SEA-FISHERIES LABORATORY. 101 
in proportion to its length: the herrings “ put on flesh.” In 
the case of an average-sized fish, of (say) 23-5 ems. (that is 94 
inches) the average weight will be about 73 grms. (that is about 
240zs.) at the beginning of the season. But by the end of the 
season, herrings of the same length will weigh about 121 germs. 
(that is about 4 ozs.). This increase in weight is due partly to . 
the growth of the ovaries and testes and partly to the increase 
in tissue. 
It may be useful to state these latter results in greater detail. 
When the samples were received, the fish were sorted out 
into centimetre groups, thus all those over 20 and less than 21 
ems. long were placed in a group with mean length of 20-5 cms. 
and so on. All the fish in each group were then weighed and 
mean weights were calculated. Thus we get series, as, for in- 
stance :— | 
9 June, 1916, 24 herrings. 
Mean length = 22:5 23:5 24-5 25:5 26-5 27-5 28-5 cms.; 
Mean weight = 79 92 95 104 114 124 161 grams. 
A freehand curve could then be drawn, plotting mean 
leneth against mean weight. 
But it is more accurate to calculate a probability curve, 
thus avoiding bias in drawing a graph for such rather irregular 
data. It can easily be shown that the curve that represents, 
with greatest probability, the increase of weight with increasing 
length is :— 
Mean weight = a constant + al + bl? + cl, &e. 
Where a, 6 and ¢ are coefficients and / is the mean length. For 
such small samples as these we may take the modified function. 
Mean weight = al®. 
Further it is easy to show that the coefficient a is given by 
4 (weight of all the fish in the sample) 
Uy 
_ Where /, is the highest mean length + 0-5 em. and /, is the 
lowest mean length — 0-5 cm. 
