In general, shape index was found to be the most  s u i t a b l e measurement of egg shape. S h e l l Quantity Egg weight, s h e l l thickness, percent egg as s h e l l , and s h e l l weight per u n i t area were h i g h l y i n t e r c o r r e l a t e d and a l l had h i g h p o s i t i v e c o r r e l a t i o n s w i t h both measures of s h e l l  30 strength.  S h e l l thickness alone accounted f o r 45.6,  62.4, and  ?4.2 percent of the v a r i a t i o n I n f o r c e a t f a i l u r e , and 19.0,  9.8,  and 26.2 percent of energy absorbed i n pooled-egg, b i r d  average per p e r i o d , a n d . o v e r a l l b i r d average analyses respectively. P a r t i a l c o r r e l a t i o n analyses (Table B7) showed ,that s h e l l thickness was second only to s t i f f n e s s i n e x p l a i n i n g r e s i d u a l v a r i a t i o n of f o r c e at f a i l u r e i n pooled-egg and b i r d average per p e r i o d samples a f t e r a l l other v a r i a b l e s were considered.  I n corresponding analyses (Table B8), thickness was  the most important c h a r a c t e r i s t i c w i t h respect to e x p l a i n i n g r e s i d u a l v a r i a t i o n i n energy absorbed. S h e l l Hardness Importance to S h e l l Strength Egg s h e l l hardness measured a t the .25 s h e l l l e v e l had s i g n i f i c a n t c o r r e l a t i o n s of .207 and .277 w i t h f o r c e a t f a i l u r e i n pooled-egg and b i r d average per p e r i o d analyses.  In  i t s c o r r e l a t i o n w i t h energy absorbed a t f a i l u r e , hardness was of s i g n i f i c a n c e only on a b i r d average per p e r i o d b a s i s . Stepwise m u l t i p l e r e g r e s s i o n of a l l v a r i a b l e s as b i r d averages per period i n d i c a t e d that hardness was important i n both force and energy absorbed a t f a i l u r e .  A f t e r a l l other  c h a r a c t e r i s t i c s were considered, hardness explained .24 and 7.77  percent of the r e s i d u a l v a r i a t i o n of load w i t h corres-  ponding percentages of .33 and 8.38  f o r maximum energy absorbed  31  i n the two analyses. The simple c o r r e l a t i o n c o e f f i c i e n t of .740 between s h e l l hardness and crushing strength reported by Brooks and Hale  (1955) and Brooks (1958) was  not confirmed by t h i s study.  Several d i f f e r e n c e s between methods of s e l e c t i n g eggs, t e s t i n g of hardness, and treatment of data were evident.  The present  study made use of a l a r g e sample of eggs produced by t e n b i r d s of a s i n g l e cross f e d a common r a t i o n and housed i n one room, whereas the e a r l i e r work was done on the ten weakest and strongest eggs of a heterogeneous sample.  Brooks and Hale considered  hardness a t the surface of the s h e l l extrapolated from measurements a t s h e l l l e v e l s . 2 5 , . 5 0 , and .75 i n contrast t o t e s t s made only a t l e v e l . 2 5 I n t h i s study.  I n view of the l a r g e  d i s c r e p a n c i e s reported f o r the Importance of hardness t o egg s h e l l strength, f u r t h e r I n v e s t i g a t i o n s are warranted t o c l a r i f y genetic and environmental e f f e c t s on s h e l l hardness. Hardness Gradient Radial s e c t i o n t e s t s of egg s h e l l s i n d i c a t e d that hardness was not uniform between s h e l l l e v e l s . 2 5 and .75. Hardness t e s t s of t a n g e n t i a l sections from l e v e l .02 t o . 9 0 revealed a c u r v i l i n e a r gradient of hardness across the s h e l l . The hardness gradient found by f i t t i n g polynomial curves t o the data of a representative s h e l l appears i n F i g . 9 t and the average gradient f o r nine s h e l l s i s i n F i g . 10.  I n a l l cases  a second degree polynomial expression was observed t a f i t the  32  .1  .2  Shell Fig.  9.  .3  Level  .4  .5  .6  .7  .8  .9  Out9ide  From  Hardness G r a d i e n t o f S h e l l on a T a n g e n t i a l S e c t i o n .  No. 19a.  T e s t s Made  Equation o f the Curve:  D.P.H. = 178.2 - 340.6x + 552.6X - 244. 7X R = .968 Standard E r r o r of Estimate = 3.84, 3  2  2  Shell  Fig. 10.  Level  From  Outside  Average Hardness Gradient of S h e l l s of B i r d s No. 5 , 9 , 1 9 . Tests made on Tangential Sections.  Equation of the Curves D.P.H. = 1 7 4 . 3 - 2 1 0 . I X + 2 1 6 . 6 X  2  Standard E r r o r of Estimate = 9 . 3 8 ,  R  2  = .7^2  34  data s a t i s f a c t o r i l y w i t h only a small decrease i n the standard e r r o r of estimate on using the cubic equation. Comparison of r a d i a l and t a n g e n t i a l hardness t e s t s of the same s h e l l between s h e l l l e v e l s . 2 0 and . 7 0 r e s u l t e d i n s i m i l a r curves.  The data f o r three s h e l l s of one b i r d were  p l o t t e d i n F i g . 1 1 w i t h separate curves f i t t e d to r a d i a l and tangential points.  The average hardness gradient curves f o r  nine s h e l l s produced by three b i r d s were included i n F i g . 1 2 . Examination of r a d i a l and t a n g e n t i a l t e s t r e s u l t s revealed that the gradient of hardness across the egg s h e l l from l e v e l s . 2 0 to . 7 0 was l a r g e l y independent of s h e l l o r i e n t a t i o n . Mechanical and chemical s h e l l membrane removal were compared by d u p l i c a t e t a n g e n t i a l hardness t e s t i n g between l e v e l s . 0 2 and . 9 0 of three s h e l l s that gave the f o l l o w i n g hardness gradient equations: - Mechanical membrane removal D.P.H. = 1 8 0 . 3 - 248.2X + 253-OX Standard E r r o r of Estimate =  2  13.01,  R  2  =  .689  - Chemical membrane removal D.P.H. = 1 7 2 . 6 -  2 2 1 . 5 X + 224.IX  2  2 Standard E r r o r of Estimate  =9.21,  R =  .779  Graphs of the two gradients were examined v i s u a l l y and judged to be e s s e n t i a l l y s i m i l a r .  On the b a s i s of t h i s  comparison,  chemical removal of s h e l l membranes was assumed t o have no appreciable e f f e c t on s h e l l  hardness.  F i g . 1 1 . Comparison o f Radial (upper) and Tangential (lower) Hardness Gradients of S h e l l s 1 9 a , b, a R a d i a l Data, x Tangential Data.  Equations of the Curves: D.P.H. (Radial)  = 182.6 - 283.2X + 318. 7X  2  Standard E r r o r of Estimate = 7.42, D.P.H. (Tangential)  R  2  = .558  = 177.5 - 260.4X + 289.4X  Standard E r r o r of Estimate = 6.27,  2  R  2  = .6l4  36  F i g . 12.  Comparison of R a d i a l (upper) and T a n g e n t i a l (lower) Hardness G r a d i e n t s of S h e l l s o f B i r d s No. 5, 9, 19. o R a d i a l Data, x T a n g e n t i a l Data.  Equations o f the Curvess D.P.H. ( R a d i a l ) = 168.6 - 199.9X + Standard E r r o r of Estimate  = 8.83,  233.4X  2  R  2  = .317  D.P.H. ( T a n g e n t i a l ) = 174.2 - 233.OX + 262.9X Standard E r r o r of Estimate  = 8.37,  R  2  2  = .396  37  Pig. 1 3 .  Photomicrograph of a R a d i a l Section of Egg S h e l l Showing Indentations at S h e l l Levels . 2 5 (A), and . 7 5 (B). (Mag. x 2 1 0 )  The discovery of a c u r v i l i n e a r gradient of hardness across the thickness of the egg s h e l l with a maximum at the outer edge, a minimum midway and a r e l a t i v e high again near the inner edge was not compatible with the report by Brooks and Hale  (1955)  er s h e l l edge.  of a l i n e a r gradient Increasing toward the outThe main point of disagreement was that of the  hardness at s h e l l l e v e l . 7 5 because both studies contended that hardness was greater at l e v e l . 2 5 than , 5 0 D i f f i c u l t y was experienced when t e s t i n g hardness near the inner edge of the s h e l l i n r a d i a l sections because indent a t i o n s often caused cracking of the s h e l l (see F i g . 1 3 , B )  38  which produced unusually l a r g e , i n v a l i d indentations.  Hardness  c a l c u l a t e d from indentations enlarged by s h e l l cracking would r e s u l t i n s p u r i o u s l y low values; t h e r e f o r e , such indentations were discarded i n t h i s study.  Tangential t e s t s of s h e l l s be-  tween l e v e l s .02 and .90 were found to minimize the incidence of cracking near edges of the s h e l l and to confirm the presence of a p a r a b o l i c hardness gradient across the egg s h e l l .  Hard-  ness and i t s gradient across the thickness of the s h e l l i s worthy of f u r t h e r i n v e s t i g a t i o n . Non-Destructive Estimation of S h e l l Strength M u l t i p l e regressions of non-destructive measurements on egg s h e l l strength measured as f o r c e at f a i l u r e were .examined i n r e l a t i o n to corresponding regressions containing a l l s h e l l c h a r a c t e r i s t i c s (Table  5). TABLE 5  COMPARISON OF NON-DESTRUCTIVE SHELL PROPERTIES WITH ALL SHELL MEASUREMENTS IN REGRESSION ON FORCE AT FAILURE. GROUP 1 . _ _ _ _ _ _ _ _ _ _ _  A l l Shell Properties Non-Destructive Properties*  Pooled-Egg Basis  B i r d Av„ Per Period  62.2  79.6  89.0  60.5  77.7  86.3  _ _ _  Overall Bird Av c  * S t i f f n e s s , egg weight, width, l e n g t h , and shape index. D e l e t i o n of d e s t r u c t i v e measurements of s h e l l quant i t y caused small reductions i n the c o e f f i c i e n t s of m u l t i p l e  39 determination.  The a b i l i t y of non-destructive  measurements to  e x p l a i n a l a r g e p r o p o r t i o n of the v a r i a t i o n i n f o r c e at f a i l u r e Indicated t h e i r Importance i n estimating t h i s measure of s h e l l strength. Egg weight, egg width, egg l e n g t h , and shape index may  be measured q u i c k l y and p r e c i s e l y by methods o u t l i n e d i n  t h i s study.  S h e l l s t i f f n e s s may  be estimated with the use of  a device s i m i l a r to that of Schoorl and Boersma  (1962) which  a l l o w s measurement of deformation under a non-destructive or a compression t e s t i n g machine that has been modified  load, to  a u t o m a t i c a l l y terminate l o a d i n g at a predetermined f o r c e . SUMMARY Egg s h e l l strength measured as maximum force and energy absorbed under q u a s i - s t a t i c l o a d i n g was  studied i n  r e l a t i o n to s h e l l s t i f f n e s s , egg s i z e , egg shape, s h e l l quant i t y and hardness. 1. Losses caused by egg s h e l l f a i l u r e were estimated about 590  thousand d o l l a r s i n B r i t i s h Columbia and  m i l l i o n d o l l a r s i n Canada f o r the year  4.2  1965.  2. P h y s i c a l p r o p e r t i e s of s h e l l s accounted f o r 62.2, 89.O  to be  79.6,  percent of the v a r i a t i o n i n strength measured as  force at f a i l u r e i n pooled-egg, b i r d average per period, and o v e r a l l b i r d averages r e s p e c t i v e l y .  Corresponding  f i g u r e s f o r s h e l l strength measured as energy absorbed  40 at f a i l u r e were 20.2, 41.1, and 6 l . 8 percent i n the three analyses. 3. Mean values f o r s h e l l c h a r a c t e r i s t i c s were recommended when evaluating s h e l l strength of i n d i v i d u a l b i r d s due to i n t r i n s i c strength v a r i a t i o n of the b r i t t l e s h e l l m a t e r i a l . 4. S h e l l s t i f f n e s s was found t o be the most important s i n g l e p r e d i c t o r of crushing strength.  Egg s i z e , egg shape,  s h e l l q u a n t i t y , and hardness were a l s o r e l a t e d to s h e l l strength. 5. The t h e o r e t i c a l l y derived conclusion that s t i f f n e s s was r e l a t e d to s h e l l q u a n t i t y , egg s i z e and shape was v e r i f i e d by s t a t i s t i c a l a n a l y s i s of the data. 6. Shape Index proved to be the most s a t i s f a c t o r y measure of egg shape when compared w i t h roundness and s p h e r i c i t y concepts. 7.  Egg s h e l l s were hardest a t the outer surface, r e l a t i v e l y hard near the inner surface, and s o f t e s t midway across the s h e l l .  8. S i m i l a r gradients of hardness were observed i n r a d i a l and t a n g e n t i a l t e s t sections of s h e l l m a t e r i a l . 9. The non-destructive p h y s i c a l p r o p e r t i e s of s t i f f n e s s , egg s i z e , and shape may be used to estimate crushing strength of an egg s h e l l .  41 LIST OF REFERENCES Brooks, J . , and H.P. Hale. 1955. Strength of the s h e l l of the hen's egg. Nature 175: 848-849. Brooks, J . 1958. Mono. No. 7.  Strength i n the egg. Soc. Chem. Ind. Texture i n Foods, London. 149-178.  Brown, W.E., R.C. Baker and H.B. Naylor. 1966. biology of cracked eggs. P o u l t r y S c i . 45: Cray, R.E., money.  The micro284-287.  1953. Cracked eggs c o s t i n g industry too much P o u l t r y Process. Market. 59s 10.  E z e k i e l , M., and K.A. Fox. 1959. Methods of c o r r e l a t i o n and r e g r e s s i o n a n a l y s i s . 3rd Ed. John Wiley and Sons, Inc. London. Frank, F.R., R.E. Burger and M.H. Swanson. 1964. The r e l a t i o n s h i p s between selected p h y s i c a l c h a r a c t e r i s t i c s and the r e s i s t a n c e to s h e l l f a i l u r e of Gallus domestlcus eggs. P o u l t r y S c i . 43: 1228-1235. . 1965. The r e l a t i o n s h i p s among s h e l l membrane, selected chemical p r o p e r t i e s , and the r e s i s t a n c e to s h e l l f a i l u r e of Gallus domestlcus eggs. P o u l t r y S c i . 44: 63-69. Gaisford, M.J. 1965. The a p p l i c a t i o n of s h e l l strength measurements i n egg s h e l l q u a l i t y determination. Brit. P o u l t r y S c i . 6: 193-196. Hayden, W., W.G. Moffatt and J . Wulff. 1965. Structure and p r o p e r t i e s of m a t e r i a l s . Volume I I I , Mechanical behaviour. John Wiley and Sons, Inc. London. Hunt, J.R., and P.W. Volsey. 1966. P h y s i c a l p r o p e r t i e s of egg s h e l l s . 1. R e l a t i o n s h i p of r e s i s t a n c e to comp r e s s i o n and f o r c e at f a i l u r e of egg s h e l l s . Poultry S c i . 45: 1398-1404. Lund, W.A., V. Helman and L.A. Wllhelm. 1938. l a t i o n s h i p between egg s h e l l thickness and P o u l t r y S c i . 17: 372-376.  The r e strength.  Marks, H.L., and T.B. Kinney, J r . 1964. Measures of s h e l l q u a l i t y . P o u l t r y S c i . 43: 269-271.  egg  Mohsenin, N. 1963. A t e s t i n g machine f o r determining the mechanical and r h e o l o g i c a l p r o p e r t i e s of a g r i c u l t u r a l products. Penn. State Univ. Agr. Expt. Sta. B u l l . 701.  42 Mott, B.W. 1956. Micro-Indentation hardness t e s t i n g . Butterworth's S c i e n t i f i c P u b l i c a t i o n s . London. Mueller, CD., and H.M. Scott. 1940. The p o r o s i t y of the egg-shell i n r e l a t i o n to h a t c h a b i l i t y . P o u l t r y S c i . 19: I63-I66. Novikoff, M. and H.S. Gutteridge. 1949. A comparison of c e r t a i n methods of estimating s h e l l strength. P o u l t r y  S c i . 28: 339-343.  P o u l t r y Market Review. 1964. P o u l t r y D i v i s i o n and Markets Information Section, Production and Marketing Branch, Department of A g r i c u l t u r e , Ottawa, Canada. . 1965. P o u l t r y D i v i s i o n and Markets Information Section, Production and Marketing Branch, Department of A g r i c u l t u r e , Ottawa, Canada. Raffa, J . 1967. D i s t r i c t Superintendent ( P o u l t r y ) , Production and Marketing Branch, Canada Department of A g r i c u l t u r e , Vancouver. Personal communication. Ralston, A., and H.S. W l l f . i960. Mathematical methods f o r d i g i t a l computers. John Wiley and Sons, Inc. Rehkugler, G.E. 1963. Modulus of e l a s t i c i t y and u l t i m a t e strength of the hen's egg s h e l l . J . A g r i c . Eng. Res.  8: 352-35^. .  1964.  Egg handling equipment design.  Amer. Soc. A g r i c . Eng. 7: 174-177. Romanoff, A.L., and A.J. Romanoff. 1949. London: Chapman and H a l l L t d .  Trans.  The a v i a n egg.  Richards, J.F., and M.H. Swanson. 1965. The r e l a t i o n s h i p of egg shape to s h e l l strength. P o u l t r y S c i . 44: 15551558. Richards, J.F., and L.M. Staley. 1967. The r e l a t i o n s h i p s between crushing strength, deformation and other p h y s i c a l measurements of the hen's egg. P o u l t r y S c i . 46 ( i n p r e s s ) . Schoorl, P., and H.Y. Boersma. 1962. Research on the q u a l i t y of the egg s h e l l . Proc. 12th World's P o u l t r y Cong. 432-435. Shuster, D. 1959. R e l a t i o n s h i p of s h e l l strength to c e r t a i n c h a r a c t e r i s t i c s of chicken eggs. Unpublished M.S. Thesis. Pennsylvania State U n i v e r s i t y .  ^3 Sluka, S.J., E.L. Besch and A.H. Smith. 1965. A hydros t a t i c t e s t e r f o r egg s h e l l strength. P o u l t r y S c i . 44: 1494-1500. . 1966. C a l c u l a t i o n and a n a l y s i s of stresses i n egg s h e l l s . Winter Meeting. Amer. Soc. A g r i c . Eng. Paper No. 66-808. Snedecor, G.W. 1956. S t a t i s t i c a l methods. 5th Iowa State U n i v e r s i t y Press, Ames, Iowa.  Ed.  The  Stewart, G.P. 1936. S h e l l c h a r a c t e r i s t i c s and t h e i r r e l a t i o n s h i p to the breaking strength. P o u l t r y S c i . 15s 119-124. Terepka, A.R. 1963. Structure and c a l c i f i c a t i o n i n avian egg s h e l l . E x p t l . C e l l Bes. 30: 171-182. Tyler, C. 1961. S h e l l strength: I t s measurement and r e l a t i o n s h i p to other f a c t o r s . B r i t . P o u l t r y S c i . 2: 3-19. T y l e r , C., and F.H. Geake. 1961. Studies on egg s h e l l s XV - C r i t i c a l a p p r a i s a l of various methods of assessing s h e l l thickness. J . S c i . Pood A g r i c . 12: 281-289. Voisey, P.W., and J.R. Hunt. 1967a. R e l a t i o n s h i p between a p p l i e d f o r c e , deformation of egg s h e l l s and f r a c t u r e f o r c e . J . A g r i c . Eng. Res. ( i n press). . 1967b. P h y s i c a l p r o p e r t i e s of egg s h e l l s . 4. Stress d i s t r i b u t i o n i n the s h e l l . ( i n press). . 1967c. The behavior of egg s h e l l s under impact. J . A g r i c . Eng. Res. ( i n press). Wadell, H. 1933. S p h e r i c i t y and roundness of rock p a r t i c l e s . Jour, of Geology. 41: 310-331.  44  APPENDIX A  ^5 TABLE A l TESTING PERIODS AND SAMPLE SIZES  Period  Dates of Period ,  1  Jan.  2  2  Jan.  30 -  3  Feb.  4  Mar.  5  Apr. 24 - May  6  May  22 -  7  Jun.  19  8  Jul.  17 -  No. of Eggs Tested  29  342  Feb.  26  366  27 -  Mar.  26  351  27 -  Apr.  23  342  - Jan.  21  343  Jun. 18  325  16  322  13  3^2  - Jul. Aug.  T o t a l Sample Size  2,733  46  TABLE A2 EGGS TESTED BY BIRD AND PERIOD Period Bird  1  2  3  4  1*  6 6 5  6 5 1  6  6  2  3* ^  6  7  5* 6  6 5 5  7*  8 9* 10  5 5 5  7 6 6  12 13*  6  7 7 5 5  6 6  17*  5 7 5  18 19* 20  7  8  Totals  6 6 6 2 0  6  6  6  48  0  6 0  6  6 6  6 0  6  6 6  6  6 6  6 6  6  6 6  6  7  4 5  7 6  6 6  6  6 6  6 6  6  6  6  6  6  6  6  49  6 6  6 6  6 6  6  6 6 6 6 6  6  6  6  49 47 47 47 47 45 50 49  3  38 46 46  6 6 6  49  5  46  6 5  6  6 6  6 6 6 6 6 6  5  6  47  8  6 6  6  6 6 6 6 6  6 6 6 6  5  6 5  6 0  4 6 6  6  6  !  6  6 6 6 6 6 6 6 6 6 6 6 6 6 5 5 6 6 6 7  5  6  6 6  7  15* 16  0 6  11*  14  6  5  49 6  6  * S h e l l s from these b i r d s tested f o r hardness. cont'd.  46 44  47 TABLE A2 —  Continued  Period Bird.  1  2  3  4  5  6  7  8  Totals  21  5  6  6  6  6  6  6  6  47  22.5  7  6  6  6  6  6  6  23  6  6  4  6  6  6  6  24  5  6  6  6  6  6  6  25  6  8  6  6  6  6  6  6  50  26  6  5  6  6  5  5  6  6  45  27 28 29  5 6 6  7 7 7  6 6 6  6 6 6  6 6 6  6 6 6  6 6 6  6 6 6  30  6  0  0  6  6  6  6  31 32 33  5 5 6  5 6 6  6  6  6  34  6  7  6  6  6  35  7  7  36 37 38 39  5 5 6 7  6 4 6 6  6 4 7 7  6 6 6 6  6 2 6 6  40  6  7  7  6  6  6  6  6  50  41  6  6  6  6  6  6  4  6  46  42  7  6  6  6  6  6  6  6  49  4  6  7  6  6 6  6  6  6  48 46  47  6  48 49 49  6  36  6 6 6 6 0 0 6 6  6  6 6  5 5 6 6  48  49 6  6 6 6 6  44 36  6 6  3 5 6 6  6 6  50  43 37 49 50  cont'd...  48 TABLE A2 —  Continued  Period Bird  1  43 44 45 46 47  6 6 5 5 6 6 5 6 7 6 5  48  49 50 51 52 53 54 55 56 57 58 59 60  2  3,4  6 6 7 7 7 6 6 6 6 7 7 7 7 7 7 6 7 7 7 7 6 7  5  7  5  6 5 5 6 6 7  7 6 6 7 6 6  6 7 6 7 7 7  5  6 6 6 6  6 6 6 6 6 6  0 6 6  6 6 6 5 6 6  0 6 6  7  6 6 6 6 6 0  8  6 6 6 6 5 0  6 6  6 6  6 6  6  6  6  6 6 6 6  6  0 6 6 6  6 6  6  0 6 6 6  6 6  6 6 4 6  6 6  6 6 6  Totals  48 50 48 46  0 0 0 6 6 6 6 6 6 6 6 6 6 6 6  5 6 6 6 6  6  48  38 19 49 51 50 48  47 36 48 45 50 49 50  49 TABLE A3 GROUP 1.  MEANS AND STANDARD DEVIATIONS.  Pooled-Egg Basis  n=2733  Mean Load Totdef  3557.0 154.2  Width  23.30 27.54 58.94 4.267  Length  5.802  Shelwt  5.299  Stiff Energy Eggwt  Thick Persh  331.1 8.992  S.D.  578.3  3554.0  154.4 4.264 23.26 6.096 27.55 4.354 58.92 .118 4.265 .215 5.802 .574 5.292  28.79  331.0  .745 6.393  74.81  2.732  73.58 72.82  Round Trusph  97.81  Prasph  85.3^  2.955 .845 1.746  P3dsph  80.88  2.013  Shlndx  n=46l  Mean  18.51  74.89 73.62 72.87  Mgmcm2  B i r d Av. Per Period  8.977  97.80  85.31 80.85  O v e r a l l B i r d Av.  S.D.  Mean  n=53  447.2 3559.0 11.71 154.6  3.498 23.26 4.027 27.60 4.017 59.02 .109 4.270 .187  5.797  S.D.  375.2  9.202 3.062 3.142  3.308  .095 .136 .483  .521 5.295 24.30 25.55 331.0 .644 8.968 .575 5.211 5.613 74.79 1.902 2.368 73.72 2.494 72.94 1.894 .464 .569 97.79 1.112 1.472 85.39 1.743  80.94  1.397  50 TABLE A4 MEANS AND STANDARD DEVIATIONS. GROUP 2. Pooled-Egg Basis Mean Load Totdef Stiff Energy Eggwt Width Length, Shelwt Thick Persh  Mgmcm.2 Shindx Round Trusph Prasph P3dsph  D.P.H.  n-425  3766.0 151.8 25.15 28.60 59.16 4.271 5.793 5.544 3^3.7 9.359 78.08 73.77 73.03 97.63 85.44 81.00 137.7  S.D.  538.5 17.96 4.666 5.385 4.749 .129 .185 .668 28.73 .729 6.780 2.295 2.576 1.108 1.515 1.686 11.60  B i r d Av. Per Period Basis Mean  n=74  3755.0 152.4 25.02 28.59 58.95 4.264 5.789 5.506 3^2.6 9.318 77.72 73.69 72.94 97.63 85.38 80.94 137.8  S.D,  411.8 10.91 3.867 2.988 4.242 .119 .135 .625 25.30 .628 6.100 1.856 2.120 .567 1.246 1.358 6.663  51 TABLE A5 MEANS AND STANDARD DEVIATIONS; BY PERIOD  1 Mean Load Totdef Stiff Energy Eggwt Width Length Shelwt Thick Persh Mgmcm2 Shindx Round Trusph Prasph P3dsph  37^3.0 161.3  Period S.D.  Mean  2  S.D.  3 Mean  S.D.  569.0 3720.0 590.9 3620.0 511.6 17.06 18.05 150.6 17.69 151.2 4.243 23.41 3.918 24.91 4.73& 24.31 30.28 6.174 28.17 5.815 27.31 5.153 3.906 55.21 3.381 58.31 3.371 56.63 4.191 .109 .099 4.217 .099 4.244 .180 5.794 5.638 .199 .185 5.702 .562 5.318 5.034 .576 .532 5.256 28.17 28.46 338.7 331.2 29.75 335.5 .731 9.111 .785 9.117 .695 9.277 6.401 6.116 76.27 74.29 6.725 75.68 2.706 2.661 74.02 74.39 2.559 73.32 73.22 2.848 72.72 2.840 2.889 73.33 .708 97.69 .706 97.70 97.81 .745 I.665 85.55 85.62 1.658 85.25 1.703 1.880 1.944 81.17 1.994 81.45 80.67  52 TABLE A5 —  4 Mean Load Totdef Stiff Energy Eggwt Width Length Shelwt Thick Persh Mgmcm2 Shindx Round Trusph Prasph  P3dsph  Continued  Period S.D.  Mean  5  S.D.  6 Mean  S.D.  3529.0 525.1 3718.0 570.8 3398.0 557.6 154.2 17.22 154.6 19.04 18.55 155.3 23.10 3.886 24.29 4.180 22.09 3.958 5.498 28.88 6.360 26.53 27.30 6.105 4.022 60.73 4.004 59.15 3.523 59.60 4.272 .106 4.313 .099 4.278 .115 .194 5.836 5.809 .205 5.863 .185 .578 5.309 .551 5.410 .563 5.357 328.0 27.40 333.8 28.86 28.87 328.5 .728 8.971 .691 9.078 .723 8.820 74.82 6.401 6.169 75.89 6.273 74.20 73.62 2.692 73.36 2.623 2.698 73.62 74.04 2.816 73.46 2.670 3.O63 72.12 .803 97.76 97.77 .799 .733 97.89 1.794 84.91 1.578 1.645 85.69 86.03 80.88 1.926 1.983 80.88 1.975 80.69  TABLE A5 —  Mean Load Totdef  7  3418.0  154.7  Stiff  22.30  Energy  26.62  Eggwt  61.00  Continued  Period S.D.  568.1  19.55 3.994 6.307 4.344  4.183  28.33  61.31 4.322 5.906 5.325 323.9  .230 .562 27.75  .708  8.685  .711  5.886 5.394  .190  8.839  18.96 5.878  Length  Persh  151.9  545.2  25.04  .121  328.2  3277.0  S.D.  3.961  4.311  Thick  8  21.77  Width  Shelwt  Mean  .582  .120  Mgmcm2  74.48  6.278  73.30  Shindx  2.489  73.28  2.518 1.098  71.90 98.03  3.181  Trusph  73.30 72.03 97.83  Prasph  84.86  1.489  84.77  1.899  P3dsph  80.65  I.831  80.63  2.326  Round  6.207 3.150 .862  54  APPENDIX B  55 TABLE BI SIMPLE CORRELATION COEFFICIENTS GROUP  1.  POOLED-EGG BASIS.  Load  Totdef  P3dsph  .184  Prasph  .161  Trusph  -.084  .179 .047 .233 .135 .055 .191 .278 -.253 .097 .136 .056 .192 .179 .047 .234 -.351 .846 .289 -.377 .849 .263 -.321 .836 .314 -.252 .701 .279 -.050 -.010 -.066 .178 .048 .227 . 061 .071 .119 .705 .290 .904 -.457 -.027 .115 -.017 .997 .904 .122 .903 .999  Round  .163  Shindx  .185  Mgmcm2  Eggwt  .665 .650 .675 .576 -.055 .177 .117  Energy  .843  Stiff  .755 .222  Persh Thick Shelwt Length Width  Totdef  .904  Prasph Trusph r  .05  -  -  0  3  7  Stiff  11=2733.  Energy E««wt Width Length Shelwt  -.081  .403 -.715 -.105  -.109 .116 -.111 -.082  .314 -.685 -.108  .311 .123 -.200 .310 -.689 -.109 .400 -.718 -.106  .241 .128 . 188 -.045 -.123 -.022 .241 .131 .194 .640 .490 .479  .737 .867  .735 .860  .347  .957 -.087 -.066 -.075 -.046 -.311 -.348 -.074 -.045 -.086 -.066  Round Shindx Mgmcm2  .899  Persh  .905 Persh .950 Mgmcm2 -.091 Shindx -.092 Round -.276 Trusph -.093 Prasph -.092 P3dsph Thick  56 TABLE B2 SIMPLE CORRELATION COEFFICIENTS GROUP 1. BIRD AVERAGE PER PERIOD BASIS. Load  P3dsph Prasph Trusph Round Shindx Mgmcm2 Persh Thi ck Shelwt Length Width Eggwt EnergyStiff Totdef  Totdef  .065 .230 .230 .070 -.139 .398 -.311 .231 . .231 .070 .245  .264  .244  .264  .111  Prasph Trusph  .05  =  .064  .773 -.486 .918 .769 -.505 .921 .790 -.451 .914 .649 -.370 .755 ^..081 -.136 .014 .164 .099 .206 .134 .011 .118 .849 .523 .452 .854 = .513 -.002 -.025 -.019 .999 .941  r  S t i f f Energy  .092  .941  n=46l.  Eggwt Width Length Shelwt  .350 -.016 .421 -.682 -.069 .319 -.055 .349 -.682 -.081 .090 .135 .276 .119 -.232 .320 -.055 .3^8 -.683 -.082 -.016 .421 -.683 -.069 .3^9 .292 .183 .230 .899 .401 .388 -.012 -.093 .010 .722 .436 .281 .182 .223 .868 .356 .680 .547 .510 -.142 .733 .372 .262 .920 Persh .893 .118 .951 .967 Mgmcm2 -.081 -.083 -.074 Shindx .942 -.075 -.064 -.086 Round .106 -.376 -.429 -.312 Trusph .942  -.074  -.064  -.086  Prasph  .999  -.080  -.081  -.073  P3dsph  Round Shindx Mgmcm2  = .120  r  01  Persh  Thick  57 TABLE B3 SIMPLE CORRELATION COEFFICIENTS GROUP  Load  1.  OVERALL BIRD AVERAGE BASIS.  Totdef  n=53  S t i f f Energy  Eggwt Width Length Shelwt  .024  .389  .166  .542  -.593  .019  P3dsph  .226 ! .324  Prasph  .170  .283  -.005  .317  .140  .500  -.617  .001  Trusph  -.113  .523  -.323  .172  .095  .073  -.278  Round  .166  .287  -.009  .316  .143  -.614  -.002  Shindx  .233  .320  .032  .393  .165  .241 .504 .540  -.595  .025  Mgmcm2  .842  -.556  .958  .473  .388  .258  .313  .928  Persh  .792  -.630  .944  .390  .129  ^12  .142  .793  Thick  .861  -.520  .956  .512  .395  .276  .318  .915  Shelwt  .809  -.376  .853  .535  .703  .514  Length  .137  -.070  .074  .68?  Width  .291  .531  .912  .134  .285  .430  Energy-  .415 .401 .844  .169 .218  .569 .354  .501  Stiff  .886  .413 -.574  Eggwt  .984  .019  .999  .151  .985  Prasph Trusph r  =  .268  Persh  .962  .981  Mgmcm2  -.120  -.049  Shindx  -.086  -.140 -.085 .145 -.404 -.459 -.331 .984 -.080 -.133 -.080  .985 .022  -.136  Totdef  -.062  .940  1.000  -.070  Round Shindx Mgmcm2 r  .oi  " -  3  M  -.129 Persh  -.057 Thick  Round Trusph Prasph  P3dsph  TABLE B4  i  58  SIMPLE CORRELATION COEFFICIENTS GROUP  2.  POOLED-EGG BASIS.  n=425  Load Totdef S t i f f Energy Eggwt Width Length Shelwt Thick  p. P.R; .207 -.136 .265 .067 -.073 -.159 .009 .184 .275 P3dsph .119 .059 .039 .139 .095 .472 -.539 .014 -.045 Prasph .145 .049 .068 .149 .068 .370 -.500 .029 -.014 Trusph -.172 .203 -.268 .004 .000 .265 .053 -.223 -.279 .144 .047 . 068. .147 .067 . 368 -.501 .028 -.013 Round Shindx .118 .059 . 038 .139 .095 .473 -.539 .013 -.045 Mgmcm2 .683 =.503 .866 .-201 .482 .361 .377 .923 .947 Persh .655 - . 514 .854 .171 .210 .106 .172 .773 .898 Thick .703 -.477 . 864- .233 .474 .354 .382 .882 Shelwt .628 -.423 .765 .210 .781 . 647 .604 Length .170 -.125 .216 .. 047 .767 .486 .957 Mgmcm2 Width .304 -.066 .266 .198 .900 ~. 035 -.074 Shindx .862 .005 -.017 Round Eggwt .328 -.139 .336 .166 Energy .777 .644 .171 .035 .198 -.304 -.339 Trusph Stiff .750 -.625 .037 .999 .863 .006 017 Prasph .863 .198 .861 .999 -.034 -. 074 . P3dsph Totdef .027 -.159 -.090 -.214 -. 091 -.161 .301 .358 D.P.H.  P3dsph Piasph Trusph Round Shindx Mgmcm2 Persh r  0 5  =  -095  59 TABLE B5 SIMPLE CORRELATION COEFFICIENTS GROUP 2. BIRD AVERAGE PER PERIOD BASIS. n=74 Load Totdef Stiff Energy Eggwt Width Length Shelwt Thick D.P.H. .27? .039 .213 .283 -.133 -.225. .042 . 071 .195 P3dsph .188 .021 .090 .244 .3^6 .621 - 3^0 .168 .051 Prasph .241 .059 .116 . 320 .287 .532 -.346 .161 .075 Trusph •-. 308 .290 -. 349 -.121 -.072 .127 -.127 -. 31^ -.378 Round .234 .058 .111 .311 .283 .529 -. 3^9 .155 .069 Shindx .184 .023 .087 .242 .341 .618 -.344 .163 .048 Mgmcm2 .831 -723 .923 .390 .623 .503 .557 .943, .969 Persh .812 -. 706 .902 .378 .380 .258 .391 .812 .924 Thick .869 -.704 .942 .442 .616 .503 .553 .919 Shelwt . 76? -.656 .846 .369 .847 .738 .706 Length .324 -.390 .428 .065 .756 .525 .959 Mgmcm2 .042 -.076 Shindx Width .436 -.305 .435 .273 .942 Eggwt .483 -.392 .518 .254 .907 .066 -.024 Round Energy- .775 .233 .415 .158 .249 -.411 -.458 Trusph Stiff .150 .999 .907 .073 -.018 Prasph .895 -. 733 Totdef -.427 .906 .248 .906 1.000 . 046 -.073 P3dsph -.284 -.182 -.244 -.191 -.288 .177 .247 D.P.H. \  P3dsph Prasph T  Q5  = .227  r  Trusph Round Shindx >  0  1  =  .296  Mgmcm2  Persh  60 TABLE B6 SIMPLE CORRELATIONS BETWEEN LOAD AND SELECTED VARIABLES FOR EACH TEST PERIOD  r  Pd.  1  n=342  Pd.  2  n=366 Pd.  3  Pd.  4  n=351 n=342  Pd.  5  n=343 Pd.  6  -0  S t i f f . Eggwt  Width  Length Shindx Round P3dsph  .106 .138 .103 .134 .105 .137 .106 .138 .106 .138 .109  .772  .263  .273  .080  .111  .029  .108  .773  .239  .241  . 060 .109  .081  .109  .752  .301  .295  .114  .100  .059  .101  .753  .284  .307  .071  .130  .082  .129  .706  .255  .358 -.032  .271  .171  .271  .739  .255  .312  .041  .199  .142  .199  .109  .726  .325  .3^7  .064  .226  .210  .224  .106 .138 .037  .744  . 250 .322 -.025  .226  .205  .225  .755  .117  .177 -.055  .185  .163  .184  1  n=325  .142  n=322  .143  Pd. ?  Pd. 8 n=342 A l l pds.  n=2733  .049  61 TABLE B7 SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN LOAD AND SELECTED VARIABLES. Pooled- -Egg B a s i s n:=2733  B i r d Av. Per Period n=46l  GROUP 1. O v e r a l l B i r d Av. n=53  100(sc ) * 100(sc)* '* 0 100(sc) * 2 ! 100(pc) ** 10O(pc) ** ioo(x>cr** 2  2  ?  78.52  7.60  .65  1.6.08  .24  4.26  .17  17.25  2.44  .65  .02  1.87  1.45  .76  65.42  3.49  57.05  17.64  72.91  Eggwt  1.37  .00  1.78  Width  3.12  . 22  .05  Stiff .  Length  .30  13.62  Shelwt  33.21  .37  42.12  Thick  45.58  1.43  62.38  2.86  74.17  2.21  Persh  42.19  .08  59.09  • 96  62.6,5  1.44  Mgmcm2  44.16  59.68  .00  70.91  .83  Shindx  3.43  .03 .07  5.93  .17  5.45  8.93  Round  2.67  .49  5.35  .70  2.77  5.56  Trusph  .71  .00  1.92  1.23  1.28  4.45  Prasph  2.60 3.39  .46  5.29  •43  2.88  2.27  .37  5.98  .03  5.09  4.64  .16 .24  .84 1.43  .86 1.47  7.20 12.12  15.44  P3dsph  p_ 05*** o  p=!oi***  .16 .24  9.24  * 100(simple c o r r e l a t i o n ) ** 1 0 0 ( p a r t i a l c o r r e l a t i o n ) ^ *** 100(minimum c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t a t indicated l e v e l ) ?  62 TABLE B8 SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN ENERGY AND SELECTED VARIABLES. Pooled-Egg  n=2?33  100(sc)  2  Basis  Bird Av. Per Period n=461  GROUP 1 • O v e r a l l B i r d Av.  n=53  100(sc) * 100(sc) * 100(pcr*« 100(pc) ** •*  *100(pc) 2  2  2  9  2  Stiff  8.43  .01  20.43  .07  25.12  1.41  Eggwt  1.41  28.21  1.82  .01  2.02  •33  12.69  .59 .16 .03 .70  .20  1.64  18.99  3.26  .05  15.03 16.05  .08  12.21  .26  10.25  P3dsph  5.41  .05 .23 .19  .81  Prasph  5.16 .43 7.79 9.83 6.92 8.32 5.45 3.69 .94 3.65  1.39 6.86  18.49  Width  .02 .06  1.03 .00 .13 .63 1.32 .37 .01  .16  .16  Length Shelwt Thick Persh Mgmcm2 Shindx Round Trusph  P=.05*** P=.01***  .24  .04  10.16  12.27 .84  1.43  .24  .86  1.47  .55  1.69  28.62  26.23 15.23  3.55 2.47 .74  22.37  1.20  15.47  8.84  9.96 2.95  4.58 3.39  10.02  1.82  15.09  4.48  7.20  12.12  9.24  15.44  * 100(simple c o r r e l a t i o n ) ** 1 0 0 ( p a r t i a l c o r r e l a t i o n ) *** 100(minimum c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t a t ^ indicated l e v e l ) 2  63 TABLE BOSQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN STIFFNESS AND SELECTED VARIABLES. GROUP 1 Pooled-Egg Basis Bird Av. PerPeriod Overall Bird Av. n=2733 n=46l n=53 100(sc) 2* 100(pc)  100(sc) * 100(sc ) * 100(pc) ** 100(pc) ** 2  2  2  2  2  .03  1.40  . 02  8.12  .02  Width  .51 .23  .04  .97  .04  3.00  Length  .01  .00  .02  .01  Shelwt  49.11  .04  57.02  .62  Thick  69.82  4.70  83.50  8.17  Persh  72.08  .04  84.90  .06  4.74 2.85 72.71 91.30 89.19  Mgmcm2  71.62  .10  84.18  .84  91.74  10.28  Shindx  .22  .00  .41  .00  .10  .29  Round  .31  .15  .49  . 01  .12  .00  9.66  10.44  .63 .30 .59  Eggwt  Prasph  .31  .09  .49  .54 .31 .25  P3dsph  .22  .02  .43  .02  .06  P=.05***  .16 .24  .16 .24  1.43  .84  .86 1.47  12.12  Trusph  p=.01***  6.40  .00  7.20  1.02  5.32 6.16 3.78  9.24  15.44  * 100(simple c o r r e l a t i o n ) ** 1 0 0 ( p a r t i a l c o r r e l a t i o n ) 100(minimum c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t a t indicated l e v e l ) 2  2  64 TABLE BIO SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN LOAD AND SELECTED VARIABLES. Pooled-Egg Basis  GROUP 2.  B i r d Av. Per Period  n=425  n=74  Basis  lOO(so) *  100(pc) »»  lOO(sc) *  100(pc) »»  Stiff  56.19  15.39  80.17  22.63  Eggwt  10.76  1.06  23.32  5.82  Width  9.22  .20  19.04  .97  Length  2.89  •98...  10.47  2.21  Shelwt  39.38  1.60  58.80  Thick  49.41  2.32  Persh  42.88  .01  75.43 65.90  Mgmcm2  46.69  .47  69.12  Shindx  1.40  .09  3.40  .44 9.49 5.56 .66 .03  Round  2.06  .33  5.45  2.91  Trusph  2.97  .18  9.48  4.22  Prasph  2.10 1.41  D.P.H.  4.27  .24  5.79 3.53 . 7.69  3.37  P3dsph  .38 .07  7.77  .94  5.18  6.25  2  p=.05*** P..01***  .91  1.55  2  1.60  2  8.78  2  .04  10.56  * 100(simple c o r r e l a t i o n ) ** 1 0 0 ( p a r t i a l c o r r e l a t i o n ) *** 100(minimum c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t a t indicated 2  level)  65 TABLE B l l SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN ENERGY AND SELECTED VARIABLES. Pooled-Egg Basis  B i r d Av. Per Period  n=425  lOO(sc) * 2  Stiff  GROUP 2.  n=74  lOO(pc) ** 2  lOO(so) * 2  .15 .89 .19 .87  17.24  13.58 19.50  Basis  lOO(po) ** 2  .16  Eggwt  2.93 2.75  Width  3.92  Length  .22  Shelwt  4.43  Thick  5.42  1.35 2.56  Persh  2.92  .00  14.29  6.32  Mgmcm2  4.03  15.18  1.50  Shindx  1.94 2.16  5.84  .00  9.68  3.31  1.47  4.64  10.21  3.85 .06 8.38  6.25  6.44 7.45  1.21  A3  1.87  Trusph  .00  Prasph  2.22  .37 .15 .33 .16 .38  P3dsph  1.94  .02  D.P.H.  .45  .33  5.95 8.03  p=.05***  .91  .94  5.18  Round  P=.01***  1.55  1.60  8.78  4.71  .04 10.02  10.56  * 100(simple c o r r e l a t i o n ) ** 1 0 0 ( p a r t i a l c o r r e l a t i o n ) *** 100(minimum c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t a t indicated 2  level)  66  TABLE B12 SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN STIFFNESS AND SELECTED VARIABLES, GROUP 2, Pooled-Egg Basis n=425  B i r d Av. Per P e r i o d n=74  26.81  .41  .02  18.96  .00  4.67  .68  18.34  .03  Shelwt  58.54  2.06  71.54  .49  Thick  74.68  9.50  88.76  27.20  Persh  72.88  .82  81.40  > .82  Mgmcm2  74.91  1.18  85.17  .01 .40  Eggx?t  11.32  Width  7.06  Length  1.52  Shindx  .14  .10  .76  Round  .47  .15  1.24  Trusph  7.17  .51  12.19  .13  Prasph  .46  .13  1.35  1.61  P3dsph  .15  .65  .81  .38  D. P „ H,  7.00  .03  4.55  .22  .94  5.18  Par„ 0 5 * * *  P=° 01***  .91  1.55  1.60  8.78  Basis  1.66  6.25  10.56  * 100(simple c o r r e l a t i o n ) ** 1 0 0 ( p a r t i a l c o r r e l a t i o n ) *** 10Q(minimum c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t a t indicated 2  level)  67  APPENDIX C  68 TABLE C l STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 1, POOLED-EGG BASIS.  n=2733  F - Ratio 1  Independent Variable Analysis 1  2  4  3\  582. 04  586. 72  581. 40  Eggwt  • 10  Width  4. 35  13. 74  29. 33  Length  1. 09  1. 01  1. 03  Shelwt  9. 57  10. 80  28. 02  28. 04  77. 48  Thick  39. 53  39. 45  39. 84  39. 77  41. 18  Persh  1. 91  2. 24  2. 77  2. 47  57. 81  Mgmcm2  1. 01  92  1. 16  1. 30  —  Shindx  2. 24  2. 14  2. 10  7. 37  6. 80  Round  13. 21  14. 90  16. 95  19. 04  19. 24  Trusph  0 20  011  Prasph  12. 23  13. 93  16. 23  18. 33  18. 55  P3dsph  9. 56  9. 79  10. 75  11. 18  10. 37  62. 2  62. 2  62. 2  62. 2  10 OR  2  F  .05 = ' 3  8 / +  581. 49  582. 47  Stiff  -  —  •  —  62. 2 F  .oi  =  6  -  89. 06  -  >-  88. 06 —  —  - ^ 6  69 TABLE C2 STEPWISE MULTIPLE REGRESSION WITH ENERGY AS THE DEPENDENT VARIABLE GROUP 1.  POOLED-EGG BASIS.  i  n=2733  F - Ratio Independent Analysis 1 Variable  3  2  Stiff  .22  .22  Eggwt  .84  .75  Width  1.14  Length  .14  Shelwt  Shindx  9.52 45.27 .67 1.86 2.58  Round  6.71  Trusph  1.89 5.93 5.23  Thick Persh Mgmcm2  Prasph P3dsph  20.2  10 OR  2  F  .o - ' 3  5  8i+  1.01  5 _  .74 1.03 —  —  4  1.18  .60 —  12.42 —  --  9.38  9.46  11.98  11.50  45.21  48.93  48.99  49.30  .63 1.84  .65 1.89  4.85  4.87  7.39 1.79 6.57 5.36  7.51 1.79 6.65  20.2 F  .01  5.40 20.2  = 6.64  —  —  11.70  11.23  5.63 6.87  7.69 6.29  3.04  76.21  6.03 5.25  5.44  20.1  4.73 20.1  70  TABLE C3 STEPWISE MULTIPLE REGRESSION WITH STIFFNESS AS THE DEPENDENT VARIABLE GROUP 1.  POOLED-EGG BASIS.  n=2733  F - Ratio Independent Variable Analysis 1  2  3  4  Eggwt  .57  1.22  1.64  .87  Width  1.22  6.43  10.69  17.43  14.48  —  —  —  .06  Length  .30  1.41  1.34  1.1.2  2.17  65.02  Thick  134.53  135.17  135.41  136.09  145.53  Persh  .88  .92  .86  —  3.33  3.59  3.39  19.64  Shelwt  Mgmcm2  .04  Shindx Round  —  4.41  4.09  —  —  5.00  Trusph  .03  Prasph  2.40  2.55  2.96  P3dsph  .68  1.01  1.75  1.0 OR  76.1  2  p  .o5  -  y-^  ;  —  3.57 .  —  233.89 —  18.15  —  76.1  76.1  .oi " -  p  6  61t  2.16  — —  76.1  76.1  71 TABLE C4 STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 1. :• BIRD AVERAGE PER PERIOD BASIS.  n=46l  F - Ratio Independent Analysis 1 Variable  2  3  4  5  71.85  71.59  71.49  72.98  Stiff  70.32  Eggwt  3.51  6.06  11.28  11.28  11.18  Width  1.08  1.02  —  —  —  —  —  Length  .06  Shelwt  4.37  12.71  12.06  12.12  12.09  Thick  13.05  13.35  1.3.61  14.71  15.36  Persh  3.64  13.24  12.53  12.40  1.1.96  —  Mgmcm2  .15  —  —  —  Shindx  .97  .88  .82  —  —  91.04  Round  3.46  3.34  3.87  4.49  Trusph  6.05 2.20  26.15 2.52  33.41  Prasph  10.13 2.09  P3dsph  .21  .26  79.6  10 OR  2  F  .0  5  3.86  79.6 F  .0l  -79.6 6.69  2.48  31. 36 —  —  79.5  79.4  72 TABLE C5 STEPWISE MULTIPLE REGRESSION WITH ENERGY AS THE DEPENDENT VARIABLE GROUP 1.  BIRD AVERAGE PER PERIOD BASIS.  n=46l  F - Ratio Independent Variable Analysis 1  2  ?  4  5  Stiff  .35  .33  .32  —  —  Eggwt  3.00  3.41  11.25  11.19  Width  .94  .89  6.03 1.03  —  —  Length  .13  .16  —  —  —  Shelwt  3.72  12.39  12.53  12.03  12.07  15.02  15.24  15.52  17.62  4.24  13.23  13.32  12.42  11.99  Mgmcm2  .05  —,  —  —  —  Shindx  .82  .82  1.54  .76  —  Round  3.04  3.00  3.73  3.19  108.41  Trusph  6.22  6.36  11.22  30.58  37.03  Prasph  1.84  1.80  2.34  1.96  P3dsph  .12  .12  Thick  14.93  Persh  100R p  41.1  2  .05 " 3  8 6  p  —  —  41.0  41.1 .oi - 6  6 9  —  40.8  40.5  73 TABLE C6 STEPWISE MULTIPLE REGRESSION WITH STIFFNESS AS THE DEPENDENT VARIABLE GROUP 1.  n=46l  BIRD AVERAGE PER PERIOD BASIS. F - Ratio  Independent Variable. Analysis 1  4  i  2  Eggwt  .13  .12  Width  .14  .18  Length  . 04  • 06  Shelwt  2.89  2.89  3.93  6.78  Thick  39.98  40.15  40. 26  42.09  Persh  .28  .28  Mgmcm2  3.87  3.88  33 4.33  Shindx  .02  >  1. 88  •  —  —  2.42  2.68  2. 73  Trusph  1.46  1.45  2. 88  Prasph  1.13  1.27  1. 28  P3dsph  .16  .29  90.3  2  F,  0 5  = 3.86  1.  90.3 F  2.02  •-  Round  10 OR  5  90.3  .01 - ' 9 6  6  —  —  127.00 • 41.20  —  25.57 —  10.11  2.67  179.09 —  93.93 19.83 —  1.78  90.2  90.2  74 TABLE C 7 STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 1.  OVERALL BIRD AVERAGE BASIS.  n=53  F - Ratio Independent Variable Analysis 1  2  3  4  5  2.50  3.84  5.3^  Stiff  3.06  Eggwt  .07  —  Width  .79  .92  Length  .46  Shelwt  1.17  .48 4.58  3.68  1.12  1.17  —  —  —  —  —  —  Thick  .84  Persh  Shindx  .45 .30 3.09  Round  2.85  —  —  4.20 —  3.05 —  2.60  14.42  -10.53  4.10  3.39  3.09  2.48  2.04  —  1.87  3.39 2.30  3.62  3.70  5.28  Trusph  1.49  2.74  1.84  1.23  .—  Prasph  .65  .84  P3dsph  1.37  1.39  Mgmcm2  100R F r  2  .05  .oi  89.0  4.09 7.33  88.8  4.07 7.27  8.68  1.43  88.5  87.8  87.2  4.07  4.06  4.05  7.26  7.23  7.20  75  TABLE C8 STEPWISE MULTIPLE  REGRESSION  WITH ENERGY AS THE DEPENDENT V A R I A B L E GROUP 1.  n=53  OVERALL BIRD AVERAGE B A S I S . F  Independent Variable Analysis 1  - Ratio  2  3  Stiff  .59  Eggwt  .09  Width  .67  Length  .58  Shelwt  1.12  3.87  2.61  Thick  .95  1.53  .87  Persh  .25  Mgmcm2  .38  3.56  Shindx  3.24  Round  4  5  1.03  4.40  3.14  2.41  18.67 -  __  1.83  14.40  2.27  2.37  17.52  2.93  2.16  1. 70  1.60  1.84  2.39  2.12  Trusph  1.24  1.78  Prasph  .55  .63  P3dsph  1.44  I.83  10 OR  p  p  .o  2  61.8  —  61.0  5.82  .94 —-  1.37 59.3  1.13  57.8  55.8  4.09  4.07  4.06  4.05  4.04  7.33  7.27  7.24  7.21  7.19  5  .oi  76 TABLE STEPWISE  C9  MULTIPLE REGRESSION  WITH STIFFNESS AS THE DEPENDENT GROUP 1.  OVERALL  BIRD AVERAGE BASIS.  F Independent Variable  Analysis  Eggwt  .01  Width  1.23  1  VARIABLE  n=53  - Ratio  2  3  4  — 2.62  5.96  10.61  17.32  2.35  —  —  4.03  26.25 —  Length  M  Shelwt  2.04  .67 4.17  Thick  2. ?4  3.04  3.21  15.37 3.05  Persh  1.56  1.80  1.92  1.69  Mgmcm2  4.27  7.42  7.51  11.54  Shindx  .17  Round  .16  2.97  3.97  .27 .03 .27  1.08  1.14  Trusph Prasph  P3dsph 10 OR  P  F  05 .0l  2  95.9  5  .27  —  5.24  36.30  —  2.66  — —  —  .35 95.9  —  95.9  95.6  95.2  4.08  4.07  4.06  4.05  4.04  7.31  7.27  7.24  7.21  7.19  TABLE CIO STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 2.  POOLED-•EGG BASIS.  n=425  F - Ratio Independent Variable Analysis 1  2  3  4  5  75.28  75.01  74.44  8.61  12.81  1.09  74.75 7.25 2.97  2.56 2.98  --  Width  74.74 4.79 .83  Length  4.41  4.33  3.08  Shelwt  8.95 10.06  8.57  Thick  7.07 9.63  Persh  .04  Stiff Eggwt  5.18  —  9.54 -7.25 2.77  Round  .52 .99  7.59 3.74 .83  Trusph  .80  .80  —  Prasph  1.16  .99  .74  P3dsph  .18  D.P.H.  .99  Mgmcm2 Shindx  10 OR  2  P  .0 = 3.86 5  2.26  60.2  —  9.51 9.23  8.80 10.11  9.06 —  8.27  2.33 —  8.73 — — —  _=  .99 60.2  1.07  60.0  P_ =6.70 01  -59.9  59.6  78 TABLE C l l STEPWISE MULTIPLE REGRESSION WITH ENERGY AS THE DEPENDENT VARIABLE GROUP 2.  POOLED--EGG BASIS.  , n=425  F - Ratio Independent Analysis 1 Variable  2  3  4  4.84  6.59  7.82  12.55  Width  .60 4.09 .78  1.05  2.87  2.42  —  Length -  3.81  4.00  2.71.  2.58  Shelwt  6.18  8.54  8.19  9.04  7.89 9.97  Thick  10.66  10.43  9.79  9.42  9.21  Stiff Eggwt  .03  Persh  Shindx  1.92 .64  Round  1. 01  Mgmcm2  Prasph  1.18  P3dsph  .06  D.P.H.  1.36  10 OR  11.8  2  Q 5  =  3.86  —  —  6.89 3.51 .97  .73  Trusph  F  _ _  6.58  7.52  2.52  2.08  8.23 —  —  .80  —  1.13  .71  --  —  1.42  11.7 F  .01  1.51 11.3  == 6.70  —  10.8  10.2  79 TABLE C12 STEPWISE MULTIPLE REGRESSION WITH STIFFNESS AS THE DEPENDENT VARIABLE GROUP 2.  P00LED-•EGG BASIS.  n=425  F - Ratio Independent Variable Analysis 1 Eggwt  6.46  Width  .06  2  ,  8.01  3  4  5  10.50  10.26  10.03  —  —  43.90  5.01 9.99 43.72  4.74 9.98 44. 38  4.70 9.74 44. 30  3.91  4.24  4.07  4.16  5.77 . 36 .49  6.37  6.24  6.14  2.06  2.67  4.14  Prasph  .35  .42  P3dsph  2.69  2.71  .29 6.17  D.P.H.  .14  Length  2.71  3.26  Shelwt  9.21  Mgmcm2  8.93 43.63 3.65 5.32  Shindx  .44  Round  .41  Trusph  Thick Persh  10 OR  79.3  2  P  0 5 " 3'  86  -.35  —  .30 3.88  —  -4.06  »=.  5.89  6.35  —  79.3 F  .01  79.3 == 6.70  79.2  79.2  80 TABLE C13 STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 2.  BIRD AVERAGE PER PERIOD BASIS.  n=74  F - Ratio Independent Variable Analysis 1  2  3  4  •5  17.58  16.88 6.47  16.91  8.43  Width  3.38 .67  16.89 7.72  1.02  3.42  .19  Length  1.21  1.74  3.42  3.62  8.22  Shelwt  6.29  6.10  6.19  Persh  2.72  4.73  6.35 4.77 --  6.95 5.07 5.51  6.84  Thick  .44 6.13  Stiff Eggwt  16.97  Mgmcm2  .17  —  Shindz  .09  .35 1.36  --  3.47  Prasph  1.44 2.47 1.70  2.95 1.44  P3dsph  .00  D.P.H.  4.92  Round Trusph  10 OR  2  F  .o .oi  87.1  —  5.52 87.0  4.00  4.00  7.08  7.07  5  p  1.63  7.58 86.7  3.99 7.05  —  5.02  5.44  — —  —  —  7.98  -—  —  8.97  85.7 3.99 7.04 .  9.50 85.7  3.99 7.03  81 TABLE Cl4 STEPWISE MULTIPLE REGRESSION WITH ENERGY AS THE DEPENDENT VARIABLE GROUP 2.  BIRD AVERAGE PER PERIOD BASIS.  n=74  F - Ratio Independent Variable Analysis 1  2  3  4  5  Stiff  .11  Eggwt  2.77  3.21  4.77  4.50  9.43  Width  .68  .94  2.57  1.96  --  Length  1.10  1.16  2.57  3.90  11.34  Shelwt  .15  .19  Thick  6.43  7.97  8.12  7.94  7.09  Persh  2.93  3.50  5.53  5.01  6.20  Mgmcm2  .42  .47  6.72  6.14  7.50  Shindx  .05  .20  Round  1.59  1.81  2.16  Trusph  2.57  2.84  2.61  Prasph  1.89  2.14  2.53  P3dsph  .00  D.P.H.  5.38  5.57  5.89  8.80  46.2  46.1  45.8  42.2  .05  4.00  4.00  3.99  3.99  3.99  '.01  7.08  7.07  7.05  7.04  7.03  100R  2  —  —  2.15  —  9.54 40.3  82 TABLE C15  .  STEPWISE MULTIPLE REGRESSION WITH STIFFNESS AS THE DEPENDENT VARIABLE GROUP 2.  BIRD. AVERAGE PER PERIOD BASIS. '  -  p  Independent Variable Analysis 1  2  Eggwt  .17  .52  Width  .00  —  Length  .04  .04  Shelwt  .26  1.90  22.57  23.45  Thick  Ratio  2.41  2.90  .  —  ; 1.90  2.36  .97  Mgmcm2  .00  —  Shindx  .19  .20  Round  .96  Trusph  .08  Prasph  .94  P3dsph  .15  . 20  .84  D.P.H.  .16  .16  —  P  F  ,05  .01  90.8 4.  00  7.08  1.23 •  1.01  90.8 4.  00  7.07  _ _  —  —  438.08  .93 •  —  i—  .88  1.03 .15  28.26  27.11  .44  2  7.78 —  Persh  100R  n=74  v  —  :'i  -31  •  —  .86  90.8  —  .  —  6.34  4.59 —  '.  ;  90.6  90.0  3.99  3.99  3.99  7.05  7.04  7,03  •  83 TABLE C16 SELECTED NON-DESTRUCTIVE CHARACTERISTICS GROUP 1  I N MULTIPLE REGRESSION ON LOAD. 11=2733  POOLED-EGG B A S I S .  Analysis Stiff  2  1  103.5* 3731.3**  4  3  102.5  IO3.2  101.5  3748.7  3911.9  3745.6  —-;  5  101.5  3724.3  Eggwt  -51.1  28.4  -46.6 25.8  -31.3 95.1  Width  3239.3  2069.0  I691.6  Length  -542.8  175.8  Shindx  -61.7 2.6  —  —  31.8 150.6  —  Sy  363.9  364.0  364.1  369.2  370.4  -1973.5  -5950.4  -4205.2  60.5  60.4  60.4  Constant 10 OR F  2  84 .o - 3: 5  17.8 1.4  204.0  72.7  •  —•-• ,•  691.3  132.0  3.2  P. 0 1 = 6.64  * P a r t i a l Regression Coefficient ** F - R a t i o  -1146.6 59.3  -1759.2 59.0  84 TABLE Cl? SELECTED NON-DESTRUCTIVE CHARACTERISTICS IN MULTIPLE REGRESSION ON LOAD. GROUP 1 BIRD AVERAGE PER PERIOD BASIS. n=46l  Analysis  2  1  111.0* 111.2 1365.1** I369.6  Stiff  109.1 1444.1  Eggwt  -82.5 16.7  -85.9 1.8.3  -41.9 57.6  Width  1377.1 1.2  3012.5 31.5  1.8 76.1 85.8  Length  1564.3 4.1  477.1 5.2  Shindx  90.9 2.1  Sy Constant  10 OR  2  212.6 -15807.5 77.7  .05 " 3-86  F  * P a r t i a l Regression ** F - R a t i o  —  .  —  —  212.8 -9586.2 77.5 F  .01  4  3  213.8 -4517.2 77.3 = 6.69  Coefficient  5  107.6 1375.0  107.6 1256.6  —  —  —  —  35.8 69.7 217.3 -1582.3 76.5  505.3 27.0 —  -226.6 -1104.0 74.4  85 TABLE C18 SELECTED NON-DESTRUCTIVE CHARACTERISTICS IN MULTIPLE REGRESSION ON LOAD. OVERALL BIRD AVERAGE BASIS.  2  Analysis 1 Stiff  110.3* 109.8 221.8** 221.1  105.8 225.1  -114.3 4.9  -114.6 4.9  -35.2 5.1  Width  188.3 .0  4073.1 8.7  2018.5 14.4  Length  3690.0 1.6  867.7 2.6  Shindx  225.3 .9  Constant  10 OR  2  .05 .01  F  F  4.05 7.20  —  —  146.2 146.1 -31061.2 -•14655.3 86.0 86.3  n=53  4  3  Eggwt  Sy  GROUP 1  —  148.4 -5442.5 85.3  107.8 223.6 —  —  —  40.4 12.1 159.0 -1928.1 82.7  5 102.3 204.0 —  922.8 15.9 —  —  154.4 -2762.3 83.7  4.04  4.04  4.03  4.03  7.19  7.18  7.17  7.17  * P a r t i a l Regression C o e f f i c i e n t ** F - Ratio  86 TABLE C19 SELECTED NON-DESTRUCTIVE CHARACTERISTICS IN MULTIPLE REGRESSION ON LOAD FOR EACH TEST PERIOD F - Ratio of Independent V a r i a b l e Period  1  472.26  3.08  .59  .23  .03  62.4  2  504.14  2.51  1.77  .17  .34  62.0  3  424.04  5.74  1.13  .23  .01  60.4  4  420.69  .72  1.06  .09  .13  6O.5  5  336.96  4.40  5.18  .52  1.03  57.7  6-  462.08  23.71  2.09  .91  .08  63.4  7  3^5.51  .15  .08  .51  .64  60.4  8  462.92  5.38  .10  5.62  F  . 0 5 = 3.87  F  . o i "« 6  72  4.26  63.3  

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