xx-.j THEOEY OF APPROXIMATION. 465 



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 dissT 

 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/ to apply the more strict 

 resu ts of chemical analysis to correct the numbers obtained 

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



!ow a li ea fVT 6r f CaS6S ', Without usin S to m * ch liberty 

 towards the due severity of scientific research " 



of all T>l? W - 0f I* 1 * C n i e rVati n f ener ^' one of the wid est 

 o all physical generalisations, rests upon the same footina 

 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 

 mnot even prove the indestructibility of niatter; for 

 were an exceedingly minute fraction of existing matter to 



^ ^ * te ** 



Successive Approximations to Natural Condition*. 



When we examine the history of scientific problems we 

 ma that one man or one generation is usually able to 



for t e h. fi \ r gle ? 6P at a time " A P roblem is sol ved 

 famKR + le y 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 

 desired. Careful examination, however, will show that 

 series ol minor inaccuracies remain to be corrected and 

 explained, were our powers of reasoning sufficiently great 

 and the purpose adequate in importance? 



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



H H 



