MECHANICS AND PHYSICS 195 



based his theories on certain simple laws of equilibrium, 

 taken as self-evident. Thus he made the science of 

 equilibrium an independent science which owes nothing 

 to the other branches of physics ; he established 

 statics. 1 But the rigour and lucidity which he obtained 

 were bought at the price of a real sacrifice of the 

 generality and fecundity of the method. 



The laws which govern the equilibrium of two heavy 

 bodies suspended from the arms of a lever have been 

 deduced from hypotheses peculiar to this problem. 

 They are of no use when there arises a case of equili- 

 brium in entirely different conditions ; when analysed, 

 they cannot give any indication as to the choice of 

 new hypotheses. So that, when Archimedes studied 

 the equilibrium of floating bodies, he was obliged to 

 have recourse to principles which have no analogy 

 to the requirements of the theory of the lever. 



As M. Duhem remarks : " Although an admirable 

 method of demonstration, the path followed by 

 Archimedes in mechanics is not a method of invention ; 

 the certainty and lucidity of his principles are largely 

 due to the fact that they are gathered, so to speak, 

 from the surface of phenomena and not dug out from 

 the depths." 2 



It seems to us that this is the reason why the 

 demonstration of Archimedes is not entirely satisfactory 

 even from a logical point of view, for it finally comes 

 back to the disguised verification of a fact. 



Doubtless, by virtue of the principle of symmetry, 

 we can logically maintain that two equal weights A 

 and B suspended from two equal arms of a lever will 

 be in equilibrium ; but we cannot know a priori 

 what will happen if we replace one of these weights 

 A by two smaller weights a and a 2 which are in 

 equilibrium and whose sum is equal to A. Experience 



x n Duhem, Origines, I, p. 11. 

 % Ibid., p. 12. 



