PROFESSOR KARL PEARSON AND MR. LESLIE RRAMLEY-MOORE, 
ing the labour of extraction I therefore weighted the different coverings on the 
basis of a small preliminary investigation as follows : 
Case (iv.) Number of coverings, 4 to 5 inclusive, loaded with 2. 
,, 6 to 9 ,, ,, 3. 
,, „ 10 to 15 „ ,, 4. 
,, „ 16 to 18 ,, ,, 2. 
,, ,, 19 to 2G ,, 1. 
The resulting system of frequencies was : 
54, 42-5, 45-5, 47, 45-5, 4G-5, 4G, 45, 45, 4G, 4G-5, 45-5, 47, 45-5, 42 5, 54. 
This system is not so uniform as in Case (ii.). I had hoped that the 744 frequencies 
would have been fairly closely the double system of Case (ii.). The main irregularitv 
occurs at the terminal groups, or those having fecundities nearly zero and nearly 
perfect. These I considered would be relatively infrequent, when we started with as 
many as four coverings, and had an average failure of about 37 in 100. The sequel 
showed that the assumption was legitimate, so far as regards zero fecundity, but that 
perfect fecundity was sufficiently frequent to cause a hump in the frequency curve 
for fecundity, corresponding to the group-element 29/30 to 1. The frequency of 
this group is greater than that of the group 27/30 to 29/30, when we start from at 
least four coverings. This hump entirely disappears, however, if we start with at 
least eight coverings. Thus I take the hump to be purely spurious,” he., a result of 
the arithmetical processes employed, and not an organic character in fecundity. It 
depends upon our definition of fecundity, which is not a truly continuous quantity. 
As the theory of correlation applied is not in any way dependent on the form of 
the correlation surface, beyond the assumption of nearly linear regression, the hump 
cannot, I think, sensibly affect our conclusions. Had I known, however, a priori, 
what the frequency of different coverings and the nature of the fecundity frequency 
curve would be, 1 should have attempted to choose such a group-eiement, that, with 
proper weighting of the coverings, there would have been no arithmetical bias to 
the terminal groups. As it was, it seemed to me that the group-element of 1/15 
gave fairly little arithmetical bias—at any rate where the bulk of the frequency would 
occur—and it was accordingly adopted as a basis for classifying fecundities. 
The dfficulty illustrates tlm point I have referred to, namely, that in statistical 
investigations the best classification can only be found d posteriori, but the classifi¬ 
cation adopted has usually to be selected d priori. 
The 1/15 element being selected, the letters a, h, c, d, e, f, g, h, i,j, k, I, m, n, p), q 
were given to the IG groups of fecundities from 0 to 1, as cited under Case (ii-)-'^ 
* A table was formed of the 368 actually-occurring fecundities, from whicli it was possible to at once 
read olf the group (or it might be two groups, e.g., "5 falls half into h and half into ?.) into which they 
each fell. 
