SEA-FISHERIES LABORATORY. 87 



January, k attains its maximum value later in the year. 

 These remarks apply to immature fish and males. In 

 the case of mature females the development of the ovary 

 and the subsequent spawning produce variations which 

 have nothing to do with the question of the seasonal 

 changes of " condition." 



This coefficient k is the only convenient index of 

 condition. It is true that the average weight would be 

 just as useful, but we should then have to compare fish 

 of the same lengths. The coefficient can, however, be 

 found for an entire catch of fish, so that samples which 

 differ with respect to their range of lengths can easily be 

 contrasted. 



r 



To find k we use the formula g = k^r~~ , putting it 

 in the form 



100 g 



k = 



2 (/') 



g being the weight of all the fish in the catch, I the mean 

 length of each centimetre group, and / the frequency 

 at each mean length. The arithmetic involved is 

 laborious Avhen, as is generally necessary, the fish are 

 arranged in centimetre groups; for the cube of each 

 mean length has to be found* and multiplied by the 

 number of specimens in the group, and the values found 

 have then to be summed. 



But in the investigation of a catch of plaice, average 

 weights for each group are usually calculated in any 

 case. In the International Fishery Investigations the 

 lengths recorded are always means, thus all fish 

 between, say, n and n + 1 cms. are recorded as 

 n'b cms. The graph of average weights is therefore a 

 " liistograph " — a series of columns of base 1 cm. in 

 length, and the numbers arc areas— the sum of the 



