Dr. C. K. Akin on the History of Force. 471 



" Si sestimetur agentis actio ex ejus vi et velocitate conjunctim, 

 et similiter resistentis reactio pestimetur conjunctim ex ejus partium 

 singularum velocitatibus et viribus resistendi ab earum attritione, 

 coheesione, pondere, et acceleratione oriundis ; erunt actio et reactio 

 . . . sibi invicem semper sequales." 



The dots (. . .), indicating an elision, stand for thewords in omni in- 

 strumentorum usu. Now, I cannot help thinking that the omis- 

 sion of these words completely alters the meaning of the above 

 passage. Newton, in the passages preceding the above, is bent 

 upon showing that the effective force of a moving system may 

 be measured by its momentum (mv) ; and he states that this as- 

 sumption is proved by the fact that, in machines, the moving 

 force may be so estimated, — the velocity being always inversely 

 proportional to the mass or inertia, after the resistance has been 

 subtracted. " Cseterum mechanicam tractare," Newton adds, "non 

 est hujus instituti. Hisce volui tan turn ostendere, quam late 

 pateat quamque certa sit lex tertia motus," i. e., that action is 

 always opposed by an equal reaction. Yet this law, however 

 important, cannot but be considered as a corollary from, rather 

 than equivalent to, the principle of the conservation of force itself. 

 Moreover, in the same scholium occurs a passage relative to the 

 state of imperfectly elastic bodies after collision, which will 

 scarcely be considered to favour the advocacy of Prof. Tait : — 



"A congressu et collisione corporum nunquam mutabatur quan- 

 titas motus, quae ex summa motuum conspirantium et differentia 

 contrariorum colligebatur .... Porro ne quis objiciat regulam .... 

 prsesupponere corpora vel absolute dura esse, vel saltern perfecte 

 elastica .... addo quod ... si regula ilia in corporibus non perfecte 

 duris tentanda est, debebit solummodo reflexio minui in certa pro- 

 portione pro quantitate vis elasticse." 



How does Newton account for, in this case, the velocities lost ? 

 But doubtful, if not impossible, as Newton's authorship of the 

 principle in question appears from the above passages, Query 

 31 in his ' Optics' will be found still less compatible with it. 

 Perhaps the remark of John Bernoulli concerning parts of this 

 query — " ridiculum dicerem, si a tanto Viro non scripta essent " 

 [Opera, vol. iii. p. 253) — may be rather too severe, yet its con- 

 tents will be found difficult to reconcile with the assertion of 

 Prof. Tait :— 



" Some other principle [than inertia] was necessary for putting 

 bodies into motion ; and now they are in motion, some other prin- 

 ciple is necessary for conserving the motion. For .... it appears, 

 that motion may be got or lost. But .... motion is more apt to be 

 lost than got, and is always upon the decay. For .... if two equal 

 bodies [e.g.~\ meet directly in vacuo, they will, by the laws of motion, 

 stop where they meet, and lose all their motion . . . unless they be 



