Motion of heavy Bodies. 169 



ufe. Now it is evident, that if each of the parts of a body receive 

 the same velocity, the whole will move only with the velocity 

 that any detached portion would have received ; so that the 

 velocity which gravity impresses upon any mass whatever, does 

 not depend upon the magnitude of this mass ; it is the same for 

 a large body as for a small one. It is true, however, that all 

 bodies are not observed to fall from the same height in the same 

 time ; but this difference is the effect of the resistance of the air, 

 as we shall see hereafter ; and when bodies are made to fall in 

 close vessels, from which the air has been withdrawn, though of 

 very different masses, they are found to descend through the 

 same space in the same time. 



It may be well to notice here the distinction between the effect 

 of gravity and that of weight. The effect of gravity is to cause, or 

 tend to cause in each part of matter, a certain velocity, which is 

 absolutely independent of the number of material particles. But 

 weight is equal to the effort necessary to be exerted, in order to 

 prevent a given mass from obeying its gravity. Now this effort 

 depends upon two things; namely, the velocity that gravity tends to 

 cause in each part, and the number of parts on which this force 

 is exerted. But as the velocity which gravity tends to give, is 

 the same for each part of matter, the effort to be exerted in or- 

 der to prevent a given mass from obeying its gravity, is propor- 

 tional to the number of parts, that is, to its mass. Thus weight 

 depends upon the mass, whereas gravity has no relation to it. 



273. Having made known these particulars with regard to 

 gravity, we proceed to the laws of motion of heavy or gravitating 

 bodies. 



Since gravity acts equally and without interruption, at what- 

 ever distance the body is from the surface of the earth (at least, 

 so far as our experience extends), gravity is a uniformly accele- 

 rating force, which at each instant causes in a body a new degree 

 of velocity, that is always the same for each equal instant ; so 

 that the velocities acquired, increase as the times elapsed ; the 

 spaces passed over are as the squares of the times, or as the 

 squares of the velocities ; the velocities are as the square roots 

 of the spaces described ; the times are also as the square roots 

 of the spaces described ; in short, all that we have said respect- 

 Mech. 22 



