454 THE PRINCIPLES OF SCIENCE. 



computers had to solve simultaneous equations involving 

 seventy-seven unknown quantities. The reduction of the 

 levellings again required the solution of a system of 

 ninety-one equations. But these vast calculations present 

 no approach whatever to 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 abso- 

 lutely rigid, but it is expressly remarked by Forbes", 

 that not even an approximate solution of the mathe- 

 matical conditions of such a moving mass can yet be pos- 

 sible. ' 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 practicable. But the very 

 simplest problem in appearance will often give rise to 

 impracticable calculations. Mr. Todhunter seems to 

 blame Condorcet, because in one of his memoirs he men- 

 tions a problem to solve which would require 



2 



successive integrations. Now if our mathematical sciences 

 are to pretend to cope with the problems which await solu- 

 tion, we must be prepared to effect an unlimited number 

 of successive integrations ; yet at present, and almost 

 beyond doubt for ever, the probability that even a single 

 integration, taken haphazard, will be found to come within 

 our powers is exceedingly small. 



In some passages of that most remarkable work, the 



n ' Philosophical Magazine,' 3rd Series, vol. xxvi. p. 406. 

 o ' History of the Theory of Probability,' p. 398. 



