xxxi.] LIMITS OF SCIENTIFIC METHOD. 767 



what would be requisite for the complete treatment of any 

 one physical problem. The motion of glaciers is supposed 

 to be moderately well understood in the present day. A 

 glacier is a viscid, slowly yielding mass, neither absolutely 

 solid nor absolutely rigid, but it is expressly remarked by 

 Forbes, 1 that not even an approximate solution of the 

 mathematical conditions of such a moving mass can yet be 

 possible. " Every one knows," he says, " that such problems 

 are beyond the compass of exact mathematics ; " but though 

 mathematicians may know this, they do not often enough 

 impress that knowledge on other people. 



The problems which are solved in our mathematical 

 books consist of a small selection of those which happen 

 from peculiar conditions to be solvable. But the very 

 simplest problem in appearance will often give rise to 

 impracticable calculations. Mr. Todhunter 2 seems to blame 

 Condorcet, because in one of his memoirs he mentions a 

 problem to solve which would require a great and imprac- 

 ticable number of successive integrations. Now, if our 

 mathematical sciences are to cope with the problems which 

 await solution, we must be prepared to effect an unlimited 

 number of successive integrations; yet at present, and 

 almost beyond doubt for ever, the probability that an 

 integration taken haphazard will come within our powers 

 is exceedingly small. 



In some passages of that remarkable work, the Ninth 

 Bridgewater Treatise (pp. 113 115), Babbage has pointed 

 out that if we had power to follow and detect the minutest 

 effects of any disturbance, each particle of existing matter 

 would furnish a register of all that has happened. "The 

 track of every canoe of every vessel that has yet disturbed 

 the surface of the ocean, whether impelled by manual force 

 or elemental power, remains for ever registered in the future 

 movement of all succeeding particles which may occupy its 

 place. The furrow which it left is, indeed, instantly filled 

 up by the closing waters ; but they draw after them other 

 and larger portions of the surrounding element, and these 

 again, once moved, communicate motion to others in endless 

 succession." We may even say that " The air itself is one 

 vast library, on whose pages are for ever written all that 



1 Philosophical Magazine, 3rd Series, vol. xxvi. p. 406. 



2 History of the Theory of Probability, p. 398. 



