If now the length from the base of this triangle to the umbilicus be taken, and the differences between the child and the adult represented proportionately, it will be found that they are as 1 to 2.42, or less than the general growth of the torso. From these figures we may conclude that the portion between the nipples and the upper part of the thorax grows more rapidly than that between the firstnamed points and the umbilicus. I am now assuming that Quetelet's figures are correct on this point, and should mention that he expressly states that they apply only to the male sex, since this part of the body is subjected to so much artificial treatment in the female that it is not possible to come to accurate conclusions respecting it.

A comparative representation of the infantile and adult figures.

Fig. 10. A comparative representation of the infantile and adult figures, both being shown as of the same height. The relation between the various parts of the body and of the limbs is shown by the dotted lines. Convergence of the line towards the side of the adult shows proportional diminution of size, and divergence increase, or, in other words, less or greater increase of size during the time of growth (Langer).

Triangles showing growth of thorax and upper part of abdomen (Quetelet).

Fig. 11. Triangles showing growth of thorax and upper part of abdomen (Quetelet).

The upper extremity, with the hand included, is three and a half times longer in the adult than in the infant. The hand, however, grows more slowly than the remaining parts, doubling between the fifth and seventh years, and tripling between this date and the termination of development. If the arm be considered without the hand, it doubles between four and five, triples between thirteen and fourteen, and is four times the infant size at the termination of growth. The forearm grows more than the arm proportionately, the proportion between the former in the child and adult being as 1 to 4.26, and of the latter as 1 to 3.78. The circumferences at the biceps and elbow increase two and three-quarter times nearly.

The lower extremities, measured from the fork to the sole of the foot, double their length before the third year; at twelve years they are four times, and at twenty years five times, their original length. These are (Quetelet's figures. According to Marshall, the whole lower extremity increases four and a half times during the process of development. The various segments do not increase at the same rate, for the thigh grows more rapidly than the leg, and the leg than the foot. Thus there is this difference between the growth of the upper and the lower extremities: that the greatest amount of growth in the former takes place in the middle segment, whilst in the latter it is in the segment which is nearest to the trunk. It will also be remarked that the lower extremity increases proportionately to a greater extent than either the stature, the torso, or the upper extremity. Turning now more particularly to the growth of the various segments of the lower limb, the thigh in the adult is 7.31 times the length of the same part in the child. Thus the increase in this part is far in excess of that of any other part of the body.

The leg, measured from the lower edge of the patella, increases four and a half times, the height of the foot three and a quarter times, and its length three and a half times.

As I have had occasion at an earlier part of this lecture to call your attention to the differences between the proportions of the arm and the forearm in the European and the negro, I think that the following remarks on that subject in connection with the rate of increase with which I have just been dealing may not be without interest to you. 'With regard to the proportions of the different segments of the extremities,' says Humphry, 'in the earliest periods the arm and thigh are respectively shorter than the forearm and leg, and the latter are respectively shorter than the hand and foot. During development and growth these proportions gradually become reversed; but the final relations between the several segments are not established until after puberty. At birth the arm, leg, and foot are of about equal length, and the hand is a little longer than the forearm. These facts are interesting as showing clearly that in its earlier conditions the most perfect human form presents more numerous approximations to the type of the negro, and likewise to that of the quadrumanous animal, than at subsequent periods.

They show, also, that it is during the work of development and growth that the lower extremities attain their greater relative dimensions, and that the proximal segments of both upper and lower extremities come to bear that large proportion to their distal parts whereby the European type is characterized. Thus the difference in type between the negro and the European is reduced to a mere matter of growth, and it is shown that, so far as the extremities are concerned, a transient condition of the one corresponds with a permanent condition of the other. The same remark applies also to the dimensions of the trunk. Till the period of puberty the European and the negro more nearly correspond. It is not till after that period that the greater proportionate breadth of chest and pelvis is attained in the former.'

I must in conclusion say a very few words as to the influence of occupation upon the proportions of man. This, however, is a matter upon which much further work will be necessary before it is possible to draw any conclusions of real value. Everyone is aware that occupation, or at least certain occupations, produce a very marked effect upon the person and the physiognomy, but exactly in what this difference anatomically consists is not always so easy to say. The same remarks may be made respecting the influence of the general environment upon the stature - a subject on which Quetelet, from observations made upon dwellers in the cities and country parts of Belgium, remarks that the average stature in the towns is very much the same as that of the country people, though the former have a slight advantage in point of height. Speaking on this point, Topinard says: 'Have mountaineers longer or shorter legs? Both opinions have been maintained, but theoretically. Do some professions lengthen the parts employed and atrophy those disused Every-body says so, but there are no direct proofs.' The most important document which was at Topinanl's disposal in this matter is a comparison between soldiers, sailors, and students in America, which I give in a tabular form:

10,876

1,061

291

soldiers.

sailors.

students.

Vertex to seventh cervical vertebra

14.81

15.28

14.82

Seventh cerv. vert, to perineum

38.93

37.22

38.34

Perineum to knee.......

18.55

19.48

18.59

Perineum to ground

27.71

28.02

28.25

Acromion to elbow

20.25

19.95

20.14

Elbow to end of middle finger

23.16

23.28

22.47

Each of these figures is referable to the stature, which is considered as 100. From the table it follows that the sailors have, in relation to the soldiers, a shorter trunk, longer portions of the lower extremity, a shorter arm, and a slightly larger forearm. Amongst the students, in comparison with the soldiers, the trunk, the leg, and the forearm are a little shorter. What can be deduced from these facts? Is it the influence of occupation which ought to be invoked? In the case of the sailors, undoubtedly so. But amongst the students there is another factor to be considered, that of age, for their average age was only about twenty years, that of the soldiers being thirty-five.