MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 4038 
Placing statistics and theory side by side, we have : 
High } 
0 1 2 3 4 5 6 7 8 9 10 
blossoms 
Statistics 325 83 66 ol 36 36 18 7 6 1 1 
Theory 303°22 106°12 69°99 49°27 35°23 24°93 17°07 10°96 6:27 2:79 °52 
The agreement between theory and observation is here all that could be desired, 
except in the case of 0 and 1 high blossoms. Here 22 blossoms have in actual 
counting been transferred from the theoretical group of 1 to the theoretical group of 
zero high blossom. I consider it highly probable that the theory here gives better 
results than the actual statistics ; and this, for the simple reason that it must be 
very difficult to distinguish between any one of the low blossoms and a very slightly 
extended axis bearing only one blossom, that is to say, the extension of the axis 
passes insensibly into one of the low blossoms, or vice ver'sd, and in a certain proportion 
of cases it must be difficult to distinguish between the categories 0 and 1. The com- 
parison between theory and observation is represented by curve and histogram, 
Plate 15, fig. 15. 
Examples X. to XII. will suffice to illustrate the application of our theory to 
extreme cases of skew distribution. 
(33.) Example XIII.—It must not be supposed that in every case of variation by 
units (as in the buttercup and clover examples), the curve will be found to be of 
Types I. or LI. It is impossible to illustrate, in anything short of a treatise 
on statistics, the infinite variety of statistical distributions, but the occurrence of 
Type IV. in zoological, as distinguished from botanical measurements, is so persistent 
that it seems well to illustrate this for the special case of discontinuous variation. 
Professor WELDON has kindly given me the following statistics of dorsal teeth on the 
rostrum of 915 d and ? specimens of Palemonetes varians from Saltram Park, 
Plymouth. 

Teeth. Cases. 

NI Ot CO DOR 
we) 
J 
bo 




The centroid-vertical here lies *313661 of a tooth beyond 4, ze., at 4°313661 teeth. 
The following are the moments about centroid-vertical :— 
3 Ff 2 
