RELATIVE GROWTH 



225 



relation of Qq (oxygen consumption/mg dry weight) to body weight (Fig. 7, 

 p. 186). 



Statistical calculation of the constants a, b, the standard deviation S\og >■ . log xi and the 

 correlation coefficient (p) can be made by application of least-square methods. There are 

 certain mathematical difficulties (Sholl, 1948) inasmuch as application of the least-square 

 method to v = bx^ or to logjv = log b + 01. log .v, i.e. supposition of a normal distribution 

 either of the numeri or the logarithms, yields different values for a and b. This discrepancy 

 appears to arise when the values for y are widely scattered on a short interval of x ; in 

 general, the error committed by application of the least-square method to the logarithms 

 is insignificant (Brody, 1945). 



The meaning of the allometric equation is that the specific growth rate of a 

 component or process, y, stands in a constant ratio to the specific growth rate of 

 another component or the total organism, x: 



dj 1 dx I 

 . : . _ = a 



dt j> dt X 



integrals of this equation being (7.1). 



In view of criticisms of the principle of allometry (Sholl, 1954) it should be 

 mentioned that the allometric relation is not trivial. That the specific growth rate 



(7-3) 



1000 



100 



PIG 



Length 200 mm 



10 



100 



1000 

 mm 



Length of body 



Fig. 29. Relative growth of rostrum in the spoonbill cat, Polyodon, as an example where 

 the allometric equation does not apply. After Thompson from Hersh, 1941. 



Lileralure p. 253 



