Correlation and Variatio)i in the Toad 605 



ical or dimensional relations. This is indicated by the fact that 

 the ratios between the average values of external characters are 

 the same among individuals of various sizes. Table III showed 

 the exact correspondance between these ratios in the male and 

 female toad, and Donaldson ('98) has thoroughly demonstrated 

 the same fact in a series of bullfrogs of various sizes. In frogs of 

 all sizes and both sexes the sum of the leg bones is a nearly con- 

 stant fraction of the length of the entire frog, and the proportional 

 lengths of the several bones are also nearly constant. So it is for 

 most external characters. 



But with internal characters there is good reason for questioning 

 the exactness of this relation between size and efficiency. As a 

 matter of fact there are almost no data bearing upon the subject 

 from which to form an opinion. It is generally believed from 

 the evidence so far produced that there is no exact relation 

 between size of brain and intellectual ability. There is a fairly 

 close correlation between size of head and size of brain but 

 Pearson (02a) was unable to find any appreciable correlation 

 between size of head and intellectual ability. The only data 

 which I have been able to find comparing the value of a 

 function with physical measurement of the organ functioning 

 is in the case of muscle. Weber's law that the absolute power 

 of a muscle is proportional to its cross-sectional area (/. e., 

 to the number of fibers) is true only in the most general way. 

 Weber found the absolute power of the human gastrocnemius 

 and soleus to be about i kg. per sq. cm., while others have 

 found values of 6.25 and 8.0 kg. in other human muscles. In the 

 frog's muscle Weber gives 0.6 kg. per sq. cm. as the absolute power 

 while Rosenthal ('67) gives 2.8 to 3.0 kg. for frog's semimembran- 

 osus and adductor magnus and i .0 to i .2 kg. for the gastrocnemius. 

 Howell ('05) summarizes the matter by stating that "the absolute 

 power of a frog's muscle of i sq. cm. cross-area is estimated at 

 from 0.7 to 3.0 kgs." — rather wide limits. Indeed when we con- 

 sider the number and complexity of both external and internal 

 factors affecting such a comparatively simple process as muscular 

 contraction it seems useless to attempt at present any exact com- 

 parison between size and efficiency. Many of the phenomena of 



