10 Prof. Oliver Lodge on 



can be dissected bit by bit without ceasing to be a system 

 within the scope of the first law, it follows that no stress can 

 contain an unbalanced force or couple. 



If the law be doubted for the case of a pair of bodies attract- 

 ing each other from a distance, Newton says* (virtually): — 

 Jam the bodies apart with a rigid obstacle, then you have re- 

 duced their action to contact action ; and since you have a 

 balanced stress at each point of contact, and likewise between 

 the ends of the introduced obstacle, it follows that the attract- 

 ing forces of the distant bodies are also balanced. 



Now Dr. MacGregor's objections are (1) that Newton's 

 proof only aims at extending the law from contact action to 

 actions across a distance, while for contact action he is con- 

 tent to assume it as an axiom or to verify it by experiment ; 

 and (2) that the proof breaks down for a particle or single 

 body which cannot be analysed into parts. 



It is quite possible that Newton thought it best to state his 

 third law as an axiom ; because the fact that the centre of 

 mass of a complex system of bodies obeys the first law is 

 hardly an experience that can be confidently appealed to, even 

 though all the bodies are in contact. That fact and the third 

 law are intimately connected, but whichever is the simpler had 

 better be stated as the axiom, and the other be made a deduc- 

 tion from it. Thus the centre of mass statement follows 

 from the third law, and so very likely Newton preferred to 

 arrange it. It is frequently difficult to know which of two 

 very simple statements is the more axiomatic ; and methods 

 of proof are notoriously susceptible of considerable variation. 

 The important thing is to notice the link or tie between two 

 facts, to show that they mutually strengthen each other, not 

 to pretend that one is beneath the other and supports it. 



Attempts to build even so simple a structure as geometry 

 in the form of a single column, stone upon stone, have been 

 found artificial and in the long run impracticable. An en- 

 larged basis of direct appeal to experience is not only 

 necessary but desirable, and all fundamental matters should 

 be kept low down, as nearly in contact with first principles 

 as possible. 



The so-called deduction of the third law from the first or 

 second is important as a clear and strong cross-connexion 

 between the two things, and need not be considered as a 

 rigorous proof. It is rigorous enough if the premisses are 

 granted, but if not, then there is a certain outstanding axio^ 

 matic or unprovable character to be shared between them ; 

 but this outstanding portion is, by reason of the cross-connexion, 



* Principia, Scholium to Axiomata, 



