404 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
po = 910906 | 
#3 = ‘233908 Swhere the unit = 1 tooth. 
ju, = 2°625896 
For the normal curve these give 
Standard deviation = "9544, 
Maximum ordinate = 382°5. 
For the skew curve we have 
B, = 072222, By = 3164684. 
Hence 
26, — 38, — 6= 122702, 
or, we have a curve of Type IV. The values of 8, and f,, however, show that it will 
not differ very widely from the normal type. 
Proceeding to determine the other constants we find 
— 111°398, 
v = — 109047 (v is negative since ps, is positive), 
— 716613, m = 56°699, 
Distance of origin from centroid-vertical = 7°0149, 
log yy = 18°4431056. 
Thus 
Yy — Yo cost#389 EeaionTe: 
t= (166138 tan 
give the form of the curve. This curve, the normal curve, and the observations are 
drawn, Plate 13, fig. 16. A comparison of the observations and the normal curve shows 
an amount of skewness in the tails of the former, which would be very improbable if 
the normal curve really expresses the distribution. The skew curve really accounts 
for this divergence and is a sensibly better fit. The mean percentage errors in the 
ordinates are for the two cases 8°67 and 3°88. The skew curve is thus an excellent fit. 
The discontinuity in these teeth probably corresponds to a hypergeometrical polygon, 
of which the skew curve is a limiting form. 
(84.) Hxample XIV.—Another extremely interesting illustration of skew varia- 
tion will be found in the statistics of pauperism for England and Wales, to which my 
attention was drawn by Mr. G. U. Yuus, who had plotted the statistics from the raw 
material provided in Appendix I. of Mr, Cuartes Booru’s ‘ Aged Poor; Condition’ 
In Plate 14, fig. 17, we have 632 unions distributed over a range of pauperism varying 
from 100 to 850 per 10,000 of the population for the year 1891. The observations 
