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HYPOTHESES OF DYNAMICS. 11 



illustrative comments by saying : " This law holds also in eases of attraction, as will be 

 proved (probabilur) in the following Scholium." The fact that his third law states action 

 and reaction to be equal and opposite bv\t says nothing as to their being in the same 

 straight line, forms corroborative evidence that he regarded his law as applicable directly 

 to contact actions only. For in such actions it would follow, from the opposition of 

 action and reaction, that they must be in the same straight line. 



It would thus appear that Newton regarded the application of the third law to at- 

 tractions as capable of deduction. If so, the argument by which the deduction is made 

 is as follows : — " In attractions I prove the law briefly in this way. Imagine any 

 obstacle interposed between any two mutually attracting bodies A and B, preventing 

 their coming together. If either of the bodies, say A, is attracted more strongly towards 

 the other, B, than B is towards A, the obstacle will have a greater pressure exerted upon 

 it by A than by B, and will not therefore remain in equilibrium. The greater pressure 

 will prevail and will cause the system of the two bodies and the obstacle to move in a 

 straight line directed towards B, and to go with an ever-increasing velocity in free space 

 to infinity. This is absurd and contrary to the first law. For by the first law the system 

 ought to maintain its state of rest or of uniform motion in a straight line, and therefore 

 the bodies will exert equal pressures on the obstacle and therefore attract one another 

 equally." ' Then follow the description of an experiment by which this result is tested 

 in the case of a system of bodies which included a luagnet and a piece of iron, and an 

 application of the above argument in the particular case of the gravitational attraction 

 between two portions of the earth. 



This argument contains two assumptions. First, it assumes the applicability of the 

 third law to contact actions. Immediately before giving this argument Newton had 

 described his experiments on the impact of spheres by which he had verified its applica- 

 bility in such cases. In the argument itself he refers to the contact stresses between the 

 obstacle and the attracting bodies ; and his statement that with the assumed inequality 

 in the action and reaction of the attraction, the system must haA'e an acceleration, implies 

 that in the case of the contact stresses action and reaction were taken to be equal. Even, 

 therefore, if Newton's argument be considered sound, the third law, as a whole, is not 

 shown to be capable of deduction, but only its applicability to attractions. 



The second assumption, however, seems to me to vitiate the argument, viz., the 

 assumption that the acceleration of a system of attracting bodies acted upon by no 

 external forces is inconsistent with the first law. That Newton himself regarded the 

 first law as directly applicable to single bodies only is obvious from the fact that in his 

 comment on it he illustrates it by reference to single bodies only, and from the further 

 fact that in the fourth corollary to the laws of motion he deduces the law of the con- 



' In attractionibus rem sic breviter ostendo. Corporibus duobus quibisvis A, B se mutuo trabentibus, concipe 

 obstaculum quodvis interponi, quo congressus eorum impediatur. Si corpus alterutrum A magis trahitur versus 

 corpus alterum B, quam illud alterum B in prius A, obstaculum magis urgebitur pressione corporis A quam 

 pressione corporis B ; proindeque non manebit in sequilibrio. Prsevalebit pressio fortior, facietque ut systema 

 corporum duorum et obstaculi moveatur in directum in partes versus B, motuque in spatiis liberis semper accele- 

 rata abeat in infinitum. Quod est absurdiim et legi primœ i;ontrarium. Nam per legem primam debebit systema 

 perseverare in statu suo quiescendi vel movendi uniformiter in directum, proindeque corpora sequaliter urgebunt 

 obstaculum, et idcirco sequaliter trahentur in invicem." — Principia : Scholium to Axiomata. 



