SEA-FISHERIES LABORATORY. 127 
HERRING INVESTIGATIONS. 
By W. RippeEti, M.A. 
The following is a brief account of an attempt to apply 
Professor Karl Pearson’s “ goodness of fit’? method to the 
question of herring races. Being given two samples, which 
may be either of the same or of different populations, this 
method enables us to find the probability that as great, or 
greater, divergence would be found between two random 
samples drawn from one population. In other words, it gives 
us an estimate of the probability that the two samples belong 
to one population.* 
The first investigations ito the question of herring 
races in this country are due to Matthews.t He paid attention 
mainly to the distinction between winter and summer fish, 
and came to the conclusion that there was no real racial 
distinction between the two. Matthews’ figures, or rather 
his method of employing them, have been criticised by 
Heincke,t who claims that they give as much proof of dis- 
tinction between the two races as any of Heincke’s own. 
By testing Matthews’ tables by the present method, 
we find that Heincke’s contention is justified. Matthews, 
unfortunately, only published his tables in percentages of 
the total number of fish, and we have not either his actual 
measurements or the total number of fish dealt with in the 
tables. 
But taking his figures as they stand, we find the following 
results :— 
* Pearson, Phil. Mag., L, p. 157; Biometrika, VIII, p. 250, X, p. 85. 
+ Ann. Rep. Fish. Bd., Scotland, IV, 1884 (1885), p. 61; V, 1886 (1887), 
p. 295. 
{‘*Naturgeschichte des Herings,’’ Abhandl. d. Deutsch. Seefischerei- 
Vereins, Bd. II, Hit. 1, 1898. 
