Thus, in the case of plaice, when we deal with the mean values for a large number of specimens, and when we are careful to deal only with such as are caught in a particular locality and at a particular time, we see that _k_ is by no means constant, but steadily increases to a maximum, and afterwards slowly declines with the increasing size of the fish (Fig. 21). To begin with, therefore, the weight is increasing more rapidly than the cube of the length, and it follows that the length itself is increasing less rapidly than some other linear dimension; while in later life this condition is reversed. The maximum is reached when the length of the fish is somewhere near to 30 cm., and it is tempting to suppose that with this “point of inflection” there is associated some well-marked epoch in the fish’s life. As a matter of fact, the size of 30 cm. is approximately that at which sexual maturity may be said to begin, or is at least near enough to suggest a close connection between the two phenomena. The first step towards further investigation of the {100} apparent coincidence would be to determine the coefficient _k_ of the two sexes separately, and to discover whether or not the point of inflection is reached (or sexual maturity is reached) at a smaller size in the male than in the female plaice; but the material for this investigation is at present scanty. [Illustration: Fig. 22. Periodic annual change in the weight-length ratio of Plaice.] A still more curious and more unexpected result appears when we compare the values of _k_ for the same fish at different seasons of the year[131]. When for simplicity’s sake (as in the accompanying table and Fig. 22) we restrict ourselves to fish of one particular size, it is not necessary to determine the value of _k_, because a change in the ratio of length to weight is obvious enough; but when we have small numbers, and various sizes, to deal with, the determination of _k_ may help us very much. It will be seen, then, that in the case of plaice the ratio of weight to length exhibits a regular periodic variation with the course of the seasons. {101} _Relation of Weight to Length in Plaice of 55 cm. long, from Month to Month. (Data taken from the Department of Agriculture and Fisheries Plaice-Report, vol._ II, _p._ 92, 1909.)