MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 405 
are at once seen to give a markedly skew distribution. Taking 50 paupers as unit of 
variation, we find 
Wy =  6°31889, - By = 3060017, 
fs = 662.465, B,= 173942. 
fog = 122-1815; 
Hence 
38, — 28, + 6 = -401791, 
or the curve is of Type IL. 
The other constants were found to be 
(— 2 owl Oils. 
e = 148°0886, 
m, = 20:169714, Oh, = 24:2203 
i — te III 00) C—O ot 2 
Yo = 99°9065. 
Range = 31°4196. 
Maximum = ‘60434 to left of centroid vertical. 
Skewness = ‘24. 
The equation to the curve is thus 
2 fe v \ 5:9953 / a 20°1697 
y = 99°9065 (1 71993) ( ee ase) 
For the normal curve, 
Standard deviation = 27514, 
Maximum ordinate = 100°301. 
Both skew curve and normal curve are drawn on Plate 14, fig. 13. ‘The former is at 
once seen to be an excellent fit. We might fairly have simplified our work by taking 
zero paupers as the commencement of our range, but preference was given to the more 
general results in order to demonstrate that they give no appreciable amount of 
“negative pauperism.” The range determines a limit of about 15 per cent. as the 
greatest possible amount of pauperism. The normal curve is seen to diverge very 
widely from the statistics besides giving an appreciable amount (3 to 4 unions) with 
“negative pauperism.” The point-binomial for these statistics is also figured on the 
plate. Its constants are p = ‘833, g = ‘167, n = 14°4834, c = 1°70306, the start of 
the binomial being 5°81503 to the left of the centroid-vertical: see § 5. The fit isa 
very close one, the mean error of ordinate = 5°37, and the suggestiveness of such 
results for social problems needs no emphasising. 
The case is of peculiar interest, because the statistics of pauperism are known to 
give a definite trend to the distribution, «.c., if the statistical curve of pauperism for 
1881 be compared with that of 1891, for example, the maximum frequency of the 
