Henky H. Donaldson 



weights. To raise these logarithms to the value of the observed weights of the 

 central nervous system they required to be multiplied by a constant factor. It was 

 found that the factor which gave a correct value for the smallest frog was too small 

 for all of the succeeding cases, the resulting numbers falling more and more below the 

 observed numbers as the frog became larger. In order, therefore, to make the curve 

 based on the calculated weights fit with that based on the weights observed, there was 

 needed a second factor, the value of which should steadily increase as the body- 

 weights of the frogs became heavier. Such a factor was found in the length of the 

 frog, which increases rather rapidly at first and more slowly later. The unmodified 

 lengths showed, however, too rapid an increase in the course of the series, but various 

 trials revealed that the fourth root of the lengths gave a set of numbers which could 

 be satisfactorily used. 



It was found, then, that the number obtained by multiplying the logarithm of the 

 body-weight by the fourth root of the length of the body was always a nearly constant 

 fraction of the observed weight of the central nervous system. In the case of the 

 bullfrog the fraction thus obtained was one-thirtieth of the observed weight, while in 

 the case of the leopard frog it was one twenty-eighth. It could, therefore, be made 

 equal to the observed weight by multiplying it by a constant factor having the value 

 of the denominator of the fraction. In this manner a formula was developed as follows : 



C.N.S. = (Log W X i/L) C. 



Here the weight of the central nervous system [C.N.S.), in milligrams, is made 

 equal to the logarithm of W, the body-weight, expressed in grams, multiplied by the 

 fourth root of L, the length of the body, in millimeters, the product of these factors 

 being raised to the value of the observed weight of the central nervous system by 

 multiplying by a constant, C. This constant, in the case of the bullfrog, has the 

 value of 30, and, in the case of the leopard frog, the value of 28. To illustrate the 

 application of this formula, we may take as an example the first record. No. 6, in Table 

 I, p. 7. Here W, the weight of the body, is 5,02 grams, and L, the length of the 

 body, is 93 millimeters. As this is a bullfrog, the value of the constant C is 30. Thus : 



C.N.S. = (Log W X l^Z) 30 

 = (0.7007 X 3.105)30 

 = (2.17) 30 = 65.1 = 65 milligrams. 



The calculated weight of the central nervous system is therefore 65 milligrams. The 

 observed value was 62 milligrams ; thus the calculated exceeded the observed value by 

 4.8 per cent. In like manner the weight of the central nervous system was calculated 

 in each of the cases entered in the table. While the formula applies to all the cases 

 which are presented in the tables given in this paper, it does not apply to all the cases 

 in the original tables (Donaldson, 1898, pp. 328-30; Donaldson and Schoemaker, 

 1900, pp. 120, 121), and its validity can, therefore, be seriously questioned, unless we 

 are able to show that those cases to which it does not apply are capable either of 



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