On Machines in General. 217 



metrical movements : but it must be remarked that there \^ 

 a case where geometrical movements are not the only ones 

 which can answer the same purpose, and where some other 

 movements may be employed in the same way, in order to 

 extract from the general equation (F) determinate equations: 

 this happens when these other movements, without being 

 absolutely geometrical, become so, nevertheless, merely on 

 suppressing some of the small wires or rods we have sup- 

 posed to be interposed between the adjacent particles of the 

 system, at the time, I say, when these rods or wires supposed 

 to transmit the movement from one corpuscle to another, 

 transmitted none at all in fact ; i. e, when the tension of 

 some of these wires, or- the pressure of some of these rods, 

 is equal to zero ; for then by suppressing these wires or 

 rods, the tensions or pressures of which are null, we evi- 

 dently change nothing at all of the reciprocal action of the 

 bodies, and nevertheless it is possible that we may thereby 

 render the system susceptible of some geometrical move- 

 ments, which could not otherwise take place : there is nothing 

 therefore to prevent us from regarding these rods and wires 

 as annihilated, since they have no influence upon the state of 

 the system ; and as we consequently employ as geometrical 

 the movements which, without being so effectively, become 

 so nevertheless by this suppression. 



Further, when two bodies are contiguous to each other, 

 it is evidently the same thing to suppress the small rod 

 which we have imagined 'to be interposed between two, to 

 hinder them from approaching, or to suppose that these 

 bodies are permeable to each other^ i. e. that they may be 

 penetrated as easily as the empty space is penetrated by all 

 bodiesf; whence it evidently follows, that in general, in any 

 gystem of bodies acting upon each other, immediately or by 

 wires and rods, i. e. by the intermedium of any machine, 

 if there be any wire, rod, or other part of the machine 

 which exercises no action upon bodies applied to it, i, e, 

 which may be annihilated without any change resulting in 

 the reciprocal action of these bodies, we shall be able to 

 treat as geometrical all the movements which, without 

 being so effectively, would becopae sq by this suppression, 



iu 



