452 THE PRINCIPLES OF SCIENCE. 



general public into the fallacious notion that mathematics 

 is a perfect science, which accomplishes what it under- 

 takes in a complete manner. On the contrary, it may be 

 said that if a mathematical problem were selected by pure 

 chance out of the whole variety which might be proposed, 

 the probability is infinitely slight that a human mathe- 

 matician could solve it. Just as the numbers we can count 

 or frame to the mind are literally nothing compared with 

 the numbers which might exist, so the whole accomplish- 

 ments of a Laplace or a Lagrange are, as it were, the 

 little corner of the multiplication table, which has really 

 an indefinite extent. 



I have sufficiently pointed out that the rude character 

 of all our observations prevents us from being aware of 

 the existence of the greater number of effects and actions 

 of nature. It must be added that, if we perceived them, 

 we should usually be incapable of including them in our 

 theories from want of mathematical power. Some persons 

 may be surprised that though nearly two centuries have 

 elapsed since the time of Newton's discoveries, we have 

 yet no general theory of molecular action. Some approxi- 

 mations have been made towards such a theory. Joule 

 and Clausius have measured the velocity of gaseous 

 atoms, or even determined the distance between the col- 

 lision of atom and atom. Sir W. Thomson has approxi- 

 mated to the number of atoms in a given bulk of sub- 

 stance. Rankine has formed some reasonable hypotheses 

 as to the actual constitution of atoms, but it would be a 

 mistake to suppose that these ingenious results of theory 

 and experiment form any appreciable approach to a com- 

 plete solution of molecular motions. There is every 

 reason to believe, judging from the spectra of the elements, 

 and from other reasons, that even chemical atoms are very 

 complicated structures. An atom of pure iron is probably 

 a vastly more complicated system than that of the planets 



