302 On Machines hi General. 



tbese passive forces from which nolhing can be subtracfccJ 

 being always resisting, it is evident that the movement mnst 

 continually slacken : and from what we have said (XLV.), 

 we see that if bodies are not solicited by any motrix force, 

 the amount of the active forces will be reduced to nothing ; 

 i. e. the machine will be reduced to a state of rest, when 

 the momentum of activity, produced by the friction since 

 the commencement of the motion, will have beconie equal 

 to half the amount of the initial active forces: and if the 

 bodies are heavy, the motion will finish when the momen- 

 tum produced by the frictions shall be equal to half the 

 amount of the initial active forces, plus the half of the ac- 

 tive force which would take place if all the points of the 

 system had one conmnon velocity, equal to that which is 

 owing to the height of the point where the centre of gravity 

 was at the first instant of the motion, above the lowest point 

 to which it can descend : this is evident from (XLfl). 



It is easy to apply the same reasoning to the case of springs, 

 and in general to all cases in which the friction being sub- 

 tracted, the soliciting forces are obliged, in order to make 

 the machine pass from one position to another, to exercise 

 a momentum of activity as great as that which is produceti 

 bv the resisting forces when the machine returns from thia 

 last position to the former. 



The motion would end much sooner if some jicrcussion 

 toolc place, since the sum of the active forces is always di- 

 minished in such cases (XXIII). 



It is therefore evident, that we ouaht entirely to despair 

 of producino- what is called a perpetual motion, if it be true 

 that all the moving powers which exist in nu*ure are no- 

 thing else than aitractions., and tlial this force, as it should 

 seem, has a general property, that of being always the same 

 at equal distances between given bodies, i. e. of being a 

 futiction which only varies in cases where the distance of 

 these bodies itself varies. 



LXII. One general observation resulting from all that has 

 been said, is, that the kind of quantity to which I have given 

 the name of viomcvtum of actmly, performs a very conspi- 

 cuous part in the theory of machines in a slate of motion ; 



for 



1 



