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Percentage Shell as a Function of Shell Thickness, Egg Volume, and Egg Shape
POULTRY SCIENCE July, 1940, Vol. XIX, No. 4
Percentage Shell as a Function of Shell Thickness, Egg Volume, and Egg Shape V. S. ASMUNDSON AND G. A. BAKER Divisions of Poultry Husbandry and of Mathematics and Physics, University of California, Davis (Received for publication October 20, 1939) /
V
"T~ HE avian egg may be divided into J- four parts: the yolk, the albumen or white, the shell membrane, and the shell. The absolute and relative weight of the yolk, the albumen, and the shell varies for different species and also within narrower limits for eggs of the same species as shown by the summary of Grossfeld (1938, pp. 70-78). Asmundson (1939) has also shown that the absolute and relative weight of the shell membrane varies for different species, the turkey (Meleagris gallopavo) egg having a heavier shell membrane than the chicken (Gallus demesticus) egg. There was also some indication that the shell on the larger turkey eggs may weigh relatively less than the shell on the smaller chicken eggs, although the shell on turkey eggs is thicker, on the average, than the shell on the chicken eggs. This finding prompted us to inquire into the influence of egg volume, egg shape, and shell thickness on percentage of shell. SPECIES DIFFERENCES IN THE THICKNESS OF T H E SHELL
Taylor and Lerner (1939), using White Leghorn chickens, have demonstrated an
inherited difference in the thickness of the shell. They concluded that percentage of shell was, for their purposes, a satisfactory measure of amount of shell when compared with measures requiring more elaborate computation such as that of Hendricks, Lee, and Godfrey (1931). Percentage of shell may not be a satisfactory measure of amount of shell when comparing the eggs of different species if the thickness varies significantly. To determine whether there are species differences in the thickness of the shell the data in Table 1 were compiled. From the data given in Table 1 it is apparent that the shell of the ringneck pheasant egg is thinner than that of the turkey egg but the percentage of shell on the former is nevertheless greater than on the latter. Other groups of turkey eggs, however, had up to 9.26 percent of shell on the average, a value which is still slightly lower than for the chickens and pheasants. The thickness of the chicken egg shells in Table 1 is not known, but Hays and Sumbardo (1927) have shown that the thickness of the shell varies from .280 to .345 mm. on eggs from different hens, or an average
[227]
228
V. S. ASMUNDSON AND G. A. BAKER
of .309 mm. An analysis of variance of the original data for ringneck pheasant (Phasianus colchiens torquatus) and turkeys summarized in Table 1 and the data published by Hays and Sumbardo (1927) shows that the thickness of the shell differs significantly for these three species. The few silver pheasants (Gennaeus nycthemerus) eggs available had shells of about the same thickness as those on turkey eggs.
EFFECT OF EGG VOLUME AND EGG SHAPE ON PERCENTAGE OF SHELL
Pearl and Surface (1914) have found that an egg can be represented as a perfect prolate spheroid, as far as volume is concerned, with only an error of 2.2 percent on the average. This error is an excess. We shall be concerned with the ratio of surface area of an egg to its volume. If the volume is slightly in excess the surface area will probably be in excess also, so
TABLE 1.—Data for the eggs of jour species Shell No. of eggs Ringneck pheasant Silver pheasant Chickens Turkeys
23 7 64* 64
Weight of egg 26.66 44.09 55.81 90.37
Lengthbreadth index 78.68 75.07 72.68 74.01
Weight
Thickness
egg
shell
grams
percent
mm.
1.085 1.083 1.082 1.075
2.325 2.288 2.235 2.174
2.58 4.88 5.28 7.48
9.68 11.07 9.46 8.28
0.26 0.36 0.35
* Average for eggs from each of 64 hens or 384 eggs.
The specific gravity was determined by obtaining the weight W in air and the weight Ww in water. The specific gravity was calculated from the formula Specific gravity=
W W-W w
The data obtained are summarized in Table 1. Those for chickens do not differ significantly from those obtained by Hays and Sumbardo (1927), Olsson (1934), and others. The values for the specific gravity of turkey eggs and shells are slightly lower than those for the other three species but the significance of the differences is doubtful. Since the thickness of the shells and the specific gravity of the eggs and shells will not satisfactorily explain the apparent differences in the percentage of shell on the eggs of the four species considered, other factors must be at least partly responsible.
that the ratio of these quantities calculated for a prolate spheroid should give a very good result. Let P = percentage shell D s = density of shell D e = density of egg T s = thickness of shell in centimeters S = surface area of the egg V = volume of the egg in cubic centimeters Then by definition D . ST, (1)
p=—rxioo.
STS = volume of the egg shell if the shell thickness is T s over all the egg. Now if DsT s
is constant then P will depend
only on S/V or perhaps this dependence can be stated in terms of V only. A prolate spheroid is generated by re-
229
PERCENTAGE SHELL
volving the upper half of the ellipse, (2)
V—=l,a>b, b2
a2
about the x-axis. In (2) a represents onehalf the length and b one-half the width of the egg. The volume is given by the equation V=—rb 2 a. 3
(3)
The surface area is given by the equation ra
4xb (4) S =
a2
, V a « - ( a » - b * ) \ ! dx
Jo 2-ira2b = 2irb -|—-. 2 2 sin 2
Fr=-)
Va -b If the eggs of different sizes are similar in a geometric sense, that they are is indicated by figure l, then for all such similar eggs b = Xa, X < l. If b = Xa we obtain sm-Vl-X2\
/ (5)
'
2Xa
tionality being p, then the value of the ratio surface area for the new egg is (1/p) ' k. volume In (7) P is considered as function of V; that is, X is considered constant. X is a parameter that determines the shape of the egg. It may be of interest to regard P as a function of the shape or X. V will then be regarded as constant. If X is constant (7) is of the form
But V = 4/3 7rb2a = 4/3 7rA2a3
so that \4*X2 /
Hence (S) becomes sin-'Vl— X 2 \
/ (•fii
s
V
Vl-x 2
/
2i/3 \ « i v 1 ' 3
W
and (1) becomes
(7)
yi P= -
sin-Vl-A2
*"' rx+
2" 3 V s
FIG. 1. Eggs selected as reasonably typical of those laid by birds of four species. They should not be used to furnish an absolute figure for the relative length and breadth of eggs laid by these species.
)„,
K
(9) Ta 100 V1'3
D„
The following proposition can be stated about eggs, considered as solids of revolution, whether the longitudal cross section is an ellipse or not. If the ratio, S/V = k, has been found for any shaped egg and the value of this ratio is desired for any similar shaped egg, the factor of propor-
yvs where K is constant. If V is constant then (7) is of the form (10)
/
survi-x2 \
Typical graphs of (9) and (10) are shown in Figures 2 and 3. Figure 2 shows what happens to the percentage shell as the size of eggs similar to a typical hen egg,
230
V. S. ASMUNDSON AND G. A. BAKER
within ordinary limits. The length-breadth index, calculated for the eggs of SO species of wild birds (Grossfeld, 1938, pp. 2-3), ranged from 62.9 percent to 83.8 percent. Such variation in shape might cause a variation of 1 percent in the shell whereas the actual range is from 3.9 to 12.1, or a difference of 8.2 percent.
X — j4, changes. Percentage shell changes fairly rapidly with change in volume especially for the smaller eggs. Obviously species that lay small eggs must lay eggs with thinner shells than species that lay large eggs or their eggs would have a high percentage of shell. Thus the data presented by Grossfeld /
> ^s ^<0
/a
fc /o
^J^= .035" cm.
$
J.^> s Vl
^ *
6
rs~.t 726 c,77
O
/O
£0
30
40
JO
60
70
Vo/c//f?e //? o/6/c
SO
SO
/OO
//O
/20
/30
cent/meters
FIG. 2. Functional relationship between percentage shell and egg volume for two shell thicknesses, .035 and .026 centimeters. It is assumed for purposes of illustration that "k = 3/4, T s = .035 cm. or .026 cm., D e = 1.08, D s = 2.26. If these quantities are different the corresponding curve may be obtained from either curve by multiplying by a proper factor. Either curve above may be derived from the other by multiplying by a factor. If X is quite different say X < 0.5 allowance may have to be made for this fact.
(1938) indicate that birds laying small eggs; for example, canaries, must lay eggs with relatively thin shells since the percentage of shell is less than found on the eggs of gallinaceous birds. Figure 3 shows what happens to percentage shell as the shape of a hen egg of typical volume changes. Percentage shell is very little affected by changing shape
Figures 2 and 3 use the values X = %, D e — 1.08, D s = 2.26 for Ringneck and Silver pheasant, chicken, and turkey eggs. These figures are averages from data in Table 1. Figure 2 is based on a shell thickness of .035 cm. which applies approximately to turkey eggs and .026 cm. which is the approximate thickness of the shell on Ringneck pheasant eggs, Figure 3 uses
PERCENTAGE SHELL
51.7 ex. as the volume of an average hen egg. The equations of the curves in Figure 2 are (11)
P=
35.92
and
231
If D s = D' s and D e = D' e then it is only necessary to multiply the ordinates of (1) by T' s /T s . The graph of (12) can be obtained by multiplying the ordinates of (11) by .026/.035. From Table 1 and Figures 2 and 3 it is
26.68
(12)
P=-
V'/3
The equation for Figure 3 is (13)
P = 4.754(X2'3+
sin-Vl-*2 X2 /
If D e = 1.08 for each species, then from Table 1 the average volumes are 24.7, 40.8, 51.7, and 83.7 c.c. The calculated percentages of shell are 9.2, 10.4, 9.6, and 8.2. The corresponding observed averages from Table 1 are 9.7, 11.1, 9.5, and 8.3. The agreement is fairly close. Special values of X, T s , D e , D s , are assumed in (11) and (12). Other values of these quantities may be appropriate to the discussion of other eggs. The curves of Figure 2 corresponding to a new set of specified conditions can be obtained by multiplying the ordinates of one curve of Figure 2, say (11), by a proper factor. Let K of equation (9) be written as
(14)
K = 32'V«-
\
Vl-X2 2>'3X«
/
D,T, De
100 •
The part of K involving X changes so slowly and eggs of different species are so similar that for practical purposes it may be considered constant. This leaves D8T8 , =h D„
which can be calculated for (11). Suppose new values D' s , T' s and D' e so that - = h'. D'.T'. D' e To obtain the ordinates corresponding to h' multiply the ordinates of (11) by h'/h.
> •§ * •**
*?
A • ratio t>f m'dM of egg to /e/;gt/i ofegg
FIG. 3. Functional relationship between percentage shell and egg shape for a typical chicken egg. It is assumed that T s = .035 cm., D e = 1.08, Ds = 2.26, and V = SI.7. If other values are taken the ordinates of this curve must be multiplied by a suitable factor.
apparent that shell thickness and egg volume are by far the more important factors influencing the percentage shell. The question arises as to which of these has the greater effect when the other factors, egg density, shell density, and egg shape, are considered constant, which they practically are for eggs of one species. Let AP = change in percentage shell ATS = change in shell thickness AV = change in egg volume Then
(15)
^,pil_i^l
P L T. approximately.
3 VJ
232
V. S. ASMUNDSON AND G. A. BAKER
Equation (IS) shows that the effect of a relative change in shell thickness is three times as great and opposite in direction to the effect of the same relative change in volume on the relative change in percentage shell. Equation (IS) is a good approximation so long as ATS and AV are not too large. Thus the approximation should be good within a species.
These relationships are shown graphically in Figures 2 and 3. Equation (15) shows that within a species a relative change in shell thickness has three times as great an effect in the opposite direction as the same relative change in volume on the relative change in percentage shell. LITERATURE CITED
SUMMARY
Ringneck pheasant eggs were found to have thinner shells than chicken eggs (data of Hays and Sumbardo, 1927) which in turn had thinner shells than turkey eggs. The differences were statistically significant. The few Silver pheasant eggs examined had shells of the same thickness as turkey eggs. Calculations based on data for eggs of gallinaceous birds show that when the thickness of the shell remains constant, (a) the shape of the egg has a negligible effect on the percentage of shell which, for eggs of average shape, decreases slightly with an increase in the relative breadth of the egg, but (b) the percentage of shell decreases significantly with an increase in the volume or size of the egg.
Asmundson, V. S., 1939. The formation of the egg in the oviduct of the turkey (Meleagris gallopavo). Jour. Exp. Zool. 82:287-304. Grossfeld, J., 1938. Handbuch der Eierkunde. Julius Springer, Berlin. Hays, F. A., and A. A. Sumbardo, 1927. Physical characters of eggs in relation to hatchability. Poul. Sci. 6:196-200. Hendricks, W. A., A. R. Lee, and A. B. Godfrey, 1931. Effects of cod liver oil and ultra-violet irradiation, as influenced by oyster shell in the diet of confined laying hens. Jour. Agri. Res. 43 :517-S3S. Olsson, N., 1934. Studies on specific gravity of hens' eggs. Otto Harrassowitz, Leipzig. Pearl, R., and F. M. Surface, 1914. A biometrical study of egg production in the domestic fowl. III. Variation and correlation in the physical characters of the eggs. U.S.D.A. Bur. Anim. Ind. Bull. 110, pt. 3. Taylor, L. W., and I. M. Lerner, 1939. Inheritance of eggshell thickness in White Leghorn pullets. Jour. Agri. Res. 58:383-396.
Percentage Shell as a Function of Shell Thickness, Egg Volume, and Egg Shape V. S. ASMUNDSON AND G. A. BAKER Divisions of Poultry Husbandry and of Mathematics and Physics, University of California, Davis (Received for publication October 20, 1939) /
V
"T~ HE avian egg may be divided into J- four parts: the yolk, the albumen or white, the shell membrane, and the shell. The absolute and relative weight of the yolk, the albumen, and the shell varies for different species and also within narrower limits for eggs of the same species as shown by the summary of Grossfeld (1938, pp. 70-78). Asmundson (1939) has also shown that the absolute and relative weight of the shell membrane varies for different species, the turkey (Meleagris gallopavo) egg having a heavier shell membrane than the chicken (Gallus demesticus) egg. There was also some indication that the shell on the larger turkey eggs may weigh relatively less than the shell on the smaller chicken eggs, although the shell on turkey eggs is thicker, on the average, than the shell on the chicken eggs. This finding prompted us to inquire into the influence of egg volume, egg shape, and shell thickness on percentage of shell. SPECIES DIFFERENCES IN THE THICKNESS OF T H E SHELL
Taylor and Lerner (1939), using White Leghorn chickens, have demonstrated an
inherited difference in the thickness of the shell. They concluded that percentage of shell was, for their purposes, a satisfactory measure of amount of shell when compared with measures requiring more elaborate computation such as that of Hendricks, Lee, and Godfrey (1931). Percentage of shell may not be a satisfactory measure of amount of shell when comparing the eggs of different species if the thickness varies significantly. To determine whether there are species differences in the thickness of the shell the data in Table 1 were compiled. From the data given in Table 1 it is apparent that the shell of the ringneck pheasant egg is thinner than that of the turkey egg but the percentage of shell on the former is nevertheless greater than on the latter. Other groups of turkey eggs, however, had up to 9.26 percent of shell on the average, a value which is still slightly lower than for the chickens and pheasants. The thickness of the chicken egg shells in Table 1 is not known, but Hays and Sumbardo (1927) have shown that the thickness of the shell varies from .280 to .345 mm. on eggs from different hens, or an average
[227]
228
V. S. ASMUNDSON AND G. A. BAKER
of .309 mm. An analysis of variance of the original data for ringneck pheasant (Phasianus colchiens torquatus) and turkeys summarized in Table 1 and the data published by Hays and Sumbardo (1927) shows that the thickness of the shell differs significantly for these three species. The few silver pheasants (Gennaeus nycthemerus) eggs available had shells of about the same thickness as those on turkey eggs.
EFFECT OF EGG VOLUME AND EGG SHAPE ON PERCENTAGE OF SHELL
Pearl and Surface (1914) have found that an egg can be represented as a perfect prolate spheroid, as far as volume is concerned, with only an error of 2.2 percent on the average. This error is an excess. We shall be concerned with the ratio of surface area of an egg to its volume. If the volume is slightly in excess the surface area will probably be in excess also, so
TABLE 1.—Data for the eggs of jour species Shell No. of eggs Ringneck pheasant Silver pheasant Chickens Turkeys
23 7 64* 64
Weight of egg 26.66 44.09 55.81 90.37
Lengthbreadth index 78.68 75.07 72.68 74.01
Weight
Thickness
egg
shell
grams
percent
mm.
1.085 1.083 1.082 1.075
2.325 2.288 2.235 2.174
2.58 4.88 5.28 7.48
9.68 11.07 9.46 8.28
0.26 0.36 0.35
* Average for eggs from each of 64 hens or 384 eggs.
The specific gravity was determined by obtaining the weight W in air and the weight Ww in water. The specific gravity was calculated from the formula Specific gravity=
W W-W w
The data obtained are summarized in Table 1. Those for chickens do not differ significantly from those obtained by Hays and Sumbardo (1927), Olsson (1934), and others. The values for the specific gravity of turkey eggs and shells are slightly lower than those for the other three species but the significance of the differences is doubtful. Since the thickness of the shells and the specific gravity of the eggs and shells will not satisfactorily explain the apparent differences in the percentage of shell on the eggs of the four species considered, other factors must be at least partly responsible.
that the ratio of these quantities calculated for a prolate spheroid should give a very good result. Let P = percentage shell D s = density of shell D e = density of egg T s = thickness of shell in centimeters S = surface area of the egg V = volume of the egg in cubic centimeters Then by definition D . ST, (1)
p=—rxioo.
STS = volume of the egg shell if the shell thickness is T s over all the egg. Now if DsT s
is constant then P will depend
only on S/V or perhaps this dependence can be stated in terms of V only. A prolate spheroid is generated by re-
229
PERCENTAGE SHELL
volving the upper half of the ellipse, (2)
V—=l,a>b, b2
a2
about the x-axis. In (2) a represents onehalf the length and b one-half the width of the egg. The volume is given by the equation V=—rb 2 a. 3
(3)
The surface area is given by the equation ra
4xb (4) S =
a2
, V a « - ( a » - b * ) \ ! dx
Jo 2-ira2b = 2irb -|—-. 2 2 sin 2
Fr=-)
Va -b If the eggs of different sizes are similar in a geometric sense, that they are is indicated by figure l, then for all such similar eggs b = Xa, X < l. If b = Xa we obtain sm-Vl-X2\
/ (5)
'
2Xa
tionality being p, then the value of the ratio surface area for the new egg is (1/p) ' k. volume In (7) P is considered as function of V; that is, X is considered constant. X is a parameter that determines the shape of the egg. It may be of interest to regard P as a function of the shape or X. V will then be regarded as constant. If X is constant (7) is of the form
But V = 4/3 7rb2a = 4/3 7rA2a3
so that \4*X2 /
Hence (S) becomes sin-'Vl— X 2 \
/ (•fii
s
V
Vl-x 2
/
2i/3 \ « i v 1 ' 3
W
and (1) becomes
(7)
yi P= -
sin-Vl-A2
*"' rx+
2" 3 V s
FIG. 1. Eggs selected as reasonably typical of those laid by birds of four species. They should not be used to furnish an absolute figure for the relative length and breadth of eggs laid by these species.
)„,
K
(9) Ta 100 V1'3
D„
The following proposition can be stated about eggs, considered as solids of revolution, whether the longitudal cross section is an ellipse or not. If the ratio, S/V = k, has been found for any shaped egg and the value of this ratio is desired for any similar shaped egg, the factor of propor-
yvs where K is constant. If V is constant then (7) is of the form (10)
/
survi-x2 \
Typical graphs of (9) and (10) are shown in Figures 2 and 3. Figure 2 shows what happens to the percentage shell as the size of eggs similar to a typical hen egg,
230
V. S. ASMUNDSON AND G. A. BAKER
within ordinary limits. The length-breadth index, calculated for the eggs of SO species of wild birds (Grossfeld, 1938, pp. 2-3), ranged from 62.9 percent to 83.8 percent. Such variation in shape might cause a variation of 1 percent in the shell whereas the actual range is from 3.9 to 12.1, or a difference of 8.2 percent.
X — j4, changes. Percentage shell changes fairly rapidly with change in volume especially for the smaller eggs. Obviously species that lay small eggs must lay eggs with thinner shells than species that lay large eggs or their eggs would have a high percentage of shell. Thus the data presented by Grossfeld /
> ^s ^<0
/a
fc /o
^J^= .035" cm.
$
J.^> s Vl
^ *
6
rs~.t 726 c,77
O
/O
£0
30
40
JO
60
70
Vo/c//f?e //? o/6/c
SO
SO
/OO
//O
/20
/30
cent/meters
FIG. 2. Functional relationship between percentage shell and egg volume for two shell thicknesses, .035 and .026 centimeters. It is assumed for purposes of illustration that "k = 3/4, T s = .035 cm. or .026 cm., D e = 1.08, D s = 2.26. If these quantities are different the corresponding curve may be obtained from either curve by multiplying by a proper factor. Either curve above may be derived from the other by multiplying by a factor. If X is quite different say X < 0.5 allowance may have to be made for this fact.
(1938) indicate that birds laying small eggs; for example, canaries, must lay eggs with relatively thin shells since the percentage of shell is less than found on the eggs of gallinaceous birds. Figure 3 shows what happens to percentage shell as the shape of a hen egg of typical volume changes. Percentage shell is very little affected by changing shape
Figures 2 and 3 use the values X = %, D e — 1.08, D s = 2.26 for Ringneck and Silver pheasant, chicken, and turkey eggs. These figures are averages from data in Table 1. Figure 2 is based on a shell thickness of .035 cm. which applies approximately to turkey eggs and .026 cm. which is the approximate thickness of the shell on Ringneck pheasant eggs, Figure 3 uses
PERCENTAGE SHELL
51.7 ex. as the volume of an average hen egg. The equations of the curves in Figure 2 are (11)
P=
35.92
and
231
If D s = D' s and D e = D' e then it is only necessary to multiply the ordinates of (1) by T' s /T s . The graph of (12) can be obtained by multiplying the ordinates of (11) by .026/.035. From Table 1 and Figures 2 and 3 it is
26.68
(12)
P=-
V'/3
The equation for Figure 3 is (13)
P = 4.754(X2'3+
sin-Vl-*2 X2 /
If D e = 1.08 for each species, then from Table 1 the average volumes are 24.7, 40.8, 51.7, and 83.7 c.c. The calculated percentages of shell are 9.2, 10.4, 9.6, and 8.2. The corresponding observed averages from Table 1 are 9.7, 11.1, 9.5, and 8.3. The agreement is fairly close. Special values of X, T s , D e , D s , are assumed in (11) and (12). Other values of these quantities may be appropriate to the discussion of other eggs. The curves of Figure 2 corresponding to a new set of specified conditions can be obtained by multiplying the ordinates of one curve of Figure 2, say (11), by a proper factor. Let K of equation (9) be written as
(14)
K = 32'V«-
\
Vl-X2 2>'3X«
/
D,T, De
100 •
The part of K involving X changes so slowly and eggs of different species are so similar that for practical purposes it may be considered constant. This leaves D8T8 , =h D„
which can be calculated for (11). Suppose new values D' s , T' s and D' e so that - = h'. D'.T'. D' e To obtain the ordinates corresponding to h' multiply the ordinates of (11) by h'/h.
> •§ * •**
*?
A • ratio t>f m'dM of egg to /e/;gt/i ofegg
FIG. 3. Functional relationship between percentage shell and egg shape for a typical chicken egg. It is assumed that T s = .035 cm., D e = 1.08, Ds = 2.26, and V = SI.7. If other values are taken the ordinates of this curve must be multiplied by a suitable factor.
apparent that shell thickness and egg volume are by far the more important factors influencing the percentage shell. The question arises as to which of these has the greater effect when the other factors, egg density, shell density, and egg shape, are considered constant, which they practically are for eggs of one species. Let AP = change in percentage shell ATS = change in shell thickness AV = change in egg volume Then
(15)
^,pil_i^l
P L T. approximately.
3 VJ
232
V. S. ASMUNDSON AND G. A. BAKER
Equation (IS) shows that the effect of a relative change in shell thickness is three times as great and opposite in direction to the effect of the same relative change in volume on the relative change in percentage shell. Equation (IS) is a good approximation so long as ATS and AV are not too large. Thus the approximation should be good within a species.
These relationships are shown graphically in Figures 2 and 3. Equation (15) shows that within a species a relative change in shell thickness has three times as great an effect in the opposite direction as the same relative change in volume on the relative change in percentage shell. LITERATURE CITED
SUMMARY
Ringneck pheasant eggs were found to have thinner shells than chicken eggs (data of Hays and Sumbardo, 1927) which in turn had thinner shells than turkey eggs. The differences were statistically significant. The few Silver pheasant eggs examined had shells of the same thickness as turkey eggs. Calculations based on data for eggs of gallinaceous birds show that when the thickness of the shell remains constant, (a) the shape of the egg has a negligible effect on the percentage of shell which, for eggs of average shape, decreases slightly with an increase in the relative breadth of the egg, but (b) the percentage of shell decreases significantly with an increase in the volume or size of the egg.
Asmundson, V. S., 1939. The formation of the egg in the oviduct of the turkey (Meleagris gallopavo). Jour. Exp. Zool. 82:287-304. Grossfeld, J., 1938. Handbuch der Eierkunde. Julius Springer, Berlin. Hays, F. A., and A. A. Sumbardo, 1927. Physical characters of eggs in relation to hatchability. Poul. Sci. 6:196-200. Hendricks, W. A., A. R. Lee, and A. B. Godfrey, 1931. Effects of cod liver oil and ultra-violet irradiation, as influenced by oyster shell in the diet of confined laying hens. Jour. Agri. Res. 43 :517-S3S. Olsson, N., 1934. Studies on specific gravity of hens' eggs. Otto Harrassowitz, Leipzig. Pearl, R., and F. M. Surface, 1914. A biometrical study of egg production in the domestic fowl. III. Variation and correlation in the physical characters of the eggs. U.S.D.A. Bur. Anim. Ind. Bull. 110, pt. 3. Taylor, L. W., and I. M. Lerner, 1939. Inheritance of eggshell thickness in White Leghorn pullets. Jour. Agri. Res. 58:383-396.