80 THE PRINCIPLES OF SCIENCE. 



that there is any inexactness in the laws of nature. We 

 may even discover a law which we believe to represent 

 the action of forces with perfect exactness. The mind 

 may seem to pass in advance of its data, and choose out 

 certain numerical results as absolutely true. We can 

 never really pass beyond our data, and so far as assu mp- 

 tion enters in, so far want of certainty will attach to our 

 conclusions ; nevertheless we may in many cases rightly 

 prefer a probable assumption of a precise law to numerical 

 results, which are at the best only approximative. We 

 must accordingly draw a strong distinction between the 

 laws of nature which we believe to be accurately stated in 

 our formulas, and those to which our statements only 

 make an approximation, so that at a future time the law 

 will be differently stated. 



The law of gravitation is expressed in the form 



F = -jp-, meaning that gravity is proportional directly to 



the product of the gravitating masses, and indirectly to the 

 square of their distance. The latent heat of steam, again, 

 is expressed by the equation log F = a + ba l + c/3', 

 in which are five quantities a, b, c, a, /3, to be deter- 

 mined by experiment. Now there is every reason to 

 believe that in the progress of science the law of gravity 

 will remain entirely unaltered, and the only effect of 

 further inquiry will be to render it a more and more 

 probable expression of the absolute truth. The law of 

 the latent heat of steam, on the other hand, will be 

 modified by every new series of experiments, and it may 

 not improbably be shown that the assumed law can never 

 be made to agree with the results of experiment. 



Philosophers have by no means always supposed that 

 the law of gravity was exactly true. Newton, though he 

 had the highest confidence in its truth, admitted that 

 there were motions in the planetary system which he 



