394 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
practically insensible before tint 1. Considering the roughness of the experimental 
method, the obtaining an actual range of about 11 instead of 8, and its covering very 
nearly the range of 8 must be held to be fairly encouraging for the method. I shall 
accordingly calculate the constants of the curve on the assumption that the range lies 
between Tints i and 9, using the method of § 15. 
We find 
u, = 2623376, po’, = 9°023803, 
y, = 327922, y= 429971. 
Whence 
Ty = PRP i BIL, 
Uy = 6144435, a, = 1°855565, 
and 
Yy = 59°5996. 
Thus we may take for the curve 
275412 Pe 83172 
PSC 2 acrg a (1 = aes) 
The curve is figured, Plate 11, fig. 10, with the first “smooth” of the observations. 
It will be seen to give the general character of the distribution, but much more elaborate 
experiments would be required before any statement could be made as to whether 
frequency of tint guesses really does follow a curve with limited range of Type I. 
On the same plate the frequency of 128 guesses distributed over 18 tints is given, 
the approximation to a curve of Type I. is fairly close considering the paucity of 
guesses. 
(28.) Example VIII.—The question may be raised, how are we to discriminate be- 
tween a true curve of skew type and a compound curve, supposing we have no reason 
to suspect our statistics d priori of mixture. I have at present been unable to find any 
general condition among the moments, which would be impossible for a skew curve 
and possible for a compound, and so indicate compoundedness. I do not, however, 
despair of one being found, It is a fact, possibly of some significance, that the best 
fitting skew curve to several compound curves that I have tested is a curve of 
Type L, and not that of Type IV. which appears to be the more usual type in 
biological statistics. Taking, as an example, the statistics for the “foreheads” of Naples 
crabs due to Professor WELDON, and resolved into their components in my memoir, 
‘Phil. Trans.’ A, vol. 185, p. 85, et seg., I find for the best fitting skew curve the 
equation 
5m (a a2 \1s77264 ‘ a  \+0469 
ioe 2320 aE ( Se 
where the origin is at 1°4274 horizontal units from the centroid-vertical in the 
