384 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
Example II. Professor Wripon’s Crab Measurements No. 4. The details of 
these are given in ‘ Phil. Trans.,’ vol. 185, p. 96. 
We have 
Cr—29 995 fini /aONOOs pg = 3°4751, 
jy = 1843039,  B, = 0267022, B, = 312807. 
In this case 
2 pla (Bog? — fy) + Bpg” = po? (6 + 38, — 2B,) = — py® X “1760334, 
and is accordingly negative. In Example J. of the barometric heights we had 
2 pty (Bptg” — My) + Byes” = fy’ X 98421. 
Since, in the latter case, this value was sufficiently small to give a good curve of 
Type III., we may expect the like result in this case. There is, indeed, a slight but 
sensible skewness even in this the most symmetrical of all Professor Wrxpon’s crab 
measurements, and the skew curve of Type III. is really a better fit than the 
normal curve. But clearly since the critical function is negative, we are dealing 
properly with a case of a curve of Type IV. The ratio of the organs dealt with in 
No. 4 series of measurements does not give a “limited range” of variation. Pro- 
ceeding by the method indicated in § 19, we find for the constants 
Tile Zas Tis Ono p= 25°7616, 
=) 212909, Hi =— 7°8802, 
G—- 321407; Skewness = 077267, Yo — aioe 
Thus the equation to the curve is : 
en 25°7616 tan-! (a/21°909) 
[1 + 2?/(21-909)?}36-812 

y = 1°75509 
To trace the curve, take : 
x = 21°909 tan 8, 
y — il "75509 cog!?64 6 @7 2°76160 
If we take a skew curve of Type III., we find for its equation : 
y = 14422 (1 + 2/33°683) "8 eH, 
where, for the centroid 
d = °226364, 
and the skewness 
= °081704. 
For the normal curve we have: 
y = 148°85 e~ Ae TOs, 
* y. was calculated by aid of the approximate formula on p. 380. 
