MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 395 
positive sense of the horizontal scale. If, now, we place this skew curve and the 
compound curve of Plate 1, ‘ Phil. Trans.,’ vol. 185, on top of the observations (see 
Plate 13, fig. 11), we see at once how much better is the fit of the compound curve. 
The skew curve gives a mean percentage error in the ordinates of 10°4, the compound 
curve of only 7°4. The determination of the best skew curve, when the compound 
curve is known, is easy, for all its details are already practically calculated. 
A criterion of whether a compound or skew curve is to be sought for ab iitio, 
would be, however, of great value. 
(29.) Example [X.—A more markedly skew curve than any we have yet dealt 
with is that giving the frequency of divorce with duration of marriage. I take my 
statistics from a paper by Dr. W. F. Wittcox, entitled “The Divorce Problem, 
a Study in Statistics” (‘Studies in History, Economics, and Public Law,’ Columbia 
College, vol. 1, p. 25). They are as follows :— 






| Duration of marriage | Divorces (1882-6). _| Duration of marriage | Divorces (1882-6). 
in years. | in years. | 
i 5314. 12 | 4089 
| 2 7483 13 | 3563 
| 3 9426 14 | 3144, 
a | 9671 15 2931 
5 | 9014 16 2721 
6 | 8274 | 17 2217 
7 7021 18 1877 
§ 6093 | ©) 1577 
9 5305 | 20 1459 
10 | 5002 | 21 and over 9401 
11 | 4384, | 





Total number of divorces granted, 109,966. 
Now these statistics suffer from a defect common to many of the class—the want 
of careful enumeration of the frequencies near the beginning and end of the series. 
It cannot be too often insisted upon that careful details of the frequencies in the 
start and finish of the distribution are requisite if we are to fit skew distributions 
with their appropriate skew curves. How, in this case for example, are we to 
distribute the 9401 divorces which occur after 21 years of married life? How, on 
the other hand, does the curve start? It is impossible to place 5314 divorces at the 
mean—6 months—of the one year duration. It is obvious that the applications for 
divorce will be far more numerous in the last half-year than the first half-year of 
matrimony. The very time required to institute legal proceedings and get a divorce 
granted must ensure this if nothing else did. Yet these two tails of 5314 and 9401, 
of which the accurate distributions are not given, are between + and § of the total 
number of divorces, and until we know how they are exactly distributed, we cannot 
hope for the very exact fitting of a theoretical curve. 
3 E 2 
