As a final illustration of the rate of growth, and of unequal growth in various directions, I give the following table of data regarding the ox, extending over the first three years, or nearly so, of the animal’s life. The observed data are (1) the weight of the animal, month by month, (2) the length of the back, from the occiput to the root of the tail, and (3) the height to the withers. To these data I have added (1) the ratio of length to height, (2) the coefficient (k) expressing the ratio of weight to the cube of the length, and (3) a similar coefficient (k′) for the height of the animal. It will be seen that, while all these ratios tend to alter continuously, shewing that the animal’s form is steadily altering as it approaches maturity, the ratio between length and weight {102} changes comparatively little. The simple ratio between length and height increases considerably, as indeed we should expect; for we know that in all Ungulate animals the legs are remarkably
| Age in months | W, wt. in kg. | L, length of back | H, height | L ⁄ H | k = W ⁄ L3 × 10 | k′ = W ⁄ H3 × 10 |
|---|---|---|---|---|---|---|
| 0 | 37 | ·78 | ·70 | 1·114 | ·779 | 1·079 |
| 1 | 55·3 | ·94 | ·77 | 1·221 | ·665 | 1·210 |
| 2 | 86·3 | 1·09 | ·85 | 1·282 | ·666 | 1·406 |
| 3 | 121·3 | 1·207 | ·94 | 1·284 | ·690 | 1·460 |
| 4 | 150·3 | 1·314 | ·95 | 1·383 | ·662 | 1·754 |
| 5 | 179·3 | 1·404 | 1·040 | 1·350 | ·649 | 1·600 |
| 6 | 210·3 | 1·484 | 1·087 | 1·365 | ·644 | 1·638 |
| 7 | 247·3 | 1·524 | 1·122 | 1·358 | ·699 | 1·751 |
| 8 | 267·3 | 1·581 | 1·147 | 1·378 | ·677 | 1·791 |
| 9 | 282·8 | 1·621 | 1·162 | 1·395 | ·664 | 1·802 |
| 10 | 303·7 | 1·651 | 1·192 | 1·385 | ·675 | 1·793 |
| 11 | 327·7 | 1·694 | 1·215 | 1·394 | ·674 | 1·794 |
| 12 | 350·7 | 1·740 | 1·238 | 1·405 | ·666 | 1·849 |
| 13 | 374·7 | 1·765 | 1·254 | 1·407 | ·682 | 1·900 |
| 14 | 391·3 | 1·785 | 1·264 | 1·412 | ·688 | 1·938 |
| 15 | 405·9 | 1·804 | 1·270 | 1·420 | ·692 | 1·982 |
| 16 | 417·9 | 1·814 | 1·280 | 1·417 | ·700 | 2·092 |
| 17 | 423·9 | 1·832 | 1·290 | 1·420 | ·689 | 1·974 |
| 18 | 423·9 | 1·859 | 1·297 | 1·433 | ·660 | 1·943 |
| 19 | 427·9 | 1·875 | 1·307 | 1·435 | ·649 | 1·916 |
| 20 | 437·9 | 1·884 | 1·311 | 1·437 | ·655 | 1·944 |
| 21 | 447·9 | 1·893 | 1·321 | 1·433 | ·661 | 1·943 |
| 22 | 464·4 | 1·901 | 1·333 | 1·426 | ·676 | 1·960 |
| 23 | 480·9 | 1·909 | 1·345 | 1·419 | ·691 | 1·977 |
| 24 | 500·9 | 1·914 | 1·352 | 1·416 | ·714 | 2·027 |
| 25 | 520·9 | 1·919 | 1·359 | 1·412 | ·737 | 2·075 |
| 26 | 534·1 | 1·924 | 1·361 | 1·414 | ·750 | 2·119 |
| 27 | 547·3 | 1·929 | 1·363 | 1·415 | ·762 | 2·162 |
| 28 | 554·5 | 1·929 | 1·363 | 1·415 | ·772 | 2·190 |
| 29 | 561·7 | 1·929 | 1·363 | 1·415 | ·782 | 2·218 |
| 30 | 586·2 | 1·949 | 1·383 | 1·409 | ·792 | 2·216 |
| 31 | 610·7 | 1·969 | 1·403 | 1·403 | ·800 | 2·211 |
| 32 | 625·7 | 1·983 | 1·420 | 1·396 | ·803 | 2·186 |
| 33 | 640·7 | 1·997 | 1·437 | 1·390 | ·805 | 2·159 |
| 34 | 655·7 | 2·011 | 1·454 | 1·383 | ·806 | 2·133 |
† Cornevin, Ch., Études sur la croissance, Arch. de Physiol. norm. et pathol. (5), IV, p. 477, 1892.
{103}
long at birth in comparison with other dimensions of the body. It is somewhat curious, however, that this ratio seems to fall off a little in the third year of growth, the animal continuing to grow in height to a marked degree after growth in length has become very slow. The ratio between height and weight is by much the most variable of our three ratios; the coefficient W ⁄ H3 steadily increases, and is more than twice as great at three years old as it was at birth. This illustrates the important, but obvious fact, that the coefficient k is most variable in the case of that dimension which grows most uniformly, that is to say most nearly in proportion to the general bulk of the animal. In short, the successive values of k, as determined (at successive epochs) for one dimension, are a measure of the variability of the others.
From the whole of the foregoing discussion we see that a certain definite rate of growth is a characteristic or specific phenomenon, deep-seated in the physiology of the organism; and that a very large part of the specific morphology of the organism depends upon the fact that there is not only an average, or aggregate, rate of growth common to the whole, but also a variation of rate in different parts of the organism, tending towards a specific rate characteristic of each different part or organ. The smallest change in the relative magnitudes of these partial or localised velocities of growth will be soon manifested in more and more striking differences of form. This is as much as to say that the time-element, which is implicit in the idea of growth, can never (or very seldom) be wholly neglected in our consideration of form[132]. It is scarcely necessary to enlarge here upon our statement, for not only is the truth of it self-evident, but it will find illustration again and again throughout this book. Nevertheless, let us go out of our way for a moment to consider it in reference to a particular case, and to enquire whether it helps to remove any of the difficulties which that case appears to present. {104}
Fig. 23. Variability of length of tail-forceps in a sample of Earwigs. (After Bateson, P. Z. S. 1892, p. 588.)