SEA-FISHERIES LABORATORY. 109 



It is quite evident from inspection of the series of 

 length-frequencies that no generalised frequency-curve 

 can be found which would express the theoretical distri- 

 bution. I have no doubt that investigation would show 

 that some of the series might be represented by a curve 

 belonging to one of Pearson's types of the generalised 

 probability curve, and that by an appropriate manipula- 

 tion of the constants many might be fitted. But the fit 

 would probably be fictitious, as none of these series deals 

 with a homogeneous group of plaice. Obviously each 

 contains fish of Age-Groups I and II, and some include 

 higher age-groups also. This is the case even when the 

 frequency-curve is apparently unimodal, and in many 

 series the curve is obviously multimodal. If a frequency- 

 curve could be found, which could be represented by an 

 equation — as in the case of most biometric series — the 

 study of fish migrations would gain immensely in exacti- 

 tude, for one could replace the observed distribution of 

 length by the theoretical distribution, and then modes 

 and other frequency-points on the curve would represent 

 the actual distribution with less improbability than the 

 actually observed values.. But this is, apparently, not 

 the case. 



The formula suggested by Edser* helps us in some 



respects. It is shown by this writer that, within certain 



limits, the distribution of lengths in a catch of plaice can 



be represented by an equation of the type log y = K + bx, 



where y is the frequency, x the length, A a constant, and 



b the tangent of the angle which the curve makes with 



the axis of x. The equation is, of course, that of a 



straight line. The whole catch of fish is represented by 



two straight lines, except near the mode. One line repre- 



* "Note on the Number of Plaice at each Length, in certain 

 samples from the Southern Part of the North Sea." Journal 

 Statistical Society, Vol. LXXI, Part IV, December, 1908, p. 4. 



