370 PHILOSOPHICAL TRANSACTtONS. [aNNO 17/8. 



this doctrine with the greatest simplicity and convenience. This part of rational 

 mechanics however is not yet generally understood, as we may fairly presume 

 from the difference of opinion which still subsists among the learned. I freely 

 own, it appears tome, that no new experiments are wanting; no new geome- 

 trical reasonings or constructions: the improved parts of geometry have been 

 already applied to the theory of motion in numberless cases, and a variety of 

 well attested experiments have been clearly explained to us by authors. The 

 laws of motion, in certain cases, are incontestible, and no author of eminence 

 contradicts them : it is from a mistaken application of these laws, that a dif- 

 ference of opinion has arisen. It is obvious, that tiie laws of motion, as des- 

 cribed by Sir Isaac Newton, may, in a certain sense, be founded on experiment; 

 and yet, if they are extended to cases where they cannot be applied, the conclu- 

 sions must still be erroneous. My design in these pages is to point out dis- 

 tinctly what is real in this difference of opinion from what is merely verbal, and 

 to explain the causes of it. This, which [)erhaps will appear to have never been 

 done with sufficient precision, seems to be the most effectual way of preventing 

 mistakes. Geometry and algebra will lead us wrong, if our principles are ill 

 founded : experiment itself, if we are not extremely careful, will deceive us in 

 forming a general deduction, or what is called a law of nature. The contro- 

 versial writings of the most able authors will embarrass and perplex our judge- 

 ments ; but when we have once discovered the grounds of their mutual mistakes 

 and misapprehensions, there is reason to think, that we shall both understand 

 the subject better than we did before, and be more on our guard for the 

 future. 



The first law of motion, as expressed by Sir Isaac Newton, is unexception- 

 able: nobody denies that a body perseveres in a state of rest or uinform motion 

 in a right line, till affected by some external influence. It is the third law of 

 motion which has produced all this confusion and perplexity. " Actioni con- 

 trariam semper et sequalem esse reactionem : sive corporum duorum actiones in 

 se mutuo semper aequales et in partes contrarias dirigi." These words of Sir 

 Isaac Newton convey to us as clear an idea as can possibly be conceived with so 

 much conciseness. It must however be confessed, that his illustration is not so 

 very perspicuous. To say, that when a man presses a stone with his finger, his 

 finger is equally pressed ; and when a liorse draws a stone by a cord, the horse 

 is drawn equally backwards towards the stone ; is a most indistmct and popular 

 way of speaking, and can never make evident what was before not understood. 



Some useful writers, wlio fiave copied after Sir Isaac Newton, have talked in 

 the same way ; and only increased the ambiguity by being more diffuse. Mr. 

 Maclaurin himself, who engaged very warmly in this debate with the foreign 

 niathiniaticians, and who, to say the truth, seems to have understood the 



