354 
GENETICS: COLE AND KIRKPATRICK 
Moreover ^/"^ is dominated by - — ^ T". Therefore equations (16) 
have the essential properties assumed to hold for (1), and their solu- 
tion converges for \t\ sufficiently small. 
It is easy to imagine a physical problem which satisfies the conditions 
of this theory. For example, suppose the number of mutually gravi- 
tating bodies in the universe whose masses are bounded from zero is 
infinite. If beyond a finite number of them (which may be arbitrarily 
great) their initial distances from one another increase, as the number 
of bodies increases, with sufficient rapidity, it is easy to show that all the 
hypotheses are satisfied. In this case there is a rigorous, though limited, 
solution of the problem of infinitely many bodies moving subject to 
their mutual attractions. 
SEX RATIO IN PIGEONS. TOGETHER WITH OBSERVATIONS 
ON THE LAYING, INCUBATION AND HATCHING 
OF THE EGGS 
By Leon J. Cole and Wm. F. Kirkpatrick 
COLLEGE OF AGRICULTURE. UNIVERSITY OF WISCONSIN 
Presented to the Academy, April 30, 1915 
The conclusions^ here presented are the results of a study of the records 
which have accumulated from 1907 to 1914 in connection with investi- 
gations of inheritance in pigeons begun at the Rhode Island Agricultural 
Experiment Station and later continued at the Experiment Station at 
Madison, Wisconsin. It is impossible in a brief space to present the 
data upon which the conclusions are based; for these the reader is 
referred to the complete report. Furthermore, although the conclusions 
are here presented somewhat dogmatically and as if of general appli- 
cation, and while we believe that they will probably be found in the 
main to apply generally to domestic pigeons, they are nevertheless 
based almost entirely on the data of the experiments mentioned and 
there is, therefore, no positive assurance that the results would be the 
same with other stock or under different conditions. The number of 
data obtained were, however, very considerable for pigeons, and it is 
felt they accordingly furnish a good foundation for the conclusions drawn. 
It is commonly believed by pigeon breeders and others that from the 
two eggs of a clutch a pair of offspring, that is a male and a female, are 
produced either invariably, or at least in a great majority of instances. 
Furthermore, it is maintained that of this pair the male hatches from the 
egg which is laid first, while the egg laid later produces the female. The 
