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_ = _w_^{_n_}, 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} _The Length of the Head in Man at various Ages._ (_After Quetelet, p. 207._) Men Women ────────────────────────── ────────────────────── Age Total height Head Ratio Height Head† Ratio m. m. m. m. 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. As regards external form, very similar differences exist, which however we must express in terms not of weight but of length. Thus the annexed table shews the changing ratios of the vertical length of the head to the entire stature; and while this ratio constantly diminishes, it will be seen that the rate of change is greatest (or the coefficient of acceleration highest) between the ages of about two and five years.