idea which, the author observes, arises naturally from the daily oc- 

 cupations of men, since any quantity of work performed is always 

 estimated by the extent of effect resulting from their exertions. Thus 

 it is well known that the raising of any great weight 40 feet would 

 require four times as much labour as would be requisite to raise an 

 equal weight 1 feet. And if weights so raised were suffered to fall 

 freely, the squares of the velocities acquired would be in proportion 

 to the quantity of labour, that is, as 4 to 1 ; and if their forces were 

 employed in driving piles, the effects produced would be in that same 

 ratio. 



This species of force has, by Smeaton, been aptly denominated 

 mechanic force ; and when by force of percussion is meant the quan- 

 tity of mechanic force which a body in motion can exert, the author 

 apprehends it cannot be controverted that the said force is in pro- 

 portion to the magnitude of the body, and the square of its velocity 

 jointly. 



But of this force Newton nowhere treats, and consequently gives 

 no definition of it ; on the contrary, in the preface to the Principia, 

 he expressly says, that he writes " de potentiis non manualibus, sed 

 naturalibus ;" and again, in the Scholium to the laws of motion, he 

 says, " Caeterum mechanicam tractare, non est hujus instituti." 



It is also evident, that in the third law of motion, when Newton 

 asserts that action is equal to reaction, he means only that the mov- 

 ing forces, or pressures opposed to each other, are necessarily equal. 

 Other persons, however, have interpreted the third law differently, 

 and conceive also a species of accumulated force, which is capable of 

 resisting a given pressure, during a time that is proportional to the 

 momentum, or quantitas motds. 



If it be of any real utility to give the name of force to such a com- 

 plex idea of vis matrix continued for any certain time, the author re- 

 commends that it should be always distinguished by some such ap- 

 pellation as momentous force, as he apprehends that, for want of this 

 distinction, both writers and readers of disquisitions upon this subject 

 have confounded and compared together vis matrix, momentum, and 

 vis mechanica ; quantities that are all of them totally dissimilar, and 

 bear no more comparison to each other than lines to surfaces, or sur- 

 faces to solids. 



In practical mechanics, however, it is at least very rarely that that 

 momentum of bodies is an object of consideration ; since the extent 

 and value of any effect to be produced depends upon the quantitas 

 mechanica of the force applied, or in other words, the space through 

 which any moving force is exerted. 



Dr. Wollaston, in the next place, compares the forces of the dif- 

 ferent bodies by means which he is inclined to think have not been 

 taken notice of by any writer on this question ; and he shows, that 

 when the whole energy of a body A is employed without loss, in 

 giving velocity to a second body B, the impetus which B receives is, 

 in all cases, equal to that of A, the squares of their velocities being 

 in the reciprocal ratio of the bodies. 



