10 Day, Variation in a Carboniferous Brachiopod. 



the horizontal and vertical lines corresponding to successive 



L L 



equal increases in the values —and — of 'OK. Each 



B D 



square therefore contained a number of points, and the 

 actual number (representing individuals) was ascertained 

 by counting. This graph is reproduced in Fig. 5, where 

 the lower number in each square represents the actual 

 number of individuals falling within its limits. 



On the same figure are shown the actual numbers of 



individuals possessing- particular — and ■— ratios. Hence, 



B D 



if there is absolutely ?io degree of correlation between these 

 ratios, it is possible to predict the chance of any individual 

 falling within a given square of the graph. This chance 

 is clearly the product of its chances of falling within the 

 respective vertical and horizontal columns whose inter- 

 section forms the square. 



For example (in Fig. 5) let us consider the horizontal 

 row of squares B corresponding to the — ratio interval 

 1*2 — 125 ; and the vertical column of squares A corres- 

 ponding to the -~ ratio interval 7 — 75. We have three 

 h 



shells (out of 1000) possessing an — ratio lying between 

 1*2 and 1*25, so that the chances of a shell occurring in the 



horizontal row of squares B are — — . Similarly in the 



1000 



vertical column A we have thirteen shells possessing an 



-pr ratio lying between "j and 75, hence the chances of a 



shell occurring in the vertical column of squares A are 



— — . It follows therefore that the chances of any shell 

 1000 



occurring in the square common to the columns A and B 



-? n 



are measured by the product of X — — or thirty-nine 



J L 1000 1000 



chances in a million ( = -039 per thousand). 



