Ill] OF THE SIZE AND AGE OF HERRING 181 



In the following table, we see (a) the sizes, and (6) the number 



of scale-rings, in a sample of some 550 herring from the autumn 

 fishery off the east of Scotland. 



Rings 3 4 5 6 7 8 9 10 11 12 Total Mean 



cm. rings 



31 — — — 1 1 _ 1 _ _ 1 4 8-5 



30 — — — 7 5 6 4 — — — 22 7-3 



29 — — 5 18 13 6 6 1 1 1 51 70 



28 — 3 29 38 11 3 3 1 — — 88 5-9 



27 2 13 41 34 5 5 2 _ _ _ 102 5-1 



26 7 43 64 29 — — 1 _ _ _ 144 5.0 



25 4 36 41 11 — — — — — — 92 4-6 



24 2 17 15 4 — — — — — — 38 4-8 



23 — 5 — — — — — — — — 5 4K) 



Total 15 117 195 142 35 20 17 2 1 2 



Mean 25-6 25-4 26-5 27-4 28-6 28-7 28-8 28-5 — — 



In this sample, the sizes of the 550 fish are grouped in a somewhat 

 skew curve, about a mode at 26 cm. ; and the numbers of scale-rings 

 group themselves in like manner, but with rather more skewness, 

 about a modal number of five rings. Either way we look at it, 

 there is only one "group" of fish; and it is highly characteristic 

 of the herring that a single sample, taken from a single shoal, 

 exhibits a unimodal curve. Accepting in principle the view that 

 scale-rings tend to synchronise with age in years, we may draw this 

 first deduction that our sample consists in part (if not in whole) 

 of five-year old fish, whose average length is about 26 cm. ; and 

 this length, of 26 cm. for 5-ringed, or 5-year-old herring, agrees well 

 with many other determinations from the same region. We shall 

 be on the safe side if we deal, after this fashion, with the one 

 predominant group, or mode, in each sample of fish; and Fig. 46 

 shews an approximate curve of growth for our East Coast herring 

 drawn in this way. 



But the further assumption is commonly and all but universally 

 made that each individual herring carries the record of its age on its 

 scale-rings. If this be so, then our sample of 550 fish is a com- 

 posite population of some ten separate broods or successive ages, 

 all mixed up in a shoal. And again, if so, the 5-year-olds in the 

 said population average 26-5 cm. in length, the 3-year-olds 25-6 cm., 

 the 10-year-olds 28-5 cm. ; but these values do not fit into a normal 



