THEORY OF APPROXIMATION. 83 



Potassium is the only element whose atomic weight has 

 been determined with great care, but which has not 

 shown an approach to a simple ratio with the other ele- 

 ments. This exception may be due to some unsuspected 

 cause of error *. A similar assumption is also made in the 

 law of definite combining volumes of gases, and Sir B. C. 

 Brodie has clearly pointed out the line of argument by 

 which the chemist, observing that the discrepancies be- 

 tween the law and fact are within the limits of experi- 

 mental error, assumes that they are due to error k . 



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.- 

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

 results of chemical analysis to correct the numbers ob- 

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

 done in a great number of cases 1, without using too much 

 liberty towards the due severity of scientific research/ 

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

 widest of all physical generalizations, must rest 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 exactly equal to what comes out of 

 it, and more nearly so the more accurately we perform all 

 the measurements. Absolute equality is always a matter 

 of assumption. We cannot even prove the indestructibility 



i Watts, 'Dictionary of Chemistry,' vol. i. p. 455. 

 k ' Philosophical Transactions/ (1866) vol. clvi. p. 809. 

 1 ' Experimental Researches in Electricity/ vol. i. p. 246. 

 G 2 



