On Growth and Form

by D'Arcy Wentworth Thompson

The rate of growth of various parts or organs[*].

The differences in regard to rate of growth between various parts or organs of the body, internal and external, can be amply illustrated in the case of man, and also, but chiefly in regard to external form, in some few other creatures[118]. It is obvious that there lies herein an endless field for the math­e­mat­i­cal study of correlation and of variability, but with this aspect of the case we cannot deal.

In the accompanying table, I shew, from some of Vierordt’s data, the relative weights, at various ages, compared with the weight at birth, of the entire body, of the brain, heart and liver; {89} and also the percentage relation which each of these organs bears, at the several ages, to the weight of the whole body.

Weightof Various Organs, compared with the Total Weight ofthe Human Body (male). (After Vierordt, Anatom. Tabellen, pp. 38,39.)

	Weight of body†	Relative weights of				Percentage weights compared with total body-weights
Age	in kg.	Body	Brain	Heart	Liver	Body	Brain	Heart	Liver
0	3·1	1	1	1	1	100	12·29	0·76	4·57
1	9·0	2·90	2·48	1·75	2·35	100	10·50	0·46	3·70
2	11·0	3·55	2·69	2·20	3·02	100	9·32	0·47	3·89
3	12·5	4·03	2·91	2·75	3·42	100	8·86	0·52	3·88
4	14·0	4·52	3·49	3·14	4·15	100	9·50	0·53	4·20
5	15·9	5·13	3·32	3·43	3·80	100	7·94	0·51	3·39
6	17·8	5·74	3·57	3·60	4·34	100	7·63	0·48	3·45
7	19·7	6·35	3·54	3·95	4·86	100	6·84	0·47	3·49
8	21·6	6·97	3·62	4·02	4·59	100	6·38	0·44	3·01
9	23·5	7·58	3·74	4·59	4·95	100	6·06	0·46	2·99
10	25·2	8·13	3·70	5·41	5·90	100	5·59	0·51	3·32
11	27·0	8·71	3·57	5·97	6·14	100	5·04	0·52	3·22
12	29·0	9·35	3·78	(4·13)	6·21	100	4·88	(0·34)	3·03
13	33·1	10·68	3·90	6·95	7·31	100	4·49	0·50	3·13
14	37·1	11·97	3·38	9·16	8·39	100	3·47	0·58	3·20
15	41·2	13·29	3·91	8·45	9·22	100	3·62	0·48	3·17
16	45·9	14·81	3·77	9·76	9·45	100	3·16	0·51	2·95
17	49·7	16·03	3·70	10·63	10·46	100	2·84	0·51	2·98
18	53·9	17·39	3·73	10·33	10·65	100	2·64	0·46	2·80
19	57·6	18·58	3·67	11·42	11·61	100	2·43	0·51	2·86
20	59·5	19·19	3·79	12·94	11·01	100	2·43	0·51	2·62
21	61·2	19·74	3·71	12·59	11·48	100	2·31	0·49	2·66
22	62·9	20·29	3·54	13·24	11·82	100	2·14	0·50	2·66
23	64·5	20·81	3·66	12·42	10·79	100	2·16	0·46	2·37
24	—	—	3·74	13·09	13·04	100	—	—	—
25	66·2	21·36	3·76	12·74	12·84	100	2·16	0·46	2·75

† From Quetelet.

From the first portion of the table, it will be seen that none of these organs by any means keep pace with the body as a whole in regard to growth in weight; in other words, there must be some other part of the fabric, doubtless the muscles and the bones, which increase more rapidly than the average increase of the body. Heart and liver both grow nearly at the same rate, and by the {90} age of twenty-five they have multiplied their weight at birth by about thirteen times, while the weight of the entire body has been multiplied by about twenty-one; but the weight of the brain has meanwhile been multiplied only about three and a quarter times. In the next place, we see the very remarkable phenomenon that the brain, growing rapidly till the child is about four years old, then grows more much slowly till about eight or nine years old, and after that time there is scarcely any further perceptible increase. These phenomena are dia­gram­ma­ti­cally illustrated in Fig. [18].

Fig. 18. Relative growth in weight (in Man) of Brain, Heart, and whole Body.

Many statistics indicate a decrease of brain-weight during adult life. Boas[119] was inclined to attribute this apparent phenomenon to our statistical methods, and to hold that it could “hardly be explained in any other way than by assuming an increased death-rate among men with very large brains, at an age of about twenty years.” But Raymond Pearl has shewn that there is evidence of a steady and very gradual decline in the weight of the brain with advancing age, beginning at or before the twentieth year, and continuing throughout adult life[120]. {91}

The second part of the table shews the steadily decreasing weights of the organs in question as compared with the body; the brain falling from over 12 per cent. at birth to little over 2 per cent. at five and twenty; the heart from ·75 to ·46 per cent.; and the liver from 4·57 to 2·75 per cent. of the whole bodily weight.