REMAINING LAWS OF NATURE. 159 



geometry, questions of quality are scarcely ever independent of 

 questions of quantity, may be seen from the most familiar 

 phenomena. Even when several colours are mixed on a 

 painter's palette, the comparative quantity of each entirely 

 determines the colour of the mixture. 



With this mere suggestion of the general causes which 

 render mathematical principles and processes so predominant 

 in those deductive sciences which afford precise numerical 

 data, I must, on the present occasion, content myself: refer- 

 ring the reader who desires a more thorough acquaintance 

 with the subject, to the first two volumes of M. Comte's 

 systematic work. 



In the same work, and more particularly in the third 

 volume, are also fully discussed the limits of the applicability 

 of mathematical principles to the improvement of other 

 sciences. Such principles are manifestly inapplicable, where 

 the causes on which any class of phenomena depend are so 

 imperfectly accessible to our observation, that we cannot as- 

 certain, 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 is likely to be ; or lastly, 

 where the causes themselves are in a state of perpetual fluctu- 

 ation ; as in physiology, and still more, if possible, in the 

 social science. The mathematical solutions of physical ques- 

 tions become progressively more difficult and imperfect, in 

 proportion as the questions divest themselves of their 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, "notwithstanding 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 



