48 
GENETICS: H. S. JENNINGS 
The table gives in the first column a letter by which the series will be 
designated (as n, B, C, J, etc). In the next column is given the method 
by which any given term of the series is formed from the preceding term, 
this preceding term being designated x. Thus, under C, the expression, 
2x+l means that to obtain any term of the series, we double the pre- 
ceding term and add 1. In some of the later series the derivation here 
given shows that the given series is formed by some combination of two 
previous series. Thus, series H is formed by substracting from any 
term of G the corresponding term of F. Any given term of a series is 
designated by a subscript representing the corresponding term of the 
series n: thus, F4 means the fourth term of the series F (it is therefore 
3) ; Jn means the ;^th term of the series J; Dn+i means the (#+l)th term 
of D; etc. At the end of each series is given certain other information; 
showing as a rule how any term of the series may be otherwise designated; 
or another method of derivation. 
The results of any system of breeding that falls in the present group 
may be given by specifying which series of the table it gives and what 
terms of the series correspond to a given generation. Examples will 
make this clear: 
(17) Self-fertilization, beginning with a cross between AA and Aa. 
After n self-fertilizations the proportions of the resulting population 
are given by the following: 
AA = Aa = aa = 
Bn + 2 + 1 Bn-l-2 
This signifies that for any generation n, the proportion of AA will be 
found by dividing the term {n+2) of the series E by the term (w+2) 
of the series B. So, after one self-fertilization the proportion that are 
AA will be 5/8; after two, 11/16; after eight, 767/1024. After five gen- 
erations the proportion that are Aa will be 1/64; of aa, 31/128; and so on. 
(18) Self-fertilization in a typical Mendehan population composed 
of AA + 2Aa+aa. After n generations: 
AA = Aa = -i-. aa = 
(19) Inbreeding, brother by sister, in the progeny derived from a 
cross of AA by aa. After n generations: 
