756 THE PRINCIPLES OF SCIENCE. [chap. 



There is every reason to believe, judging from the spectra 

 oi' the elements, their atomic weights and other data, that 

 cliemieal atoms are very complicated structures. An atom 

 of pure iron is probably a far more complicated system 

 than that of the planets and 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 great number of such stellar 

 systems united in regular order, each bounded by the other, 

 communicating with it in some manner yet wholly incom- 

 prehensible. What are our mathematical powers in com- 

 parison with this problem ? 



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 calcu- 

 lations 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 produce considerable 

 effects upon each other. There is reason to believe that 

 each constituent of a chemical atom goes through an orbit 

 in the millionth part of the twinkling of an eye. In each 

 revolution it is successively or simultaneously under the 

 influence of many other constituents, or possibly comes into 

 collision with them. It is no exaggeration to say that 

 mathematicians have the least notion of the way in which 

 they could successfully attack so difficult a problem of 

 forces and motions. As Herschel has remarked,^ each of 

 these particles is for ever solving differential equations, 

 which, if written out in full, might belt the earth. 



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 principal 

 triangulation occupied twenty calculators during three or 

 four years, in the course of which the computers had to 

 solve simultaneous equations involving seventy-seven 

 imknown quantities. The reduction of the levellings 

 required the solution of a system of ninety-one equations. 

 But these vast calculations present no approach whatever to 



' FnviUiar Lectures on Scientijlc Subjects, p. 458. 



