390 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
his plotting of RANKr’s observations agree with mine. He has added together under 
83, for example, all indices from 83 to 83°9. Thus, for the indices 81, 82, 83, 84 he 
gives the frequencies 106, 92, 111, 99, while I find 82, 116, 98, 107, a very sensible 
difference.* Stiepa’s method can introduce very sensible errors. In this particular 
case it transfers the maximum frequency of observation from 82 to 84. 
The last four examples have dealt with cases where the statistician has hitherto 
been content to assume symmetry. They have been given to indicate (i.) an 
apparently uniform trend in biological statistics of variation, and (ii.) the improved 
fitting of theory to practice which arises from using the generalised curve. I now 
pass to cases of obvious skewness, where the statistician has hitherto had no satis- 
factory theory. 
(26.) Example VI. Distribution of 8689 Cases of Enteric Fever Received into the 
Metropolitan Asylums Board Fever Hospitals, 1871-93. 



Age. Number of cases. Age. Number of cases. 
Under 5 266 35-40 299 
5-10 | 1143 40-45 163 
10-15 | 2019 45-50 98 
15-20 | 1955 50-55 40 
20-25 1319 55-60 14 
25-30 857 Above 60 13 
30-35 503 






I considered that the 13 cases “ above 60” 
8; 65-70, 4; 70-75, 1. 
Taking five years as the unit I found 
might be distributed as follows: 60-65, 
fy = 4070554, ag = 77598196, — pr, = 69°379605. 
The centroid-vertical is at 18°9691 years, z.e., 29382 unit from 15-20. 
Thus 25 (8.” — py) + 3p;”= 18°05102, or the curve is of Type I. Since, however, 
38, — 2B, + 6 = 1935 is small, a curve of Type III. will also be a good fit. 
We have for the other constants 
yr = 72:28642, d= | °98643, 
Con OF 7 Bole: Skewness = °488922, 
DS KPBS, 
my = 2° 79291, My = 67°49351, 
ar — 307801, dy = 7420511, 
Yo = 1890°83. 
* T class as 83 all from 82°6 to 83:4, dividing 82°5 between 82 and 83 evenly, and 83'5 between 83 
and 84 evenly. Thus in the Table above certain frequencies will be found with such values as 12°5 or 
71°5 skulls. 
