xxi.] THEORY OF APPROXIMATION. 466 



Faraday, in one of his researches, expressly makes an 

 assumption of the same kind. Having shown, with some 

 degree of experimental precision, that there exists a simple 

 proportion between quantities of electrical energy and the 

 quantities of chemical substances which it can decompose, 

 so that for every atom dissolved in the battery cell an 

 atom ought theoretically, that is without regard to dissi- 

 pation of some of the energy, to be decomposed in the 

 electrolytic cell, he does not stop at his numerical results. 

 " I have not hesitated," he says, 1 " to apply the more strict 

 results of chemical analysis to correct the numbers obtained 

 as electrolytic results. This, it is evident, may be done 

 in a great number of cases, without using too much liberty 

 towards the due severity of scientific research." 



The law of the conservation of energy, one of the widest 

 of all physical generalisations, rests upon the same footing. 

 The most that we can do by experiment is to show that 

 the energy entering into any experimental combination is 

 almost equal to what comes out of it, and more nearly so 

 the more accurately we perform the measurements. Ab- 

 solute equality is always a matter of assumption. We 

 cannot even prove the indestructibility of matter; for 

 were an exceedingly minute fraction of existing matter to 

 vanish in any experiment, say one part in ten millions, 

 we could never detect the loss. 



Successive Approximations to Natural Conditions. 



When we examine the history of scientific problems, we 

 find that one man or one generation is usually able to 

 make but a single step at a time. A problem is solved 

 for the first time by making some bold hypothetical 

 simplification, upon which the next investigator makes 

 hypothetical modifications approaching more nearly to 

 the truth. Errors are successively pointed out in previous 

 solutions, until at last there might seem little more to 

 be desired. Careful examination, however, will show that 

 a series of minor inaccuracies remain to be corrected and 

 explained, were our powers of reasoning sufficiently great, 

 and the purpose adequate in importance. 



1 Experimental Researches tn Electricity, vol. i. p. 246. 



H H 



