the Foundations of Dynamics. 3 



than any other equation. The improved statement of Van 

 der Waals, adding a term to p and subtracting one from 

 v, was another distinct service, and enabled a mass of experi- 

 mental evidence concerning the structure of liquids to be 

 conveniently and simply smnmarised. In its turn, however, 

 it has had to give place to more complex empirical statements, 

 and the complete law has not yet appeared. 



The examples I have chosen, one of a precise, the other of 

 an approximate, simple statement, are not indeed of the nature 

 of axioms ; and it may be held that it would be unsatisfactory 

 to base our axioms on such a tentative sort of footing. 



And yet what other course is open ? Truly axiomatic state- 

 ments can only be effectively made concerning things of 

 which the race has had a long course of experience, — things 

 to which they have grown familiarly accustomed. If they 

 can be actually proved, they are theorems, not axioms. 



The setting forth of an axiom I regard as a kind of challenge, 

 equivalent to the statement: — "Here is what seems to me to be 

 a short summary of a universal truth ; disprove it if you can. 

 I cannot prove it, it is too simple and fundamental for proof, 

 I can only adduce hundreds of instances where it holds. I 

 have indeed critically examined a few special cases and never 

 found it fail, but a single contrary instance will suffice to 

 overthrow it; hence, though it be hard to prove, yet if not true 

 its disproof should be easy : find that contrary instance if 

 you can." If no disproof is forthcoming for a few generations, 

 the axiom is likely to get accepted. Meanwhile its undeniable 

 simplicity is a practical advantage, even though in the course 

 of centuries a flaw or needful modification in its statement 

 may be discovered. 



This is the kind of basis on which such a law as that of the 

 Conservation of Energy or the Conservation of Matter rests. 

 That the perpetual motion is impossible, that matter is in- 

 destructible, that energy never diminishes in the act of transfer, 

 all these must be regarded as generalizations based on a great 

 series of experiments, some consciously directed to the upset- 

 ting of one or other of the laws if possible, some aimed at 

 establishing them, but most of a non-contentious and collateral 

 character. If we are challenged to produce direct evidence 

 that in any given chemical reaction the mass of the reagents 

 is unchanged, not only in the initial and final stages but at 

 every stage of the process, the proof may be exceedingly 

 difficult. Heat is liable to be developed which would inter- 

 fere with delicate weighings, and the reaction challenged may 

 be an explosive or otherwise inconvenient one. But we do 

 not attempt the proof, we shift the burden on to the shoulders 



B2 



