98 THE RATE OF GROWTH [ch. 



For instance, in any ordinary fish, such as a plaice or a haddock, 

 the length is not difficult to measure, but measurements of 

 breadth or depth are very much more uncertain. In cases such 

 as these, while it remains difficult to define the precise nature of 

 the change of form, it is easy to shew that such a change is 

 taking place if we make use of that ratio of length to weight 

 which we have spoken of in the preceding chapter. Assuming, as 

 we may fairly do, that weight is directly proportional to bulk or 

 volume, we may express this relation in the form WJL^ = k, where 

 k is a constant, to be determined for each particular case. {W 

 and L are expressed in grammes and centimetres, and it is usual 

 to multiply the result by some figure, such as 1000, so as to give 

 the constant k a value near to unity.) 



Plaice caught in a certain area, March, 1907. Variation of k (the 

 weight-length coefficient) with size. {Data taken from the 

 Department of Agriculture and Fislieries' Plaice- Report, 

 vol. I, f. 107, 1908.) 



Size in cm. Weight in gm. WjL^ x 10,000 WjL^ (smoothed) 



23 113 92-8 — 



24 128 92-6 94-3 



25 152 97-3 96-1 



26 173 98-4 97-9 



27 193 98-1 990 



28 221 100-6 100-4 



29 250 102-5 101-2 



30 271 100-4 101-2 



31 300 100-7 100-4 



32 328 100-1 99-8 



33 354 98-5 98-8 



34 384 97-7 98-0 



35 419 97-7 97-6 



36 454 97-3 96-7 



37 492 95-2 96-3 



38 529 96-4 95-6 



39 564 95-1 95-0 



40 614 95-9 95-0 



41 647 93-9 93-8 



42 679 91-6 92-5 



43 732 92-1 92-5 



44 800 93-9 94-0 



45 875 96-0 — 



