CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
457 
have found by considerable experience that in the case of discrete variables, to treat 
the system as a polygon and correct, as in my memoir on Skew Variation (‘ Phil. 
Trans.,’ A, vol. 186, p. 350), appears to give the best results when the areas are 
compared with the discrete groups. The point wants further investigation ; when 
we have a large number of groups it is of little importance, but it makes a consider¬ 
able difference in these excessively skew distributions of discrete variables v4ien the 
number of groups are small. 
Above all, the diagram (fig. ii.) shows how all important it is to compare areas and 
not merely the ordinates of the frequency curve with the Ijlocks representing the 
discrete frequencies in such a case as this. Tlie wide-spread custom among foreign 
investigators of comparing merely the ordinates of the theoretical frequency curve 
with the observed frequencies leads in such cases to most fallacious results. 
(8.) (C.) On the Distribution of Incidence of Scarlet Fever Cases ivith Aye. 
It seems desiraljle to give an illustration of the method of dealing with a distri¬ 
bution which falls under the class dealt with in Section (5) of this paper. Di'. 
Macdoxell, in dealing with the intensity of incidence of different diseases at various 
ages, has come across in scarlet fever a good illustration of curves of the tyjDes now 
under consideration. The whole of the arithmetical work on the present example is 
due to him, and I have to thank him very heartily for allowing me to use it here. 
Tlie statistics are taken from the ‘Report of the Metropolitan Asylums Board’ 
(Statistical Part, 1899). They involve 39,253 male cases, distributed as follows :— 
Year of life. 
Frequency. 
Year of life. 
Frequency. 
Under 1 
443 
20-25 
926 
1-2 
1456 
25-30 
420 
2-3 
2631 
30-35 
215 
3-4 
3599 
35-40 
91 
4-5 
3862 
40-45 
45 
5-10 
15791 
45-50 
26 
10-15 
7359 
50-55 
17 
15-20 
2366 
55-60 
5 
60-65 
1 
The data 1)eing grouped })artly in one and partly in five-year periods the moments 
had to l)e calculated with caution, separating tlie material into two pieces. Taking 
five vears as the unit, Dr. Macdonell found for the uncorrected moments : 
* E.g., petals of buttercups, teeth on the carapace of pravns, lips of meflusa-, as compared with veins on 
chestnut leaves, florets on ox-eyed daisy, I'cc. 
3 X 
VOL. CXCVII.—A. 
