102 Vniversity of California Publications in Zoology [Vol. 11 



VARIATION AND CORRELATION IN PROPORTIONAL 



MEASUREMENTS 



As the size of an organism at any particular developmental 

 stage is merely the summation of the extents to which each region 

 of its body has grown, it follows that the dimensions of any 

 region are functions of the size attained by the organism. For 

 this reason proportional instead of direct measurements are com- 

 monly used in taxonomy as of greater specific constancy. Still 

 the reliability of such proportions depends upon whether the 

 particular region measured grows at approximately the same 

 rate as that of the entire animal or at a very different rate. 

 Should the rates differ then the proportion would vary as the 

 animal grows larger, and if the variation be considerable it 

 might cause much confusion in identification and synonymy 

 unless the direction and extent of such variation were known. 



For instance, the tail in *?. californica is defined as varying 

 in length between 2-1 and 31 per cent of the length of animal. 

 Suppose another similar species be discovered and defined as 

 having a tail varying from 34 to 37 per cent in length, and as 

 being smaller in size. The new species would be valid if the tail 

 of its individuals were know-n to increase in length at approxi- 

 mately the same rate as the body, for the proportion (34 to 37) 

 would then be constant, whatever the length of the animal. But, 

 if the rate of increase in length of tail were less than the rate of 



.,,,„,,,.,, ,. length of tail 



increase m length ot bodv, then the proportion — -. ? — ;; -. , 



length ot animal 



— would be less in the larger animals and consequently the new 

 species might be synonymous with S. californica. Accordingly 

 if, to the definition of <S'. californica, we add that the variation 

 of the length of tail between 24 and 31 per cent is constant 

 irrespective of the length of animal or that it varies directly or 

 inversely as the animal grows larger, such confusion could not 

 arise. 



Some space is therefore devoted to determining to what extent 

 each of the proportional measurements given in table 1 is inde- 

 pendent of, or dependent on, the length of animal. 



