58 
GENETICS: PEARL AND PATTERSON 
F F M M = cf does not mendelize but is inherited plasmatically. This part 
too shows different potencies and the final result is the combined effect of both 
groups. However, it seems undesirable to insist on this point, as the decisive 
experiments, which may bring the complete solution, have not yet been 
accomplished. 
1 Goldschmidt, R., Erblichkeitsstudien an Schmetterlingen. I,, Zs. induct. Ahstammungs- 
lehre., 7, (1912); and Goldschmidt, R., und Poppelbaum, H., idem. II. Ibid., 11 (1914) 
2 The existence of such local forms could be shown by breeding experiments. The prob- 
lem of the geographical races of this moth has been for many years the object of my principal 
studies. However, the results are not yet ripe for publication. 
3 Boveri, Th., Ueber die Entstehung der Eugsterschen Zwitterbienen., Arch.Entw-Meck., 
Leipzig, 41 (1915). 
* The fact that male and female intersexes are different calls certainly for an explanation, 
but will not be discussed here. It may only be said that it is a question of the physiology 
of development. 
5 1 wish to express my sincerest thanks to Professor Wheeler and all the members of the 
staff of the Bussey Institution, Harvard University, for their kindness in granting me the 
facilities for prosecuting my work. 
^ A similar cross with the same race H but another mother has been carried out already 
with the same result by Toyama's assistant, Dr. Machida, to whom therefore belongs the 
priority of this discovery. I am indebted to him, too, for the material of the race H. I do 
not know whether he has meanwhile published this result. 
ON THE DEGREE OF INBREEDING WHICH EXISTS IN 
AMERICAN JERSEY CATTLE 
By Raymond Pearl and S. W. Patterson 
BIOLOGICAL LABORATORY. MAINE AGRICULTURAL EXPERIMENT STATION 
Received by the Academy, December 17, 1915 
In a series of 'Studies on Inbreeding' published during the past 
few years Pearl^ has described in detail a method whereby it is possible 
to measure exactly the degree of inbreeding which exists in the pedigree 
of any particular individual animal. This is done by means of coeffi- 
cients of inbreeding. These quantities may be defined as follows: 
In the genetic passage from the n + I'th ancestral generation to the 
n^th, or in other words the contribution of the matings of the n + Vth 
generation to the total amount of inbreeding involved in the production 
of an individual, the degree of inbreeding involved will be measured by 
the expression 
where pn+i denotes the maximum possible number of different individuals 
involved in the matings of the n + 1 generation, and qn+i the actual num- 
ber of different individuals involved in these matings. Zn may be called 
a coefficient of inbreeding. If the value of Z for successive generations 
