172 'Journal of Comparative Neurology and Psychology. 



When (z) < 1, the limit of z" is zero for n = oc and consequently 



s = i//(z). 



On the other hand, where (z) > 1, z" tends to cc and therefore 

 in this case S = (f) (z). (See Jordan "Conrse d'analyse," Tome I, 

 p. 320.) 



We have shown already that the brain weights in rats in which 

 the body weights are greater than 10 grams, can be calculated by 

 the formula 



y = .569 log (x-8.7) +0.554 (3) 



Later we found that the brain weights in rats in which the body 

 weight lay between 5-10 grams may be calculated l)y a special 

 formula for this portion of the curve, namely: 



y = 1.56log(x)-.87 (7) 



and therefore in the two formulas (3) and (7) y can be considered 

 as the function of log x. 



The values calculated by the latter formula (7) agree perfectly 

 with the ideal line which completes the brain-weight curve between 

 5 and 10 grams of body weight. 



As has been shown already, the formula (6) is perfectly general 

 in its application when two conditions are satisfied; namely, when 

 |z| > 1 in one case and |z| < 1 in the other. 



We also found that not only are the two formulas (3) and (7) 

 functions of log x, but that (1) is applicable to rats in which the 

 body weights are more than 10 grams or | log x | > 1, while formula 

 (7) is applicable to rats in which the body weight is less than 10 

 grams or | log x | < 1. This satisfies all the necessary conditions. 



Thus a combination of the two formulas (3) and (7) will enable 

 us to calculate the brain weight for any given body weight from 

 5 grams to 320 grams. (Extrapolation may be used towards the 

 upper end of the curve). 



The final formula is represented by the following: — 



1.56 .569 



logx (x - 8.7) - 0.316 '^ /, xl-56 



^ o ^ (x-S.7) 



r-^—- ^— 1 '.(8) 



Ll + (logx)" l + Clogx)"-' J 



in which y represents the brain weight and x the body weight. 



