PRINCIPAL AXIS OF SYMMETRY IN THE BIRD'S EGG. 347 



The table shows few peculiarities. The range of variability 

 was low (from 75 to 117). There were five eggs which had no 

 well-marked long axis; three of them had extreme angles (70, 

 117 and 124), the other two from a single clutch, were 95 

 and 96. In this case (clutch 629) the ova measured as follows: 



First egg 21.2 mm. (chalazal axis) 21.2 mm. (transverse axis) 19.3 mm. (polar axis). 

 Second egg 19.2 mm. (chalazal axis) 19.0 mm. (transverse axis) 19.0 mm. (polar 

 axis). 



IV. DISCUSSION. 



A. Variability of the Axis Angles. The data presented here 

 are the most complete that have been gathered with reference to 

 the axis angles of any bird's egg and they show that while the 

 actual angle may vary considerably, the relation between the 

 head of the embryo and the principal egg axis is very constant. 

 What I have called "inversions" (see p. 349) occur in less than 

 I per cent, of the cases. The embryo may lie in almost any 

 position compatible with the general relation between the two 

 axes. If we omit eggs that were not normal as to embryo or 

 chalazse (circ. 10 per cent, of all), and include only those which 

 could be measured accurately, the extreme axis angles are 8 

 and 135. If we compare this maximum with the maximum 

 found for any single bird, namely, 127 as compared with 86, 

 it is obvious that a given bird's eggs will show less variability 

 than the eggs from a flock. The difference between the two is 

 not fully appreciated until we realize that the maximum varia- 

 bility in the other four birds of the group studied was 40, 42, 

 53 and 55 respectively; the average maximum variability then 

 for a single bird's eggs is about two thirds of the total variability 

 observed. We may predict that a given pigeon's eggs will show 

 the embryo lying in a quadrant the center .of which is usually 

 between 45 and 95 according to the particular bird. In other 

 words the embryonic axis will cut the principal egg axis at an 

 angle which may vary 25 on either side of a mean. The varia- 

 tion we find in an individual bird's eggs makes it clear that the 

 axis angle is no mathematically constant one like the angles 

 of a crystal. There are various mechanical factors operating 

 during ovarian and oviducal stages which undoubtedly contribute 

 to the variability of the axis angle. Thus it is easy to see how 



