MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION 385 
All three curves are drawn in fig. 4 of Plate 8. It will be seen that they are all 
very close to the observations. So far as skewness is concerned, curves of Types III. and 
IV. give practically the same result (°082 and ‘077) ; in both cases the skewness is 
small, The areal deviations are in the three cases respectively : 4°4 sq. centims., 
59 sq. centims., and 6°7 sq. centims., or we have mean percentage errors in frequency 
of 4-4, 59, and 6°7 nearly ; the percentage error for the closest point binomial is 10°5. 
We thus conclude that even in a case which has been selected as the most typically 
symmetrical series of measurements out of a very considerable set of careful statistics, 
the generalised probability curve is one-third as good again as the normal curve, 
while the special case of that generalised probability curve—which is not the most 
appropriate to our observations—is itself distinctly better than the normal curve. 
This result has been confirmed by a considerable application of these generalised 
curves; in good cases of normal curve fitting, the generalised curves are always 
sensibly better ; in cases where the normal curve is almost useless, as in the case of 
barometric observations, the new curve, 2f of the appropriate type, will represent with 
a 4 to 5 per cent. mean accuracy many observations not yet reduced to statistical 
theory. It is, perhaps, unnecessary to repeat that this mean percentage is much less 
than the average of what has been allowed to pass muster hitherto in both physical 
and biological measurements. Professor EDGEWORTH’S view* thus seems untenable ; a 
curve with a comparatively easy theory of its constants has been found which excels 
the accuracy of the hitherto adopted normal curve. And this for the simple reason 
that it would pass into the normal curve, if that curve were itself the best fit. 
23. Example I[J.—The following statistics of height for 25,878 recruits in the 
United States Army, are given by J. H. Baxter, ‘ Medical Statistics of the 
Provost-Marshal-General’s Bureau,’ vol. 1, Plate 80, 1875. 
78-77 2 64-63 1947 
77-76 6 63-62 1237 
76-75 9 62-61 526 
75-74 A2 61-60 50 
74-73 118 60-59 15 
73-72 343 59-58 10 
72-71 680 58-57 6 
71-70 1485 57-56 d 
70-69 2075 56-55 3 
69-68 3133 55-54 1 
68-67 3631 54-53 2 
67-66 4054 53-52 1 
66-65 3475 52-51 1 
65-64 3019 
* «Phil. Mag.,’ vol. 24, p. 334, 1887. 
MDCCCXCV.—A. 3D 
