There are several methods of arriving at the measurements of the upper extremity, which may he divided into direct and indirect. The former are three in number. The first is to measure from the acromion to the extremity of the middle finger, the arm being extended, by which means, however, the length arrived at is somewhat too short, since the head of the humerus, which lies in the axilla, is not fully taken into account. The second is to add together the measurements of the various segments of which the extremity is composed. This also gives a somewhat false figure, since the limb in a natural condition is not extended in a perfectly straight line, the arm and forearm meeting at an obtuse angle at the elbow.

The human figure described within a circle.

Fig. 8. The human figure described within a circle.

The third is to measure from the acromion to the extremity of the middle finger when the arm is lying by the side of the body. The two indirect methods are, firstly, to ascertain the distance between the extremity of the middle finger and the superior border of the patella when the arms are lying straight by the side, as in the military position known as 'attention.' The second method is to measure the full span of the two arms when fully extended from the shoulders - a method to which I shall have shortly to return.

The length of the whole upper extremity in the male is, according to Marshall, twenty-nine and a half units, and in the female twenty-nine. The following table will show the division of these figures between the different segments of the limb :

Male.

Female.

Humerus -

13

units

12½

units

Radius -

9

"

9

"

Hand.....

"

"

29½

29

Reducing the figure in the male to terms of the stature, the latter being considered as 100, so as to compare the result with that given by Topinard, we find that the proportion is forty-four, whilst that of the French author is forty-five. The differences in the points of measurement adopted by the two authors may account for this discrepancy, which is in any case not very large. With regard to the relation of the limb to other parts of the body, it may first be mentioned that, according to Marshall, the top of the shoulder-joint is thirteen units below the vertex. It must not, however, be forgotten that this is a figure which may vary within certain limits in persons of the same stature and possessing limbs of the same length, according to whether they are square-shouldered or round-shouldered, to use the common phrases. The position of the middle finger, with regard to the trunk, in the position of 'attention' is also one of importance. In the European of average height it corresponds usually to the middle of the thigh; in subjects of short stature the extremity of the hand descends a little lower than the middle, and in very tall men it is a little higher. In the yellow and black races the extremity of the middle finger descends considerably lower than the middle of the thigh.

It is interesting to note that in the highest apes the position of the same point gradually descends still farther. Thus in the chimpanzee it is placed below the knee; in the gorilla it corresponds to the middle of the leg; whilst, finally, in the orang-utang and in the gibbon it nearly reaches to the ankle. The facts respecting the position of the middle finger in different races are also brought out by the following table, which give the distance between its point and the centre of the patella in figures relative to the stature (= 100):

1,061 sailors (white) - - - 8.73

10,875 American soldiers - - - 7.49

517 Iroquois Indians - 5.36

2,020 negroes..... 4.37

Turning now to the intrinsic measurements of the upper limb, we may first consider the relation between the arm and the forearm, a subject which has received considerable attention, what is known as the antibrachial index being founded on the measurements of the two parts when compared with one another. In the first place, in the adult condition, the forearm of the negro is much longer in comparison with the arm than that of the European. The measurements, for example, of five Congo negroes gave an average of 93.4, the arm being considered as 100, whilst the measurements of thirty Germans gave 83.5 to 100 as the proportion between the same two parts. Amongst white and yellow races, however, there is no special rule to differentiate one from another by the comparison of the segments of the limb. The relation of the hand to the body stature is a matter of considerable interest to artists, since it has been taken as the canon by several writers. Respecting the racial variations of this part, Topinard says that, speaking generally, Europeans have the smallest hands, with the exceptions of the true gipsies (Tziganes), who have still smaller. The largest hands are met with amongst the yellow races, whilst the negroes hold a middle place in this respect.

The following table will give an idea of the manner in which the hand has been used as a canon, the figures being the number of times which it was included in the stature:

Greek artiste (Topinard) - - 10.9

Vitruvius...... 10.0

Durer...... 10.0

Cousin...... 9.3

Duval...... 10.0

Roberts...... 9.0

Quetelet...................................... ... 9.0

Marshall...... 8.93

Topinard...... 8.69

Pram this table it will be noticed that artists in general, and those of antiquity in particular, have made the hand too small in proportion to the stature. It should, however, be mentioned that Duval says that his figure is subject to great variations. Taking all the figures into consideration, we may say that the hand is contained nine times in the stature of the average European.

The full span of the arms when extended at right angles from the trunk is another measurement which has attracted the attention of artists; it is the grande enrergure of the French. We have already noticed Vitruvius's statement that the span was equal to the stature, and that this is accepted as accurate in the canon of the French studios as given by Topinard. Duval says respecting this matter: 'The relation of the span of the upper limbs to the height has been expressed long since by the formula known as the square figure of the ancients. If we cause two horizontal lines to pass, one at a tangent to the soles of the feet, the other at a tangent to the summit of the head, and two vertical lines at right angles to the extremities of the two arms extended horizontally, these four lines form by their junction a perfect square; in other words, the man having the arms horizontal is enclosed within a square. This shows that the span of the arms is equal to the height. This statement is correct for a man of the Caucasian race of the middle height; but it is not so for the yellow and black races, in whom the span of the arm is greater than the height.

If from man we pass on to the superior monkeys called anthropoid (chimpanzee, gorilla, etc.), we find that the span of the arms in these becomes more and more extended as compared with the height until it becomes almost double. Thus, in the gorilla, the height being 5 feet 7½ inches, the span becomes 8 feet 9¼ inches; and in the chimpanzee, to a height of 5 feet 5¼ inches, the corresponding span is 6 feet 6 inches.' The statement, however, that the span equals the stature is not absolutely correct, for the relation between the two, though very variable, is in favour of the span as compared with the height.

The human figure inscribed within a square.

Fig. 9. The human figure inscribed within a square.

Roberts states that the theory which holds that the span is equal to the height is true only within certain limits, namely, from the time of birth to that of puberty, a statement which is true of both sexes. After puberty more decided changes in the proportions take place, the horizontal being greater than the perpendicular measurement, especially in men, whose chest and shoulders have a greater development in breadth than women. The ratio of height to the measurement of the extended arms is in the adult man as 1 to 1.045, and in women as 1 to 1.015. Duval notes certain relationships between parts of the upper extremity, which may conveniently be given here in the form of a table:

The length of the hand, less the third phalanx of the middle finger, is equal to: the clavicle, the vertebral border of the scapula, the manubrium and gladiolus sterni, taken together, the distance between the scapulas when the bands are hanging by the sides, half the length of the humerus, two-thirds of the length of the forearm.

But, as he remarks, these proportions are so variable that they cannot be insisted upon.