PRINCIPAL AXIS OF SYMMETRY IN THE BIRD'S EGG. 339 



"deviation" of 45 or more as compared with 30 per cent, of 

 the hen's eggs. 



In a clutch of six sparrows' eggs I found all the relations 

 typical of the pigeon's egg including the long axis of the yolk 

 and the ligamentum albumenis. In two of these the axis angle 

 could be measured and was found to be 45 in one, and about 

 125 in the other. 



III. Axis ANGLES. 



Before considering the relations found in the eggs of the indi- 

 vidual birds it is necessary to consider the normal range of varia- 

 bility in the pigeon's egg. The curve, Fig. 2, shows that the 

 variability is great, in fact, one may meet with almost any angle 

 from o to 1 80 degrees. The extremes met with were 3 and 180 

 both of them in eggs which had abnormal chalazse and were 

 therefore not included in the curve. The latter is unique as 

 there were no cases found between 135 and 180. All similar 

 cases in which the absence of well marked long and chalazal 

 axes made it impossible to measure the angle accurately were 

 omitted, thus eliminating about 7 per cent, of the eggs studied. 

 As is indicated in the curve, the maximum variation was 127 

 in normal eggs; there were two cases at 135 and one at 8, all 

 three of them perfectly normal typical eggs in other respects. 



The curve of axis angle variability which I published previously 

 (p. 303) shows four modes. These seemed to indicate that a 

 flock of birds could be divided into groups laying eggs with 

 similar angles. In plotting the present more extensive data the 

 curve (Fig. 2) has been compressed by making 10 instead of 5 

 degree classes and it suggests another interpretation. It shows 

 a resemblance to a curve of normal variability with its mode 

 at 70 and were there several thousand instead of a trifle over 

 five hundred cases I believe the resemblance would be much 

 more striking. It suggests in other words that the actual angle 

 between embryo and principal axis is a matter of chance. It 

 should be noted that 85 per cent, of all cases lie between 45 and 

 90. This means that in the pigeon egg the right side of the 

 embryo is practically always (98 per cent.) directed toward the 

 pointed end of the shell, but that in addition the head is usually 

 inclined in the same direction. Obviously Patterson (1910) was 

 correct as to the essential relation between the pigeon embryo 



