124 George A. Sacher 



84 per cent (Appendix 1). However, the coefficient of regres- 

 sion of X on w is more than four times larger than its standard 

 error, so the regression is highly significant. 



The multiple regression of lifespan on body weight and index 

 of cephalization is found to be (Appendix Ig) 



X = O'QSQw + 0-198Z/ + 0-471 (8) 



It will be noted that the partial regression ofxony in Equation 

 (8) is numerically equal to the coefficient of total regression of 

 cconyin Equation (2). This follows from the fact that y and w 

 are orthogonal variables, so that the regression of cC on i/ is 

 completely independent of, and unaffected by, the regression 

 of X on w. 



One further dimension of mammalian constitution that has 

 been measured for a large number of species is that of meta- 

 bolic rate. The great amoimt of data accumulated by many 

 investigators, and especially by Rubner, Benedict and Brody, 

 has been masterfully organized in Brody's treatise on Bio- 

 energetics and Growth (1945). Brody has shown that the 

 relation between basal or resting metabolic rate and body 

 weight for warm-blooded vertebrates (including birds) follows 

 a power law relation with great precision. The regression of 

 logarithm of specific metabolic rate, m (in calories per gram 

 per day), on log body weight is (Appendix Ih) 



m= - 0'2Q6y + 1-047 (9) 



The correlation coefficient is over 0-99 (Brody, 1945). In 

 view of this high correlation, the partial regression of specific 

 metabolic rate on index of cephalization must necessarily be 

 small. We can therefore assume tentatively that this cor- 

 relation is zero and substitute m (given by Equation (9) ) for ?/ 

 in Equation (8). The resulting equation for the regression of 

 lifespan on metabolic rate and index of cephalization is 



X = 0-636i£; - 0-744m + 1-252 (10) 



Sampling errors and residual variance for this relation cannot 

 be given. 



