10 Preliminary Remarks and Definitions. 



their materiality. Such are the general laws of equilibrium and 

 motion, which are deduced indeed mathematically from the sin" 

 gle property of inertia. 



14. We have already ijsed the words rest, motion, and/orce, 

 as making a part of ordinary language. It now becomes neces- 

 sary to fix their meaning with precision. We begin with defin- 

 ing the place in which the phenomena under consideration are 

 supposed to occur. In order to this let us conceive of space 

 without bounds, immaterial, immoveable, and of which all the 

 parts, similar among themselves, are capable of being penetrated 

 by matter without opposing the smallest resistance. Whether 

 space in this sense exist in nature or not, is of little consequence ; 

 the definition presents to us merely an abstract extension. Now 

 imagine in this space the particles of which we have been 

 speaking, the material elements of bodies, and let us first consider 

 with- respect to them the mere circumstance of their existence. 

 This simple fact will be capable of two distinct modifications; it 

 may be that the same particle shall remain without change in its 

 actual place, or that by the influence of external causes it shall 

 leave its place to pass to some other part of space. The first 

 of these states constitutes absolute rest, and the second motion. 



15. But we can conceive further, that two or several particles 

 are displaced at the same time, and impressed with a common 

 motion, preserving with regard to one another their respective 

 positions. Then if we consider them with reference to immove- 

 able space, they will actually be in absolute motion ; but if we 

 consider them simply in their mutual relations to one another, 

 these will continue the same as if the whole group had remained 

 at rest ; and if there were upon one of these particles an intelli- 

 gent being who should observe all the others, it would be impos- 

 sible for him to decide from this observation alone, whether the 

 whole system were in motion or not. The permanence of these 

 relations in the midst of a common motion, is what we understand 

 by relative rest. This will be the condition of a number of bod- 

 ies placed in a boat and abandoned to the course of a smooth 

 stream. This is indeed the condition of all the bodies about us so 

 long as they remain fixed to the same point of the terrestrial 

 surface. They are at rest among themselves ; but the earth 

 which turns daily on its axis, impresses upon them a common 



