Relation of Lifespan to Brain and Body Weight 123 



subdivisions of mammals, will further increase the goodness 

 of prediction, since Figs. 2, 3 and 4 give evidence that the 

 relation of brain weight to body weight for the different groups 

 cannot be described by a single allometric relation. Count 

 (1947) is only the last of a number of authors to point this out. 

 Discussion of the independent roles of brain and body 

 weights will be facilitated by the use of a transformed variable. 

 Brain weight and body weight are closely related variables, for 

 the regression of brain weight on body weight (Appendix le) 



z= 0-666?/ - 0-888 (5) 



accounts for 91 • 7 per cent of the brain weight variance. The 

 deviation of an individual brain weight value from the regres- 

 sion line is the logarithm of that fraction of the brain weight 

 of the species that is independent of the overall regression 

 of brain weight on body weight. This deviation is defined 

 to be a new variable, w, which is given by the equation 



w = z - 0-6662/ + 0-888 (6) 



This quantity is called the index of cephalization. It should be 

 understood that this is by definition a measure of brain de- 

 velopment that is orthogonal to body weight. The definition 

 contains none of the a priori considerations that have fre- 

 quently entered into the definition of this quantity since the 

 time of Dubois (1924). Von Bonin (1937) has urged that the 

 index of cephalization be defined in this objective fashion. 



The regression of lifespan on index of cephalization (w) is 

 found to be (Appendix If) 



X = 0-636r£; -i- 1-283 (7) 



By the definition of w, the regression coefficient for x on w is 

 numerically equal to the partial regression oi x on z in Equa- 

 tion (3). However, the variance of w is but 8 - 3 per cent of the 

 variance of z. In consequence the sampling error of ft^.^ is 

 larger than that for b^^y (Appendix If), and the variance 

 removed by the regression of a; on w is 23 per cent rather than 



