PRINCIPAL AXIS OF SYMMETRY IN THE BIRD'S EGG. 349 



the first and so the first is available for a measurement of the 

 axis angle. The following table shows the results. 



Normal Range of Percentage of Clutches in which 



Variability. Both Eggs have the Same 



Axis Angle. 



No. 3, 40 (from 90 to 130) 45 per cent. 



No. 4, 53 (from 52 to 105) 46 per cent. 



No. 5, 84 (from 8 to 92) 30 per cent. 



No. 6, 55 (from 43 to 98) 45 per cent. 



No. 7, 42 (from 75 to 117) 56 per cent. 



The average of these is 43 per cent, of coincidence, but if the 

 very irregular no. 5 be omitted it is 58 per cent. 



It should be said further that there is no evidence that the 

 eggs of a mother and daughter tend to resemble each other as 

 to axis angles nor that there is any noticeable difference in the 

 eggs of a bird during a first and second mating or during the 

 early or later parts of her laying period. 



We may say in conclusion that two sets of factors contribute 

 toward extreme variation; irregularities in the laying down 

 of the yolk during the final rapid growth period and irregularities 

 in the functioning of the oviduct during the passage of the ovum. 

 Aside from this we must expect normal spontaneous variation 

 to the extent of at least 20 degrees on either side of a mean. 

 This estimate of 40 as the probable maximum spontaneous 

 variation is based upon the records of no. 3 the eggs of which 

 showed no signs of ovarian or oviducal irregularities. Accord- 

 ingly, if we wish to determine the embryonic axis at a stage when 

 it is not clearly differentiated morphologically, we can distinguish 

 the cephalic from the caudal end of blastodisc or blastoderm in 

 99 out of 100 cases. The axis angle however, can only be ap- 

 proximated. If the utmost possible accuracy is desired it is 

 necessary to first measure a series of clutches, approximate the 

 mode, eliminate such birds as show great variability, and use this 

 mean angle. It is not likely to be more than 20 wrong in any 

 given egg. Nevertheless, the possibility of even greater varia- 

 tion must be considered in the interpretation of the results. 



B. Inversions. By inversions I mean those instances in which 

 the head of the embryo is directed toward the observer when the 

 egg is held in the usual manner (Figs. I and 4). Von Baer, (1828, 



