FORM AND GROWTH IN FISHES 



395 



Donaldson ('98) and Donaldson and Schoemaker ('00), work- 

 ing with frogs, measured the lengths of the tibia, femur, and 

 foot, and compared them with the total length of the leg-bones, 

 and with the length of the frog. The results bear out the con- 

 clusion that the ratios of the lengths of the different bones to the 

 total bone length, as well as to the total length of the frog, are 

 constant for each bone, for all sizes of frog. These results are 

 strictly in accordance with those given in the present paper. 



Figure 11 



For the frog, then, the various leg bones, the total length of the 

 bones, and the total length of the individual all have the same 

 rate of growth. The curves given by Crozier ('14) for the inter- 

 relation of various parts of the shell of Dosinia are open to a 

 similar interpretation, namely, that the rates of growth of the 

 different parts of the shell are identical. 



This conclusion is all the more interesting because it does not 

 apply to the growth of higher vertebrates. The literature on 

 the measurement of the growth of the surface parts of higher 



