396 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
Tn order to make the best of the “ tails” under the circumstances, their moments 
were calculated on two hypotheses, (i.) that they were triangles, (ii.) that they were 
logarithmic curves, and the mean of these extreme results taken. 
t found 
[tg = 60°7376, Ps = 809°15, 
qe IOLA == Boe sIbe 
Distance of centroid from start of curve = 9'1183, 
¥ maximum af es NDB. 
Yo = Maximum frequency = 8882'45. 
Here the curve is assumed, owing to the obviously long tail to the right and the 
abrupt start to the left, to be of Type ILI. Its equation is accordingly 
ie) VEE ‘ 
e~ 150127 5 Skewness = °8547. 
y == 8882-45 (2 + ae, 
The curve is figured, Plate 11, fig. 12, and will be seen to rise abruptly at about °47 
of a year’s duration. It may be doubted whether legal proceedings even in America 
are so rapid that a divorce suit can be complete within six months of marriage. The 
curve gives fairly well the general form of the frequency statistics. Could the 
moments have been determined with greater accuracy, most probably a better fit 
would have resulted. As it is the mean percentage error is above 6. 
(30.) Hxample X.—A still more extreme case may be selected from the field of 
economics. I take the following numbers from the 1887 Presidential Address of 
Mr. GoscHen to the Royal Statistical Society (‘Journal,’ vol. 50, Appendix IL. 
pp. 610-2). I have grouped together both houses and shops, because the details of 
the two are not in Mr, GoscHEN’s returns separated for values under £20. 
VALUATION of House Property, England and Wales, years 1885 to 1886. 







Number of houses. || Number of houses. 
| | 
Under £10 3,174,806 | £80 to £100 47,326 
£10 to £20 | 1,450,781 LOOM te 50een| 58,871 
20 ,, 30 | 441,595 | 150 ,, 300 37,988 
30,, 40 259,756 3004 75000 | 8,781 
40 ,, 50 150,968 500 ,, 1,000 3,002 
50 ,, 60 90,432 1,000 ,, 1,500 1,036 
60 ,, 80 | 104,128 | 
] 


Here clearly the curve starts with the maximum frequency, and further to any 
