183 



that we cannot, in general, always take the same proportion of 

 fish from this range in every sample. We assume that the 

 divergence of any one frequency from the mean in our series of 

 samples conforms to the normal law of error (given by the 

 Gaussian curve). We might get 19, 23, 24, 26 or 28 in any one 

 sample, but there would be a tendency for the majority of these 

 frequencies to cluster round the mean (say round 24). 



Next take the series for July, when the frequency for 

 D = 51-25 — 51-50 is 12. If we had had a number of samples 

 instead of the single one we would have found/= 9, 10, 12, 14, 15 

 (or some such numbers) and these latter frequencies would also 

 have tended to cluster round their mean (say round 12). If we 

 reduce the two series of frequencies to percentages of the 

 totals and then replace them by theoretical ones and draw 

 curves we should get some such figure as Fig. a. Here there 



Jove 



Observed- jyeQoe.^cy 

 o/ J) foT- i/ie r^Tjoe 



sizs— s/ so 



Oh scr^ved .. „ 



/r e ^ u t ^ c y o / 2) 

 fo> //i-c ->^0-T,ne S/7T ~ SfSo 



c: 



is very little doubt that the two series represent the same 

 conditions but, again, in such a case as that of the Manx 

 summer herrings of 1914 compared with those of 1920, the 

 superposed curve would be more like Fig. h. Here we have 

 little doubt that the two samples represent different conditions 

 or populations (with regard to the character D). 



