Chap. XV.
ON MECHANICAL AGENTS.
1087
CHAP. XV.
ON MECHANICAL AGENTS, OR THE FIRST MOVERS OF MACHINERY.
On the Strength of Men and Animala .—The animate moving powers most frequently em-ployed are man, the horse, and the ox, the latter chiefly for agricultural labour : theform and construction of the human body seems applicable in a peculiar degree to becomethe first mover of machinery, particularly when aided by the skill and judgment which onmost occasions are called forth to direct it. There are two methods of employing men andanimals ; one consists in making them walk with or without a load, the other in attachingthem to a part of the machine, where they are required either to push or to draw, andhence communicate motion to the several parts.
By the term daily labour is meant the work performed during twenty-four hours, theeffective duration of which is only a portion of that time, the remainder being employed inrest and taking meals. Animals of all kinds require that their work should be moderateand regular, and the machine they put into motion should never call forth more exertionthan is natural for them : the limit of this action is indicated by the fatigue which themover evinces, and which we may term the daily fatigue. Daniel Bernouilli imagined thatthe degree of fatigue was always proportionate to the action which produced it; so thatwhether the man was employed in walking, carrying a load, drawing or pushing, workingat a windlass, or raising a weight, he always produced, with the same degree of fatigue, thesame quantity of action, and consequently the same effect; and that the daily labour of aman may be estimated as raising 1,728,OCX) lbs. weight one foot high, or 60 pounds raisedthat height every second, when his daily labour was eight hours only.
Since these calculations were made, the celebrated Coulomb and Hachette have fully in-vestigated the subject, and in our description of their experiments, we prefer retaining theFrench weights and measures, which cannot be so readily reduced to their proper quantitiesin English without fractional quantities: the kilogramme maybe taken as equal to 2lbs. 3 oz.5 grs. avoirdupois, and the length of the metre, according to Captain Kater, is 39-37079inches, and to M. Bailey, 39*3696786 inches.
The daily labour of man depends on the moving power, which results from the effort ofwhich this mover is capable at each instant, and from the duration of effective work duringa day of 24 hours, a deduction being made for rest, meals, &c. The moving power has forits measure a mass M, multiplied by a space h , which each point of the mass passes over ina unit of time : let us call T the time of effective work during a day ; it is evident that thedaily labour of man has for its expression the product of the three quantities, MAT. Butkeeping the product the same, can we vary the factors at pleasure ? Daniel Bernouilli, whohas discussed this question, thought that we could, from an equal degree of fatigue, obtainthe same daily labour by changing the elements of this action. Desaguliers , differingfrom Coulomb, gives his opinion, that there is always for each man and each kind oflabour to which he is habituated a maximum of action, which corresponds to the productof the three factors, MAT. This observation destroys the opinion of Daniel Bernouilli,who thought that a man or any other animated mover, in whatsoever manner he employedhis strength, whether in walking, drawing, or by a winch, or on the cord of a pulley or anyother machine, would produce with the same degree of fatigue the same quantity of action,and consequently the same effect.
Nevertheless, if, knowing the value of the factors of the greatest daily action of man, wegive other values different from these, so that the product shall be constant, we shall be surenot to pass beyond the limits of the natural strength of man, and the effort of which he iscapable, which will be conformable to the hypothesis of Daniel Bernouilli.
The expression of daily action of man or any other animated mover may be compared tothat of a weight multiplied by the height to which this weight is raised : in effect, A beingthe space which a mass M goes over in a unit of time, the moving power is expressed byMA; and because these masses are proportional to the weight, it has for its value thequanti’.y PA, P being the weight of the mass M, that is to say, that it is capable of elevatingthe mass P to a height A in a unit of time, and to the height TA in the time T: callingthis height H, the daily labour of man has for its expression the product PH of the weightP elevated the height H.
Dar.iel Bernouilli estimates the daily labour of a rower as equal to 275 cube metres ofwater elevated one metre, and he supposes that this action is the product of 8 hours’ effectivelabour out of the 24.