Cuai\ XV.

ON MECHANICAL AGENTS.

1095

harnessed to a car, a course of 2' 13" suffices to exhaust his daily labour. The dynamometershows the pressure which a mover exercises on a fixed obstacle, and experiments onindividuals more or less strongly constituted prove that the greatest pressure which aman exercises on a spring with his hands varies from 50 to 71 kilogrammes. The scaleof traction on the same dynamometer gives HO to 150 kilogrammes as the greatest weightwhich a man can lift with the aid of his hands and loins. It is generally believed that themuscular strength of man in his savage state surpasses that of the workmen of civilisedcountries. Experiments made on the New Hollanders by M. Peron, the naturalist, provethat the English and French sailors have nearly the same strength as these savages inpressing with their hands, and are far superior to them in the action of the loins : themean measure of this action being 100 kilogrammes for the former, and 128 for the latter.

To measure the greatest effort of a horse harnessed to a vehicle, we attach the dynano-meter by one of its extremities, and the other to a large spring of wood which stretchesit gradually; or, if we have a row of continuous sledges heavily laden and fastened toge-ther by pieces of chain of a certain length, the horse then draws the first sledges, and suc-cessively those which are behind, until the resistance, increasing with the number ofsledges put in motion, equalises the greatest effort of the horse : by this procedure timeis allowed the horse to arrive at his maximum of effort. This maximum varies, accordingto the scale of traction on the dynanometer, from 300 to 525 kilogrammes.

V* hatever is the moving power there is always a certain relation between the quantitieswhich express the pressure and velocity at each instant of daily labour, and these two ele-ments have their maximum. We find in the volumes of the Academic of Petersburg,1750-1751, 1760-1761, two memoirs of Euler on this question. This geometrician hasin his second memoir considered an animated mover as a source of water falling from a de-termined height, and the resistance as the effort capable of turning a water-wheel whosefloat-boards receive the shock of the water. We call h the fall of water, a 8 the surface ofthe float-board struck by the water, a 9 h is the expression of the maximum of the pressureof the water on the float-board : calling A the maximum effort of the mover Euler supposesA = a 8 /i, calling v the velocity of the water at the end of its fall, and before the shock on thefloat-board he makes it equal to the velocity of the mover walking freely without a load.

lie designates by the letter u the velocity of the float-board after the shock of the water,and makes it equal to the velocity of the mover which corresponds to the daily action :he calls A' the pressure of the water on the float-board, which is equal to the pressure of themover corresponding to the velocity a : lastly, Euler admits, considering only tire action

of the water on the float-board, that we have the equation A' = A 1—y )*•

To verify this formula as applied to animated movers, man for example, Schulze madesome experiments which are described in a memoir to the Academy of Berlin. 1783. Heselected seven men, differing from each other in weight and shape, he found that when hemade them draw horizontally from below the shoulder, a cord passing over a pulley to theextremity of which weights were suspended, the men experimented upon stopped succes-sively at the 7 following weights:

95 105 110 100 105 100 115 livres.

The sum of these weights, 730 livres, is the measure of the maximum effort of the sevenmen acting in concert: the velocity of these same men walking freely without a load wasfound to be 5-j% Rhine feet per second. To find the velocity corresponding to their dailyaction Schulze used a machine whose levers were fixed in a vertical axle, to which twogreat cylinders of maible turning with the axle were attached: a horse was usually har-nessed to this machine whose radius was 10 Rhenish feet.

Substituting for the daily labour of a horse that of 7 men working together, he observedthat the velocity of these men in the machine was 2’45 Rhenish feet per second: of thefour quantities A', A, v, u, three are known, for we have

A = 730 livres; t> = 5 1 2 3 feet; w = 2 - 45feet.

Substituting these numbers for the preceding formula, it gives A'= 205 livres for thepressure corresponding to the daily action.

Having fixed the extremity of the cord on the vertical axis, and having rolled it round theaxis, he passed it over a pulley whence it hung over the well; he then attached diversweights to the other extremity of the cord: a weight of 215 livres gave a uniform velo-city of 2 4 feet Rhenish per second, nearly equal to that of the men applied to themachine: thus the pressure A', as found by the formula of Euler , was equivalent to aweight of 205 livres, differing 10 livres or from the observed pressure, 215 livres.

In this experiment the mean value of the draught of a horse in the machine is 205 livres,or about 100 kilogrammes: if we apply the formula of Euler to a horse harnessed to themachine, taking the facts as given before, we have for the greatest mean effort of the horse

4 a 4