TO THE THEOEY OF EVOLUTION. 
43 
data lor inheritance of stature from father to son would be that the correlation 
= '55 di '015, while the product moment method would tell us more definitely that 
its value was '52 fit ‘015. There is no question that the latter method is the better, 
but this does not hinder the new method from being extremely serviceable; for 
many cases it is the only one available. 
Illustration VI. Effectiveness of Vaccination .—To find the correlation between 
strength to resist smallpox and the degree of effective vaccination. 
We have in the earlier illustrations chosen cases in which in all probability a scale 
of character might possibly, if with difficulty, be determined. In the present case, 
the relationship is a very important one, but a quantitative scale is hardly discover¬ 
able. Nevertheless, it is of great interest to consider what results flow from the 
application of our method. We may consider our two characters as strength to resist 
the ravages of small-pox and as degree of effective vaccination. No quantitative 
scales are here available ; all the statistics provide are the number of recoveries 
and deaths from small-pox, and the absence or presence of a definite vaccination 
cicatrix. Taking the Metropolitan Asylums Board statistics for the epidemic of 1893, 
we have the table given below, where the cases of “ no evidence” have been omitted. 
Proceeding in the usual manner we find 
eq = '86929 cq = '54157 
h= 1-51139 k = '74145 
e = '782454. 
Hence the equation for r is 
'782,454 = r + '560,310r 2 - '096,378r 3 + '081,881r 4 - '000,172r 5 - '040,059?- 6 
whence r = '5954. 
Summing up we have, after calculating the probable errors, 
h = 1-5114 ± '0287, 
k= '7414 ± '0205, 
r = '5954 ± '0272. 
Strength to resist Small-pox when incurred. 
Cicatrix. 
Eecoveries. 
Deaths. 
Total. 
Present 
1562 
42 
1604 
Absent 
383 
94 
477 
Total 
1945 
136 
2081 
o 
O 2 
5 -i 
bfj 
<D Q 
