Hypotheses of Dynamics. 245 



out in detail. If I understand it aright (it is so condensed 

 as to be somewhat obscure) it is as follows : — Let A and B 

 be two mutually attracting bodies, and let F and F' be the 

 attractions on A and B respectively. Imagine any obstacle, 

 0, interposed between them so as to prevent their approach. 

 Then, provided the attractional stress between A and B be 

 independent of the existence of other stresses between them 

 and other bodies (assumption No. 1, the " physical in- 

 dependence " of stresses), F and F' will still be the attractions 

 on A and B respectively. Let R and R' be the action on A 

 and the reaction on 0, respectively, of the contact stress 

 between A and ; and let Rj and R x ' be the corresponding 

 forces for B and respectively. Since there are no external 

 forces acting on the system of A, B, and 0, it follows from 

 the law of the conservation of the motion of the centre of 

 mass* (assumption No. 2, which we may call the generalized 

 first law of motion), that the centre of mass of A, B, and 

 will move uniformly. If A, B, and be rigid bodies (this 

 restricts the argument to the case of attracting bodies kept at 

 a constant distance from one another) O's motion will also be 

 uniform. Hence the resultant force on must, by the first 

 law of motion, which is a particular case of the generalized 

 first law, be zero. But, by the law of the composition of 

 forces, which is a deduction from the second law of motion 

 (assumption No. 3), this resultant force is R' + R/f. Hence 

 R/= — R 1 '. Now, by the third law of motion regarded as 

 applicable to contact stresses (assumption No. 4) we have 

 R = — R' and R x = — R/. Hence R = — R x . But the motions 

 of A and B must be uniform for the same reason as that of 

 0. Hence by the first and second laws as above, F + R = 

 and F , + R 1 = 0. Hence also F=— F'. — If this is a correct 

 statement of Newton's argument it is obvious that it does not 

 make the deduction which is claimed for it J . 



obstaculuni magis urgebitur pressione corporis A quam pressione corporis 

 B ; proindeque non inanebit in aequilibrio. Praevalebit pressio fortior, 

 facietque ut systema corporum duorum et obstaculi moveatur in directum 

 in partes versus B, motuque in spatiis liberis semper accelerate abeat in 

 infinitum. Quod est absurdum et legi primee contrarium. Nam per legem 

 primam debebit systema perseverare in statu suo quiescendi vel movendi 

 uniformiter in directum, proindeque corpora sequaliter urgebunt obsta- 

 culurn, et idcirco asqualiter trahentur in invicem. — Principia : Scholium 

 to Axiomata. 



* Newton bad previously (Cor. 4 to Axiomata) proved this law, assum- 

 ing, in the proof, the third law as applicable to all stresses. 



t I assume, as Newton does, for simplicity, that the forces are all in 

 one straight line. 



\ See Lange, Bewegungsbegriff, p. 57. 



