1821.] Phenomena of Heat, Gases, Gravitation, S^c. 341 



to yield to any change of state, and none take place, il follows, 

 that the body is not acted on by any force ; or if it be, it must 

 be by an accumulation of opposing forces, which, in the aggre* 

 gate, destroy one another. Mathematicians usually estimate 

 force by the effect it produces, or would produce, in a given 

 time, and consider:" the intensity of the force as proportional to 

 the effect. Thus, if one of two forces produce twice the effect 

 of the other, it is considered to be doubly as powerful ; if three 

 times the effect, trebly; and so on. But this is rather estimat- 

 ing the effects than Ishe forces ; since it is possible for the same 

 primitive force, by successive actions, to produce very unequal 

 effects in equal times. 



Forces have likewise been distinguished into two kinds, pres- 

 sive and impulsive, or those which act by pressure, and those 

 which act by impulsion. The former generate changes in bodies 

 by a continued unceasing action, from the beginning to the end 

 of the stroke, or fit, of action; and, consequently, always con- 

 sume time. The latter act either by an instantaneous impulse, 

 or by a succession of those impulses ; but each impulse, indivi- 

 dually considered, occupies not the smallest portion of time. It 

 is an action that in one moment might be said not to have come 

 into existence ; and in the next to have ended. This is the kind 

 of force we have now to consider. 



If we take single impulses, it is plain that the forces and the 

 changes they produce are proportignal, under the same circum- 

 stances of action. But if a succession of impulses takes place, 

 the effects are no longer proportional to the forces, but to the 

 collected actions of the forces in equal times. When, therefore, 

 the forces are equal, the effects are proportional to the numbers 

 of their respective repetitions ; and when those forces are 

 unequal, but uniformly intense in their actions, the effects are in 

 the compound ratio of those numbers and the forces. It is 

 hence manifestly possible for a weak force, by a greater number 

 of successive actions, to produce effects equal to those of a 

 stronger by a less number of actions ; and if the impulses of the 

 two forces be at regular intervals, and yet the intervals of the 

 slower be not sensible to observation, the effects will aUvays 

 have the same ratio, Vv^hatever be the length of time in which 

 they are compared. 



These impulses may also be opposed to a pressive force, and 

 effect precisely the same things. For let us suppose a hard 

 body to be acted on from a state of quiescence by a continued 

 force, such, for instance,, as what we commonly conceive gravity 

 to be, urging it in any direction ; then, after it has been impelled 

 forward for any length of time by this force, and has acquired a 

 certain momentum, let it be met by another hard body, moving 

 uniformly v^^ith an equal momentum in the opposite direction ; 

 and by our laws of collision, it will receive such a change in its 

 motion by the contact as will give it an equal and opposite 



