286 A. FRANKLIN SHULL 
Since my incidental observations had been made on lines produc- 
ing large families, it seemed more conservative to adopt the latter 
method, of computing the percentages in each line separately, 
and taking the mean of the eight percentages. This method has 
the further advantage, as we shall see later, of enabling us to 
analyze the result. 
Most of the lines in table 1 included more than 46 generations. 
In such eases, the first 46 generations are given. In two cases 
the lines included 92 or more generations; these were divided into 
two parts, the first to the 46th generation constituting one line 
as given in table 1, the 47th to the 92d another line, while the 
remainder were omitted. Thus, lines 1 and 2 are parts of the 
same line, as are also lines 6 and 7. Generations not fully re- 
corded have been omitted, except where they were necessary (as 
they were in one case) to complete the 46 generations. The one 
case of incomplete records can hardly invalidate the results. 
These lines have been, for the most part, recorded in detail in 
my former papers (Shull, ’10, ’11 a), or are given in the following 
pages. Lines 1 and 2 are found almost complete in table 1 of those 
papers, line 3 in table 3 (right column), line 4 in table 34 (right 
column), line 5 in part in table 37 (middle column), lines 6 and 
7 almost complete in tables 20 and 34 (left column in both), 
and line 8 in part in tables 2 and 6 of this paper. As the details 
of the families may be had in the places cited, they are not 
repeated here. 
The mean percentages of male-producers in the various pairs of 
generations, given at the bottom of table 1, show great fluctua- 
tions; but the earlier generations have plainly more male-produc- 
ers than the later generations. When they are represented by a 
curve, as in fig. 1, it is obvious at a glance, notwithstanding the 
fluctuations, that there is a progressive decrease in the proportion 
of male-producers from the first generation to the last. 
If the eight lines be examined separately, it is seen that most 
of this decrease in the proportion of male-producers is due to 
three lines (1, 2, and 5), and perhaps a fourth (line 8). Lines 1 
and 2, which are two parts of the same line, are plotted in fig. 2. 
Because we have here only a single line, the fluctuations are so 
