L ^54 ] 



XXI)C. Essaf/upon M^ckinds-mghncrr'ail' Bij'M. CarnoT; 



Member of the French Institute^ &C^&c, 



! > . ) r ; t~ • ' J : ' '' [Cominued iroirt p: 1*5. J'^' ' ^ " ' ' * ' 



. X HE .sepond principle upoi> vvnicn-w;e purpose making 

 some observations, is ilic celebrated liw oV equilibrium of 

 Descartes. Tt tonics to this, that two powers in equilibrium 

 are always in reciprocal ratio tp their velocity, es-timated in 

 the direction of these forces, wlicn we svippose l^hat one of 

 the two comes to take it from tlic other in an infiiiitely small 

 degree ; so that a small movement arises from it. 



But although this proposition be very beautiful, and we 

 generally regard it as the fundamental principle of equili- 

 brium in machines, it is nevertheless infinitely less general 

 iRa'ii that which has been quoted in the first plaqe ; becaj^se 

 it is applied solely to the case where tliere are only two 

 powers in the system : and besides, it is very easily deduced 

 ffeiifi-'what has been said upon the subject of the two weights 

 A and B, since v/e evidently approximate the one case to the 

 other by substituting, by means of pulleys, weights in 

 pface of the forces which we wish to value. 



Moreover, it is to be remarked, that this principle does 

 not cjjpress the conditions of the eq^uilibrium between two 

 powers 'sb'cQihpletely as that \vhicK has teen quoted in the 

 first'place; 'for it only gives the accouiit of the quantities of 

 forccj cpmposino- equilibrium, at the place where the latter also 

 gtVe^, m some soh'^ ^thc account of'tjieir diVections ; — for ex- 

 ample, in the case of equilibrium between two weights, the 

 principle of Descartes solely teaches. that the weights should 

 te6 'in the reciprocal ratio to their, vertical velocities j but it 

 tlocs not indicate, like the first, that one of these bodies 

 should necessarily ascend, while the other descends. In 

 ftrder thai an ail^e, fcir instance, to the wheeh and cylinder 

 of which weights ar6 suspended by cords, should reniaiu 

 Tit ''eiqitili brill ni, it i;?^not sufficient that the weight applied 

 to the wheel be 16 thrii of thti cylFiider'as the radius of the 

 cylinder is to the radius of the wheel :— it must also hap- 

 pen that these weights tend to make the machine turn in 

 a contrary direction to each other ^ i. e, that thev are placed 

 io ui|[e rent sides with respect to the axis ^ else their efforts, 

 l'-'- ^ ■ % ^ *' being 



