1 70 Jotirnal of Comparative Neurology and Psychology. 

 The formula in each case was as follows: 



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



Spinal cord weight or y = .585 log (x +21 ) -0.795 (4) 



Body length or y = 143 log (x + 15 ) - 134 (5) 



Although the formulas (4) and (5) are entirely free from theo- 

 retical objections within the interval x = (5 grams, 325 grams), 

 the formula (3), however, has two defects when we apply it to 

 the case of x < 8.7. The first defect, which appears when x, the 

 body weight, is less than 8.7 grams, is due to the fact that the 

 resulting value of (x — 8.7) becomes a negative quantity and the 

 logarithm of such a quantity is necessarily imaginary'. The diffi- 

 culty thus presented is, however, merely a theoretical one, since for 

 the purpose of computation the following method may be em- 

 ployed. 



Let us consider the two cases when x is greater than a and when 

 X is less than a then we have 



(A) ^ = ^ when x > a 



dx (x-a) 



(B) ^^ = — ^ when x < a 



dx (a — x) 



Then integration of (A) leads to the foi'mula (3) which we have 

 already obtained, that is 



y=A+Clog (x-B)=.554 + .569 log (x -8.7) 



while the integration of (B) becomes 



(C) y = A - C log (/? - x) = .554 - .569 log (8.7- x) 



The formula (C) thus obtained gives results identical with those 

 obtained when we compute the value of y from the formula 



(D) y = .554 + .569 log (-C) 



In this case, of course, with an understanding that log ( — C) 



should be treated as equivalent to ■ — log C. 



As long as the results obtained by the formula (C) agree with 

 those obtained by the formula (D), the following procedure is 

 justified. 



