At Birth,

0-60 metre,

0.70

1.10

1.20

1.30

1.60

1.70

0.80 0-90 100

2. Relations between the Weight and Height. If man increased equally in all his dimensions, his weight at different ages would be as the cube of his height. Now, this is not what we really observe. The increase of weight is slower, except during the first year after birth; then the proportion which we have just pointed out is pretty regularly observed. But after this period, and until near the age of 140 puberty, the weight increases nearly as the square of 150 the height. The development of the weight again becomes very rapid at the time of puberty, and almost stops at the twenty-fifth year. In general, we do not err much when we assume that, during development, the squares of the weight at different ages are as the fifth powers of the height; which naturally leads to this conclusion, in supposing the specific gravity constant, that the transverse growth of man is less than the vertical.

However, if we compare two individuals who are fully developed and well-formed with each other, to ascertain the relations existing between the weight and stature, we shall find that the weight of developed persons, of different heights, is nearly as the square of the stature. Whence it naturally follows, that a transverse section, giving both the breadth and thickness, is just proportioned to the height of the individual. We furthermore conclude that, proportion still being attended to width predominates in individuals of small

1-80

1.90

We see that, statures being equal, woman weighs a little less than man until she attains the height of 1 metre 3 decimetres, which nearly corresponds to the period of puberty, and that she weighs a little more for higher statures. This difference, for the most part, proceeds from aged females being mingled with groups of a moderate stature sooner than males are; and, at equal statures, as we have already stated, aged persons weigh more than young ones.

We shall imme.

To apply the preceding to determine the age of a non-adult person, from a knowledge of the weight and stature only, let us suppose the height of the person to be 123 metre, and the weight 24 kilogrammes, he being, moreover, of the male sex. diately see, from the preceding table, that he is heavy in proportion to his stature; the table before informs us that, by taking the height alone, he ought to be a little more than nine years of age, and considering the weight alone, he should be under ten; so that we may pronounce, with great probability of truth, that the individual in question must be between nine and ten.

3. Weight of a Population.-Weight of the Human Skeleton.

The following table may serve to determine the weight of a population composed of men, women, and children, or of a population composed of individuals of certain limited ages: it has been formed by taking the numbers belonging to each age from a population table, and multiplying them by the weight of indi

Table of the Weight of a Population of 10,000 Souls.

Thus, the stature of men and women, fully deve-viduals of this age.* * loped and well-formed, varied in the proportion of five to six nearly: it is almost the same with the ratios of the weight to the stature of the two sexes; whence it naturally follows, as we have already said above, that the weight is in proportion to the square of the stature.*

Now, let us suppose that we have the individuals grouped, not according to age, but to stature, and that we have taken the average of the weight of each group, for example, and that we proceed by ten centimetres at a time: we shall have groups of children at first, then groups of children with whom some adult persons are classed, which will be the case with men commencing at 1:47 metres nearly, and women at 1.41 metres. If we afterwards reduce these numbers to a tabular form, we shall arrive at the following results, the weight of the clothes having been subtracted:

*The population table made use of in these calculations is one words, t2: T2:: p: P. It is the same with the numbers belonging which will be found above, taken from the Recherches sur la

* Calling t and T the statures, and p and P the corresponding weights of the smallest and the largest individuals, we have, in fact, almost exactly, t: T:: 5: 6, by the numbers of the first p P column, belonging to men, and t'T

to females.

:

Mortalité et la Reproduction. Bruxelles: 1832.

Thus, taking at once a population of 10,000 souls, without distinction of age or sex, the weight will be 457,000 kilogrammes nearly, 236,000 being that of the male portion. Thus we see that the average weight of an individual, without reference to age or sex, is 45'7 kilogrammes nearly; and, considering the sexes, 47 kilogrammes for a man [125 9-10ths lbs. troy], and 42 kilogrammes for a woman [74 lbs. troy]. The whole population of Brussels, which amounts to 100,000, would weigh 4,572,810 kilogrammes; or nearly four and a half times as much as a cube of water 10 metres square and the whole human race, computed at 737,000,000, would not weigh as much as 33 cubes of water 100 metres square: a value which at first sight appears small, since such a volume of water might be contained in a basin having a surface of less than one-third of an acre [hectare], and a depth of 100 metres.

5. In old age, man and woman lose about six or seven kilogrammes in weight, and seven centimetres in stature.

6. During the development of individuals of both sexes, we may consider the square of the weight, at different ages, as proportioned to the fifth power of their stature.

7. After the full development of individuals of both sexes, the weight is almost as the square of the stature.

From the two preceding relations, we infer, that increase in height is greater than the transverse increase, including breadth and thickness.

8. Man attains the maximum of his weight at about 40, and begins to waste in a sensible degree about the 60th year.

To the preceding data, I shall add some measurements of the human skeleton, which have been communicated to me by MM. Van Esschen and Guiette. They will throw additional light on our present sub-sured, and who were fully developed and well-formed, ject.

Dimensions.

Number of Skeletons.

No. 1.* No. 2.t No. 3.+ No. 4.§ No. 5.

9. Woman attains the maximum of her weight about the age of 50. During the period of reproduction, namely, from the 18th to the 40th year, her weight scarcely increases in a perceptible degree. 10. The weight of individuals who have been meavaries within extremes which are nearly as 1 to 2; whilst the stature only varies within limits which, at the most, are as 1 to 13. This is inferred from the following values, furnished by observation:

Maximum. Weight of man, 98.5 kilog. woman, 93.8 Stature of man, 1.890 met. woman, 1.740

extremities, Length of the lower extremities,

The two last skeletons, belonging to females, did not present any essential difference from the three first, which were males.

We see, from the preceding table, that the weight of a skeleton prepared some years, scarcely exceeds the weight of a child at birth.

From the foregoing, we deduce the following conclusions:

1. From birth there is an inequality, both in weight and stature, between children of the two sexes; the average weight of a boy being 320 kilogrammes [8 5-10ths lbs. troy], that of a girl 2.91 kilogrammes [7 7-10ths lbs. troy]; the stature of a boy is 0.496 metres, and that of a girl 0.483 metres.

2. The weight of a child diminishes a little towards the third day after birth, and does not begin to increase sensibly until after the first week.

3. At equal ages, man is generally heavier than woman: about the age of 12 years only are the individuals of both sexes of about the same weight. Between 1 and 11 years, the difference in weight is from one kilogramme to one and a half; between 16 and 20, it is six kilogrammes nearly; and after this period eight to nine kilogrammes.

4. When man and woman have attained their full development, they weigh almost exactly twenty times as much as at birth; and their stature is about three and one-fourth times greater than it was at the same period.

*No. 1. Natural skeleton of a man of about thirty-five years of age, prepared seven years.

11. At equal statures, woman weighs a little less than man before reaching the height of 13 metres, which almost corresponds to the period of puberty; and she weighs a little more for higher statures.

12. The average weight of an individual, without I reference to age or sex, is 457 kilogrammes; and, taking sex into account, 47 kilogrammes for man, and 42.5 kilogrammes for woman.

mmmm

CHAPTER III.

OF THE DEVELOPMENT OF STRENGTH OR POWER.

THE measure of strength is one of the elements which we are most anxious to ascertain with some degree of precision; not merely because this subject of investigation has occupied the attention of many observers; but since their principal object was to ascertain the useful effect of power, what they have done has a characteristic nature, which distinguishes their results from those which I propose to determine with a scientific purpose. Thus, Désaguiliers, De la Hire, Guenyveau, Coulomb, Schulze, &c., have chiefly investigated the relations which exist between the speed and the burden carried, in respect to a man employed either in carrying burdens or drawing them. I shall not enter into the details of the results which they have obtained, since they can be found in the principal treatises on practical mechanics. What is of most importance for us to know here is, I think, what relation the intensity of power which man can display (either with his hands or loins, without subjecting him to a day's labour), bears, in its development, to the age of the person: this latter question is composed of more complex elements.

To determine the different degrees of our physical power, different instruments have been proposed, the

+ No. 2. Skeleton of a man about twenty-five years of age, pre- least imperfect of which is undoubtedly the dyna

pared six years.

No. 3. Skeleton of a man. Age and date of the preparation unknown.

mometer of Régnier.* However, this instrument still

* [The dynamometer cannot well be described in mere words.

§ No. 4. Skeleton of a woman. Age and date of the preparation All that can be said of it is, that it is an instrument so contrived

unknown.

year.

No. 5. Skeleton of a woman aged fifteen years, prepared one

as to exhibit, on a dial-plate, the measure of strength resident in the arms and loins of the parties subjected to trial. M. Quetelet's observations may make this point more clear.]

leaves much to be desired; and, fully perceiving its | to M. Freycinet, instead of the lumbar powers stated defects when I commenced the experiments which I by Péron, we must read as follows:

The degrees of strength of the French, according to these observations, we see differ very much: the 14 results of Péron differing especially from those of 15 Ransonnet and Régnier.† It would appear that Péron 16 has made a mistake in reading the degrees of the dynamometer; at least this seems to be the case, from 19 the correction which has subsequently been made by 20 Freycinet and Bailly, who were of the number of 21 persons experimented on by Péron, and who are found to have a lumbar power sensibly smaller than that 40 placed opposite their names in the table. According 50

mometer, and the errors which would have resulted therefrom. It is necessary to all the preceding values, to add the weight of the dynamometer, which is certainly a part of the resistance to overcome: this amounts to one kilogramme.

If we had extremely sensible and suitable instruments for measuring the lumbar power of children, it is evident that we could not begin to make use of them before the age of two years, since before this period the child cannot stand upright alone, nor carry an additional weight. It is to be observed that, of all the individuals figured in the table, the lumbar power is sufficient to raise a load or overcome an obstacle exceeding the weight of the individual. The load a man can carry relatively to his weight, increases with his growth until maturity, and the perfect man can raise more than double his own weight.

The lumbar power of females differs less from that of males during childhood than after complete development. During childhood, the lumbar strength of boys is about one-third more than that of girls; towards the age of puberty, one-half; and the strength of a developed man is double that of a woman.

19

20

21

25

30

40

50

Professions produce a very sensible difference. I 11 have seen labouring masons and carpenters move the 12 dynamometer 20 degrees or more. The average of 13 several servants, between 20 and 40 years of age, has given me a value of 10 or 11 degrees.

60

To measure the power of the hands presents the 17 greatest obstacles. It seems to me that it is almost 18 impossible to rely on the accuracy of the results, unless the observations have been made with the greatest care, and by one and the same person. The first and greatest obstacle proceeds from the unequal size of the hands, and the difficulty of grasping the instrument. From all the corrections which I have made, I think I may rely on the accuracy of my own results; and, nevertheless, they differ so much from those obtained by the observers quoted, that I deliberated some time in using them, the more so since they are, like all the measures taken with Régnier's dynamometer, subject to undergo a previous correction, owing to the unequal size of the hands. To show how important this correction is, I made different trials with the dynamometers, placing my hands in different positions, and I have obtained extremely dissimilar values. We may judge better from the following :—

The dynamometer I have used is made, like all others, of a spring almost of an elliptic form: the lengths of the greater and lesser axis are 30 and 55 centimetres respectively; the dial and the index are so placed that the hands, when most approximated, are still 2.5 centimetres distant from each other; and pressure is made at a certain distance from the small axis, where the maximum of effect is produced. We obtain, therefore, only a part of the action which might be produced by pressing both extremities of the small axis. Moreover, it appears that the dynamometer I have used has been graduated, taking this distance into account. I was then desirous to know what would be the effect produced by increasing the distance between the hands, and I have obtained these values:

From this table we may infer, that the manual power of men, at different ages, is greater than that of women. The difference is generally smaller at early periods than afterwards: thus, before puberty, the ratio is 3 to 2, and it afterwards becomes 9 to 5. We also see that the hands, acting together, produce a greater effect than the sum of the effects they produce acting separately; this appears to be partly owing to the weight of the instrument, which is carried twice, and in an inconvenient manner, when the hands are used in succession. Lastly, the strongest hand is that one we use habitually, at least considering masses of people. The right hand is about one-sixth stronger than the left.

Now, if we compare the power of pressing, which I have observed, with that of MM. Régnier, Ransonnet, and Péron, we shall find the greatest differences, and which I can only attribute to the manner in which the hands were placed on the instrument, and the consequent space betwixt them. I have tried the instrument in different ways, and I think I may be certain that the indications are accurate, especially those for the average power of man. Those values which I ought to mistrust are those obtained for women and children; they appear to me to be less than they ought to be, for the reasons above stated.

According to the researches of MM. Régnier and Ransonnet, the average strength of man is not more than 46.3 or 50 kilogrammes [184 lbs. troy]; that is to say, that it does not come up to his weight; whence it follows, that a man could not lift himself by the pressure he can exercise with his hands. Now, experience evidently disproves such a result. Among the sailors experimented upon, there was probably not one who could not hold himself suspended, for some minutes at least, at the end of a cord firmly fixed at the other end. According to Péron, the manual force would be 69.2 kilogrammes: this value approaches nearer the truth. What I have found for a developed man is 89 kilogrammes [238 lbs. troy], nearly 19 kilogrammes more than the weight of a man

We also see, from the values which I have obtained, that it is about the age of 9 or 10 years that a man begins to acquire sufficient power in his hands to hold Birth, himself suspended for a time. Woman, at any age, does not appear capable of exercising a power equivalent to her weight; yet many women, from exercise and habits of labour, at length exceed this limit. Thus we see young girls, by practising gymnastic exercises, acquire the power of raising themselves by means of cords to different heights. It would appear, then, although my values are very superior to those of the observers quoted, that they are rather below than above the truth, at least for children and

*It would be curious to examine how long an individual could of age than in adults.] continue suspended by the pressure of his hands only.