REMAINING LAWS OF NATURE. 179 



third volume, are also fully discussed the necessary 

 limits of the applicability of mathematical principles 

 to the improvement of other sciences. Such prin- 

 ciples are manifestly inapplicable, where the causes on 

 which any class of phenomena depend are so imper- 

 fectly accessible to our observation, that we cannot 

 ascertain, by a proper induction, their numerical laws ; 

 or where the causes are so numerous, and intermixed 

 in so complex a manner with one another, that even 

 supposing their laws known, the computation of the 

 aggregate effect transcends the powers of the calculus 

 as it is, or as it is ever likely to be ; or lastly, where 

 the causes themselves are in a state of perpetual fluc- 

 tuation, as in physiology, and still more, if possible, 

 in the social science. As M. Comte* well observes, 

 the mathematical solutions of physical questions 

 become progressively more difficult and more imper- 

 fect, in proportion as the questions divest themselves 

 of tjieir abstract and hypothetical character, and 

 approach nearer to the degree of complication actually 

 existing in nature ; insomuch that beyond the limits 

 of astronomical phenomena, and of those most nearly 

 analogous to them, mathematical accuracy is generally 

 obtained " at the expense of the reality of the inquiry :" 

 while, even in astronomical questions, *' notwithstand- 

 ing the admirable simplicity of their mathematical 

 elements, our feeble intelligence becomes incapable of 

 following out effectually the logical combinations of 

 the laws on which the phenomena are dependent, as 

 soon as we attempt to take into simultaneous con- 

 sideration more than two or three essential influences." 

 Of this, the problem of the Three Bodies has already 

 been cited by us, more than once, as a remarkable 



Cours de Philosophie Positive, iii., 414 416. 



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