{99}
Now while this k may be spoken of as a “constant,” having a certain mean value specific to each species of organism, and depending on the form of the organism, any change to which it may be subject will be a very delicate index of progressive changes of form; for we know that our measurements of length are, on the average, very accurate, and weighing is a still more delicate method of comparison than any linear measurement.
Fig. 21. Changes in the weight-length ratio of Plaice, with increasing size.
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.
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}
| Average weight in grammes | W ⁄ L3 × 100 | W ⁄ L3 (smoothed) | |
|---|---|---|---|
| Jan. | 2039 | 1·226 | 1·157 |
| Feb. | 1735 | 1·043 | 1·080 |
| March | 1616 | 0·971 | 0·989 |
| April | 1585 | 0·953 | 0·967 |
| May | 1624 | 0·976 | 0·985 |
| June | 1707 | 1·026 | 1·005 |
| July | 1686 | 1·013 | 1·037 |
| August | 1783 | 1·072 | 1·042 |
| Sept. | 1733 | 1·042 | 1·111 |
| Oct. | 2029 | 1·220 | 1·160 |
| Nov. | 2026 | 1·218 | 1·213 |
| Dec. | 1998 | 1·201 | 1·215 |
With unchanging length, the weight and therefore the bulk of the fish falls off from about November to March or April, and again between May or June and November the bulk and weight are gradually restored. The explanation is simple, and depends wholly on the process of spawning, and on the subsequent building up again of the tissues and the reproductive organs. It follows that, by this method, without ever seeing a fish spawn, and without ever dissecting one to see the state of its reproductive system, we can ascertain its spawning season, and determine the beginning and end thereof, with great accuracy.