RESULTS AXD LIMITS OF SCIENTIFIC METHOD. 453 



a 



nd their satellites. A compound atom may perhaps be 

 compared with a stellar system, each star a minor system 

 in itself. The smallest particle of solid substance will 

 consist of a vast number of such stellar systems united 

 in regular order, each bounded by the other, communi- 

 cating with it in some manner yet wholly imcomprehen- 

 sible. Now what are our mathematical powers in com- 

 parison with this problem 1 



After two centuries of continuous labour, the most 

 gifted men have succeeded in calculating the mutual 

 effects of three bodies each upon the other, under the 

 simple hypothesis of the law of gravity. Concerning 

 these calculations we must further remember that they 

 are purely approximate, and that the methods would not 

 apply where four or more bodies are acting, and all pro- 

 duce considerable effects each upon the other. There is 

 every reason to believe that each constituent of a chemical 

 atom must go through an orbit in the millionth part of 

 the twinkling of an eye, in which it successively or simul- 

 taneously is under the influence of many other consti- 

 tuents, or possibly comes into collision with them. It is, 

 I apprehend, no exaggeration to say that mathematicians 

 have scarcely a notion of the way in which they could 

 successfully attack so difficult a problem of forces and 

 motions. Each of these particles is for ever solving dif- 

 ferential equations, which, if written out in full, might 

 perhaps belt the earth, as Sir J. Herschel has beautifully 

 remarked 1 ". 



Some of the most extensive calculations ever made, were 

 those required for the reduction of the measurements 

 executed in the course of the Trigonometrical Survey of 

 Great Britain. The calculations arising out of the prin- 

 cipal triangulation alone occupied twenty calculators 

 during three or four years, in the course of which the 

 m ' Familiar Lectures on Scientific Subjects,' p. 458. 



