14 Day, Variation in a Carboniferous Brachiopod. 



Now we have already seen that some correlation 



must exist, since the two ratios, , and -^, both decrease 



as the shell grows in size. This change may be shown to 

 be an inevitable result of the form of curvature of the 

 valves — a form common to nearly all bivalve shells. 

 Referring back to the curves in Fig. 4, we see that the 



mean value of the -jz ratio diminishes from IS 75 in the 



1) 



smallest shells to 1425 in the largest, while the total 

 range of variation is from 1*175 to r 9 2 5- That is, out of 

 a total range of 75, exactly one-fifth ("15) is due to 

 change of form during growth. Similarly reference to 



Fig. \ shows that the mean value of the ratio ~ diminishes 



* B 



from '925 to '825, representing a change of 1 out of a 

 total variation from 675 to 1*225. Again, the variation 

 due to growth change is very nearly one-fifth of the total. 



It is obvious that these changes in the ~ and -,-, ratios 



which occur during growth must be perfectly correlated. 



But we have seen that the extent of the correlation 

 of these ratios is one-fifth of their whole amount. Thus 

 we find that the existing correlation is just such as would 

 be anticipated from the growth changes, and we may 

 therefore confidently assume that, apart from this, the 

 variations in breadth and deptJi occur quite independently 

 of one another. 



Other Variable Characters in the Shells. 



1. Variation in sice of the Beak of Ventral Valve, 



There is a striking variation to be observed in the 

 size of the beak of the ventral, valve relative to that of the 

 dorsal valve. Some shells exhibit an umbonal region in 

 which the two beaks are practically equal in size, and 

 from these at the one extreme there is every gradation 



