On Machines in General, 213 



movemejits will he named a geometrical movement *, 2dly, I 

 say that in virtue of this geometrical movement, the adja- 

 cent corpuscles, which may be regarded as being pushed by 

 a rod, or drawn by a wire, will not approach nor recede 

 from each othe.r at the first instant, i. e. at the first in- 

 stant of this geometrical movement the relative velocity 

 of these adjacent corpuscles will be nothing : in fact, it is 

 clear, in the first place, that if m be separated from an ad- 

 jacent corpuscle by an incompressible rod, it will not be 

 able to approach it ; and that if it be separated from it by 

 an inextensible wire, it will not be able to recede from it : 

 secondly, I say that if it be separated from it by an in- 

 compressible 



♦ In order to disdnguish by a very simple example those movements 

 called geometrical from those which are not so, let us imagine two globes 

 which push each other, but in other respects free and disengaged from ever^ 

 obstacle : let us impress upon these globes equal velocities, and moved in the 

 same direction according to the line of the centres ; — this movement is geomt' 

 trical, because the bodies could even be moved In a contrary direction with 

 the same velocity, as is evident : but let us now suppose that we impress upon 

 these bodies movements equal, axKl directed in the line of the centres, but 

 which, in place of being, as formerly, moved in the same direction, tend on 

 th« contrary to recede from each other ; these movements, although possible, 

 are not what I mean by geometrical movements ; because if we wished to make 

 each of these moveable powers to assume a velocity equal and contrary to 

 that which it receives in this first movement, we should be hindered fronj 

 doing so by the impenetrability of bodies. 



In the same way if two bodies are attached to the extremities of an inex- 

 tensible wire, and if we make the system assume an arbitrary movement, but 

 so as that the distance of the two bodies may be constantly equal to the length 

 of the wire, this movement will be gcometricaly because the bodies may as- 

 sume a similar movement in quite a contrary direction ; but if these moveable 

 bodies approach to each other, the movement is not geometrical, because t]»«y 

 could not take a movement equal and contrary without receding from each 

 other; which is impossible on account of the inextensibility of the wire. 



In general it is evident, that whatever be the figiire of the system and the 

 number of bodies, if we can make it assume a movement so as there should 

 result no change in the respective position of the bodies, this movement will 

 be geometrical ; but it does not follow from this that there is no other me- 

 thod of satisfying this condition, as we shall show from several examples. 



Let us imagine an axle, to the wheel and cylinder of which are attached 

 weights suspended by cords : if we turn the machine in such a manner that 

 the weight attached to the wheel should descend from a height equal to its 

 circumference, while that of the cylinder will ascend from a height equal to 

 its circumference, this movement wiU be gFometricali because it is equally 



3 possible 



