On the. power of Men as firjl movers. 417 



unity of time, and the effort which lias for its expreffion and meafure a certain number 

 ot kilograms or unities of weight. The produce of thefe two numbers reprefcnts and 

 raeafures the aftion ; and this produft multiplied by a tiiird number, which is the time, 

 during which the aftion continues, gives the quantity of afiion or total effeft refulting 

 the work, which is, therefore, an objeft capable of being meafured and fubjeSed to 

 computation. 



Thefe notions being eftablifhed, the fundamental objeCl of rcfearch is the comparifon 

 of the work with xhtfatigue, which is the neceffary confequence. Any determinate 

 quantity of a6\ion (or the number which reprefents it) may be afforded by an infinity 

 of different combinations of the values of numbers, of which the produ6l ferves as a 

 meafure; and thefe combinations depend on the various manners in which the force of 

 men is employed. Is the fatigue equal in all cafes for equal quantities of afllon, or 

 does it vary when in different circumftances the numbers are varied which reprefent the 

 velocity, the time, and the effort ; fo as, neverthelefs, to preferve the fame conftant 

 produft ? Daniel Bernouilli, and other celebrated authors have adopted the former opi- 

 nion ; but Cit. Coulomb (hews that they were deceived, and by refuting, by proofs drawn 

 from rcafonings and experiment, an opinion, fupported by names fo refpeftable, he has 

 rendered a great fervice to the fcientific application of mechanics. 



But though fatigue be not fimply proportioned to the quantity of aflion, it is one of 

 its funftions ; that is to fay, the formula which reprefents it ought to include in fome 

 manner the velocity, the effort, and the time. It is known by the theory of mathe- 

 matical analyfis that there muft, therefore, exift a certain relation between thefe three 

 things, fuch as that a given effcft may be produced with the leafl. fatigue ; or which is 

 the fame thing, that when the fatigue is the fame the quantity of effe£l or total aftion 

 may be a maximum. This is the problem which the author has propofed to folve, and 

 in which he has confidered the various methods ot employing the force of men. 



In the firft place he examines the quantity of aftion which men can produce, when, 

 during a day, they mount a fet of fleps or flairs, either with or without a burthen. 

 The experiments he mentions on this fubjeft immediately prove the falfity of the opi- 

 nion of Bernouilli. He found that the quantity of aftion of a man who mounts with- 

 out a burthen, having his own body to raife only, is double that of a man loaded with 

 a weight of 68 kilogrammes (14941b. avoirdupois,} both continuing at work for a day. 

 Hence it is ftrikingly obfervable, how much, with equal fatigue and time, the total or 

 abfolute effort may obtain different values by varying the combinations of effort and of 

 Telocity. 



But the word effeft here denotes the total quantity of labour employed to raife, not 

 ©nly the burthen, but the weight of the man himfelf ; and what is of the greateft im- 

 portance to confider, is, the ufeful effeB ; tliat is to fay, the total effeft, deducing the 



value 



