VOL. LXVIII.3 PHILOSOPHICAL TRANSACTIONS. 371 



nature of the controversy better than any one else, is frequently unguarded in 

 his expression. In chap. 2, book 2, of his account of Newton's discoveries, he 

 is describing the laws of motion for the first time, and one naturally expects a 

 more than ordinary precision and exactness. There he blames, very justly, the 

 opposers of the Newtonian definition of motion for mistaking the direction in 

 which the motion, lost or communicated, ought always to be estimated. But in 

 p. 122, 8vo. edit, he thus expresses himself: "When two bodies meet, each 

 endeavours to persevere in its state, and resists any change ; and because the 

 change, which is produced in either, may be equally measured by the action 

 which it exerts on the other, or by the resistance which it meets with from it, it 

 follows, that the changes produced in the motions of each are equal ; but are 

 made in contrary directions." I cannot possibly conceive, that so skilful and 

 accurate a philosopher could believe, that the 3d law of motion was an inference 

 of reason, exclusive of all experiment ; and yet, if words have any meaning at 

 all, the above quotation inclines us to think so. " It is true, the change which 

 is produced in either body may be measured by the action which it exerts on the 

 other, or by the resistance which it meets with from the same: but what are we 

 to understand by action or resistance, until they are explained by more intelli- 

 gible terms .-' or, when they are explained by terms which do not necessarily 

 imply the same thing, how do we know that their measures are equal, or that 

 they are made in contrary directions, until these truths are established by ex- 

 periments ? A law of nature is not merely a deduction of reason : it must be 

 proved, either at once and directly, by some simple and decisive experiments ; or 

 if that cannot be done, by such experiments as enable us to collect its existence 

 by the assistance of geometry. However obvious these reflections may appear, 

 I thought it necessary to take notice of Maclaurin's assertion ; because in conse- 

 quence of that and similar expressions, young philosophers are extremely puzzled 

 in the beginning of their studies, and because I have known some, who are 

 more experienced, affirm, that the od law of motion is nothing more than a 

 definition. I now proceed to the consideration of particular cases. 



Case 1 . — Suppose a and b to represent the magnitudes of two spherical 

 boilies, and a and b their respective velocities in the same direction ; suppose a 

 to be greater than /', then a will overtake b ; and if the bodies are non-elastic, 

 they will proceed together in the same direction as one mass : if they are per- 

 fectly elastic, whatever effect has already been produced by the collision, will be 

 repeated ; and, because in the first case there is no relative velocity after the 

 stroke, in the 2d the relative velocity before and after the stroke will be the same, 

 and in contrary directions ; and in either case, the motion lost by the striking 

 body is found to be always equal to the motion communicated to b, and in a 

 contrary direction. In this sense action is equal to reaction ; and every experi- 



3 B 2 



