dé 
354 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
for the data given for Professor WELpDon’s Crab Measurements, No. 4, ‘ Phil. Trans.,’ 
A, vol. 185, p. 96. : 
up = 76759, pig = 3°4751, pr, = 184°3039. 
Hence, 
By = p3"/by? = 0267022, 
8, =" fal po — ol 2807. 
Thus 6 + 38, — 28, is positive, and accordingly no rational point-binomial is likely 
to fit as well as the normal curve. Asa matter of fact the fundamental cubic is now 
176032? + 1:0453272? + 0337732 — 0003709 = 0. 
The two negative roots of this equation give imaginary value for p and g. The 
small positive root gives p greater than unity and q uegative, n is also negative. 
Although I can give no interpretation to these results, it seemed well to complete in 
the latter case the solution and test how near the resulting point-binomial fitted the 
curves. I found 
2— (00866, p= 119268) .¢,=— 19268) 
n= — ‘087685, c= 661662, d= 6'6645. 
These give for the binomial 
150°0983 (1°19268 _— PIS ARiS)) 
151°89.(1 — *161552)— 087685, 
or, 
151-89 + °92532 + ‘07756 + &c. 
Thus the sensible part of the binomial to the scale of our figure is a triangle. I 
have drawn this binomial, see Plate 8, fig. 4. The reader will mark a fit very close 
on the whole to the observations. We have the following percentage mean errors of 
the ordinates :— 
INormalvcurve™. =o ee Sue enone 
Skew probability curve. . . . . 4°4, 
Bimomnvayl 2%) 1 ae ae hee ete rer aseenl toe 
We may conclude, therefore, that even if our binomial constants-have unintelligible 
values, yet our method will give, in many cases, a closely-fitting polygonal figure. 
This remark should be read in connection with Professor EpGEWoRTH’s somewhat 
divergent views* on fitting chance distributions with curves other than the normal 
error curve. It is possible in almost every case to find simple combinations of lines, 
* See ‘ Phil. Mag.,’ vol. 334, p. 24, et seq., 1887. 
