xxxi.J LIMITS OF SCIENTIFIC METHOD. 755 



understood and calculated ? How many further steps must 

 we take in the rise of mental ability and the extension of 

 mathematical methods before we begin to exhaust the 

 knowable ? 



I am inclined to find fault with mathematical writers 

 because they often exult in what they can accomplish, and 

 omit to point out that what they do is but an infinitely 

 small part of what might be done. They exhibit a general 

 inclination, with few exceptions, not to do so much as 

 mention the existence of problems of an impracticable 

 character. This may be excusable as far as the immediate 

 practical result of their researches is in question, but the 

 custom has the effect of misleading the general public into 

 the fallacious notion that mathematics is a perfect science, 

 which accomplishes what it undertakes in a complete 

 manner. On the contrary, it may be said that if a mathe- 

 matical problem were selected by chance out of the whole 

 number which might be proposed, the probability is in- 

 finitely slight that a human mathematician could solve it. 

 Just as the numbers we can count are nothing compared with 

 the numbers which might exist, so the accomplishments 

 of a Laplace or a Lagrange are, as it were, the little corner 

 of the multiplication-table, which has really an infinite 

 extent. 



I have pointed out that the rude character of our ob- 

 servations prevents us from being aware of the greater 

 number of effects and actions in nature. It must be added 

 that, if we perceive them, we should usually be incapable 

 of including them in our theories from want of mathe- 

 matical 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 approximations have been made 

 towards such a theory. Joule and Clausius have measured 

 the velocity of gaseous atoms, or even determined the 

 average distance between the collisions of atom and atom. 

 Thomson has approximated to the number of atoms in a 

 given bulk of substance. Eankine has formed some rea- 

 sonable hypotheses as to the actual constitution of atoms. 

 It would be a mistake to suppose that these ingenious 

 results of theory and experiment form any appreciable 

 approach to a complete solution of molecular - motions. 



3 c 2 



