Therefore in the female the diameter of the hips exceeds that of the shoulders, while in the male it is the diameter of the shoulders which exceeds that of the hips. This formula, as regards the female, is evidently exaggerated, as we see in a moment by comparing the actual figures. It seems, in fact, to Savage and Malgaigne, to be exaggerated, and in their works on anatomy they propose substituting the following formula: Allowing that the trunk of the male is an ovoid, with the greater extremity superior, the trunk of the female forms an ellipse - that is to say, a figure in which both extremities are of the same dimensions; therefore in the male the diameter of the shoulders exceeds that of the hips, and in the female the diameter of the hips does not exceed that of the shoulders, but is only just equal to it. Now, this last formula also exaggerates the real proportions of the hips in the female. The correct formula is as follows: In the male, as well as in the female, the trunk represents an ovoid with the greater extremity superior; but while in man the difference between the greater extremity and the lesser is very considerable, in the female this difference is very slight.

We shall see by figures that in the female the diameter of the hips, though always less, differs very little from that of the shoulders. In the male the distance from the head of one humerus to the corresponding part on the opposite side (inter-humeral diameter) is on the average 15¼ inches, and the measure taken from one great trochanter to the other (inter-trochanteric diameter) is 12¼ inches; therefore there is between the two diameters a difference of about one-fifth. In the female the inter-humeral diameter is on the average 14 inches, the mter-trochanteric diameter is 12 ½ inches; therefore there is between the two diameters a difference of only one-twelfth. These figures also serve to demonstrate that the diameter of the shoulders is much greater in the male than in the female (15 to 14), and that inversely the diameter of the hips is much greater in the female than in the male (12½ to 12¼); so that if a man and a woman of average stature are supposed to throw their shadow on the same portion of a screen, the shadow of the shoulders of the male would cover a much larger surface than the shadow of the shoulders of the female; and, on the contrary, the shadow of the hips of the woman would exceed the shadow of the hips of the man, but only to a very small extent.

'By the diameter of the hips we have in the preceding considerations understood the inter-trochanteric diameter. There is, however, a method of considering the subject which justifies to a certain extent the formulae adopted by the authors previously mentioned. It consists in comparing on the skeleton in both sexes the diameter of the pelvis (the femora being removed) with the diameter of the shoulders (the humeri being removed). Then the shoulders are represented by the inter-acmmial diameter, and the hips by the inter-iliac (from one iliac crest to the other). Under these circumstances the exact measurements show that in the male the inter-acromial diameter is twelve and three-quarter inches and the inter-iliac eleven inches; therefore, as in the preceding, the trunk, deprived of its members, still represents an ovoid, with its greater extremity superior. But we see that in the female, the inter-acromial diameter being eleven and a half inches, the inter-iliac increases to twelve inches, and therefore that here the trunk, deprived of its members, represents an ellipse or an ovoid, with its greater extremity inferior, the superior extremity differing very little in size from the inferior.

But this mode of mensuration does not express the subject as it exists; for the artist does not consider the trunk as otherwise than complete - that is to say, provided with its superior and inferior members - and it is necessary to take into account the part which they take in the diameters of the trunk by the presence of their extremities (the head of the humerus and the great trochanter). We have thought fit, however, to show here this mode of mensuration, for it explains clearly the greater diameter of the pelvis in the female compared with that of the male. If we arrange in a table the figures given in the preceding for the inter-humeral, inter-trochanteric, inter-acromial, and inter-iliac diameters in the male and in the female, or if, better still, we represent those figures by proportionate lines intended to express, on the profile of a man and that of a woman, the proportionate value of the diameters of the pelvis and the hips, and if we cause vertical lines to pass through the extremities of the inter-iliac and inter-tro-chanteric diameters, we obtain two figures which express in a striking manner all that has been pointed out (Figs. 6 and 7). We see, in fact, that in the male subject (Fig. 6) the vertical lines (y, y) passing through the extremities of the inter-trochanteric (d, d) and the inter-iliac (c, c) diameters, both fall within the extremity of the inter-humeral diameter (68), and also the inter-acromial (a, a). On the contrary, in the female (Fig. 7) we find that these same vertical lines both fall within the extremities of the inter-humeral diameter, but on the outer side of the inter-acromial.'

Diagrams comparing the diameters of the hips with the diameters of the shoulders in the male (Fig. 6) and in the female (Fig. 7).

Figs. 6 and 7. Diagrams comparing the diameters of the hips with the diameters of the shoulders in the male (Fig. 6) and in the female (Fig. 7).

The following table will supply accurate information on this point, and show the exact relations of the parts in the two sexes:

Relation of the maximum size of the hips to that of the shoulders =100

100 male Parisians - 83.0

30 female Parisians - - - - 91.8

30 male Belgians ... - 82.5

30 female Belgians - 94.5

Before leaving the subject of the trunk, there are certain points of some interest to artists which may well be disposed of in this connection, and the first of these is the position of the umbilicus. According to Vitruvius, as we have already seen, this was placed at the central point of the body, so that if a man were laid on his back with the arms and legs extended a circle might be described around them, having the umbilicus as its centre. This statement is incorrect, save for one period, and that an early one of life - that is, at two years of age. The central point of the body is, according to Roberts, at the time of birth, when the child is about the sixth of the height it will ultimately attain to, a little above the umbilicus; at two years it is at the umbilicus; at three years, when the child has attained half its total height, the central point is on a line with the upper borders of the iliac bones; at ten years of age, when the child has attained three-quarters of its total height, the central point is on a line with the trochanters; at thirteen years it is at the pubes, and in the adult man it is nearly half an inch lower. In the adult woman the central point is a little above the pubes.

Topinard gives the following table, which shows the position of the umbilicus according to various artists and anthropologists. The stature is considered as 100, and the figures show the proportion of that amount between the ground and the umbilicus:

Greek sculptors..........................................60.7

Alberti...... 60.0

Schadow...... 60.9

Gerdy...... 62.5

10 Belgians, 25 years old (Quetelet) - 60.4 100 Parisians (A. Bertillon) - 58 9

The position of the centre of gravity also differs slightly in the two sexes. The line of gravity passes through the occipital condyles, the middle of the sacrum, the head of the femur, the patella, and the arch of the foot; it is thus a little in front of the knee, and a great deal in front of the ankle. The centre of gravity in the male is three and a half units above the upper border of the acetabulum - that is to say, thirty-nine and a half units above the ground. In the female the centre of gravity is four units above the upper border of the acetabulum.