It is plain, then, that there is no simple and direct relation, holding good throughout life, between the size of the body as a whole and that of the organs we have just discussed; and the changing ratio of magnitude is especially marked in the case of the brain, which, as we have just seen, constitutes about one-eighth of the whole bodily weight at birth, and but one-fiftieth at five and twenty. The same change of ratio is observed in other animals, in equal or even greater degree. For instance, Max Weber[121] tells us that in the lion, at five weeks, four months, eleven months, and lastly when full-grown, the brain-weight represents the following fractions of the weight of the whole body, viz. 1 ⁄ 18, 1 ⁄ 80, 1 ⁄ 184, and 1 ⁄ 546. And Kellicott has, in like manner, shewn that in the dogfish, while some organs (e.g. rectal gland, pancreas, etc.) increase steadily and very nearly proportionately to the body as a whole, the brain, and some other organs also, grow in a diminishing ratio, which is capable of representation, approximately, by a logarithmic curve[122].
But if we confine ourselves to the adult, then, as Raymond Pearl has shewn in the case of man, the relation of brain-weight to age, to stature, or to weight, becomes a comparatively simple one, and may be sensibly expressed by a straight line, or simple equation.
Thus, if W be the brain-weight (in grammes), and A be the age, or S the stature, of the individual, then (in the case of Swedish males) the following simple equations suffice to give the required ratios:
W = 1487·8 − 1·94 A = 915·06 + 2·86 S.
These equations are applicable to ages between fifteen and eighty; if we take narrower limits, say between fifteen and fifty, we can get a closer agreement by using somewhat altered constants. In the two sexes, and in different races, these empirical constants will be greatly changed[123]. Donaldson has further shewn that the correlation between brain-weight and body-weight is very much closer in the rat than in man[124].
The falling ratio of weight of brain to body with increase of size or age finds its parallel in comparative anatomy, in the general law that the larger the animal the less is the relative weight of the brain.
| Weight of entire animal gms. | Weight of brain gms. | Ratio | |
|---|---|---|---|
| Marmoset | 335 | 12·5 | 1 : 26 |
| Spider monkey | 1845 | 126 | 1 : 15 |
| Felis minuta | 1234 | 23·6 | 1 : 56 |
| F. domestica | 3300 | 31 | 1 : 107 |
| Leopard | 27,700 | 164 | 1 : 168 |
| Lion | 119,500 | 219 | 1 : 546 |
| Elephant | 3,048,000 | 5430 | 1 : 560 |
| Whale (Globiocephalus) | 1,000,000 | 2511 | 1 : 400 |
For much information on this subject, see Dubois, “Abhängigkeit des Hirngewichtes von der Körpergrösse bei den Säugethieren,” Arch. f. Anthropol. XXV, 1897. Dubois has attempted, but I think with very doubtful success, to equate the weight of the brain with that of the animal. We may do this, in a very simple way, by representing the weight of the body as a power of that of the brain; thus, in the above table of the weights of brain and body in four species of cat, if we call W the weight of the body (in grammes), and w the weight of the brain, then if in all four cases we express the ratio by W = wn , we find that n is almost constant, and differs little from 2·24 in all four species: the values being respectively, in the order of the table 2·36, 2·24, 2·18, and 2·17. But this evidently amounts to no more than an empirical rule; for we can easily see that it depends on the particular scale which we have used, and that if the weights had been taken, for instance, in kilogrammes or in milligrammes, the agreement or coincidence would not have occurred[125]. {93}
| Age | Men | Women | ||||
|---|---|---|---|---|---|---|
| Total height m. | Head m. | Ratio | Height m. | Head† m. | Ratio | |
| Birth | 0·500 | 0·111 | 4·50 | 0·494 | 0·111 | 4·45 |
| 1 year | 0·698 | 0·154 | 4·53 | 0·690 | 0·154 | 4·48 |
| 2 years | 0·791 | 0·173 | 4·57 | 0·781 | 0·172 | 4·54 |
| 3 years | 0·864 | 0·182 | 4·74 | 0·854 | 0·180 | 4·74 |
| 5 years | 0·987 | 0·192 | 5·14 | 0·974 | 0·188 | 5·18 |
| 10 years | 1·273 | 0·205 | 6·21 | 1·249 | 0·201 | 6·21 |
| 15 years | 1·513 | 0·215 | 7·04 | 1·488 | 0·213 | 6·99 |
| 20 years | 1·669 | 0·227 | 7·35 | 1·574 | 0·220 | 7·15 |
| 30 years | 1·686 | 0·228 | 7·39 | 1·580 | 0·221 | 7·15 |
| 40 years | 1·686 | 0·228 | 7·39 | 1·580 | 0·221 | 7·15 |
† A smooth curve, very similar to this, for the growth in “auricular height” of the girl’s head, is given by Pearson, in Biometrika, III, p. 141. 1904.