the Conservation of Force. 87* 



are commonly made use of in the nomenclature of science, are 

 calculated to convey the idea that these are three diflferent forms of 

 one and the same thing ; but we must not suffer ourselves to fall 

 into this delusion ; we must always remember that they are three 

 totally different things. We call the siim of the motion actually 

 existing vis viva. We denote it as force, as cause of motion, 

 because it not only continues to act in accordance with the law 

 of inertia, but because it can be communicated to other bodies, in- 

 asmuch as motionless bodies can be set in motion by moving ones. 



Tension is the term applied to the cause of motion still to be 

 disposed of, which itself is not motion, wholly regardless of the 

 time in which it can generate or produce motion. Accelerating 

 force is the term applied to the increase of velocity attained by 

 a mass, or which it can attain, in an infinitely short time, divided 

 by the length of the length of this infinitely small interval. The 

 accelerating force in a system is therefore dependent at any mo- 

 ment, first on the masses which ai-e, or are to be, set in motion, 

 and the velocities which they may have already attained ; and 

 secondly, on the velocity with which tension is, or may be, trans- 

 formed into vis viva. If the accelerating force is to remain con- 

 stant for every single molecule, it is necessary that the velocity 

 with which the molecule transforms tension into vis viva, or vis 

 viva into tension, when divided by the product of its mass and 

 velocity, should give a constant quotient. 



Keeping this always in view, it will appear plain that the 

 accelerating force may increase or diminish, without at all inter- 

 fering with the principle that the sum of the tensions, added to 

 the sum of the vires viva, always gives the same quantity ; and 

 we see that by the removal of two molecules from each other no 

 portion of the force is destroyed, the indestructibility of which is 

 affirmed by the principle of the conservation of force. 



Let us suppose a portion of the masses which gravitate towards 

 each other to be destroyed ; then certainly not only accelerating 

 force, but also, according to circumstances, a portion of the ten- 

 sion or of the vis viva, or of both, would be destroyed -. but this 

 only confirms us in our way of viewing the subject. The law of 

 the indestructibility of matter has been proved as universally 

 valid as that of the conservation of force. That the destruction 

 of the one should involve that of the other, only shows us that 

 both stand in intimate connexion with each other, and proves 

 that we arc right in placing the cause of the notion of gravity 

 in the masses themselves, and not in the space between them. 



Thus in all that has been hitherto said, so far as my conscious- 

 ness reaches, so far as I am capable of distinguishing true from 

 false, and like from unlike, all known facts are brought into 

 complete liarmony with our laws of thought when wc suppose 

 forces, as the causes of phsenoraena, to reside in the masses, the 



