NATURAL SCIENCE TO GENERAL SCIENCE. 19 



applied mathematics, especially in mathematical physics, in- 

 cluding, of course, physical astronomy. From the time when 

 Newton discovered, by analysing the motions of the planets on 

 mechanical principles, that every particle of ponderable matter 

 in the universe attracts every other particle with a force vary- 

 ing inversely as the square of the distance, astronomers have 

 been able, in virtue of that one law of gravitation, to calculate 

 with the greatest accuracy the movements of the planets to the 

 remotest past and the most distant future, given only the posi- 

 tion, velocity, and mass of each body of our system at any one 

 time. More than that, we recognise the operation of this law 

 in the movements of double stars, whose distances from us are 

 so great that their light takes years to reach us; in some 

 cases, indeed, so great that all attempts to measure them have 

 failed. 



This discovery of the law of gravitation and its consequences 

 is the most imposing achievement that the logical power of the 

 human mind has hitherto performed. I do not mean to say 

 that there have not been men who in power of abstraction have 

 equalled or even surpassed Newton and the other astronomers, 

 who either paved the way for his discovery, or have carried it 

 out to its legitimate consequences; but there has never been 

 presented to the human mind such an admirable subject as 

 those involved and complex movements of the planets, which 

 hitherto had served merely as food for the astrological super- 

 stitions of ignorant star-gazers, and were now reduced to a single 

 law, capable of rendering the most exact account of the minutest 

 detail of their motions. 



The principles of this magnificent discovery have been suc- 

 cessfully applied to several other physical sciences, among which 

 physical optics and the theory of electricity and magnetism are 

 especially worthy of notice. The experimental sciences have 

 one great advantage over the natural sciences in the investiga- 

 tion of general laws of nature : they can change at pleasure the 

 conditions under which a given result takes place, and can thus 

 confine themselves to a small number of characteristic instances, 

 in order to discover the law. Of course its validity must then 

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