SEA-FISHERIES LABORATORY. 89 



It is not laborious. It is true that the curve so 

 calculated may not differ greatly from that obtained by 

 the Meek-D'Arcy Thompson formula, but in some cases 

 it does differ sufficiently to render the latter formula 

 unsuitable for exact calculations. If, for instance, we 

 attempted to calculate the numbers of plaice above and 

 below a certain length (say the mean length at sexual 

 maturity) contained in a series of catches from a specified 

 fishing ground and season, from the commercial 

 statistics, we should have to find the length-frequency 

 equation, and the length-weight equation. I don't think 

 there is any other way in which this could be done. 

 The " k formula " would in this case be unsatisfactory. 



Generally speaking, I have found that a series of 

 average weights of plaice, from a definite ground and 

 season, can be represented by the equation 



g — a + hi + cl 2 

 if the series is a small one, i.e., the range of sizes 

 varying, for instance, from 14 cms. to 24 cms. With a 

 greater range another term may be necessary. But the 

 coefficiency of Z 3 is always small and tends to vanish. It 

 may be negative, and in such a case extrapolation from 

 the curve is obviously unsafe. 



But such an equation as is thus obtained would not 



be nearly so useful as a means of comparison of the 



condition of the fish, for all the coefficients would have 



to be considered. Obviously the simpler formula is to 



be preferred for such a purpose. 



g = 83-21 + 12-20 I + 0-636 I* ; or g = 0-97 f' 



100 



g = 74-32 + 10-37 I -}■ 0-109 Z 2 ; or g = 0-96 --—- 



g = 90-77 + 14-20 I + 0-696 I* ; or g = 1-22 -?- 



g = 94-33 + 13-81 I + 0-697 I 



g = 139-15 + 17-70 I + 0-649 I* - 00015 fr 



g = 147-13 + 19-20 / + 0-934 P+ 0*0146 /' 



The fir>t term is, in all cases, the average weighl 



of the median group. 



