Robertson, Explanatory Remarks concerning the Normal Rate of Growth etc. 317 



riques' type of reasoning to its logical conclusion we should exclude 

 quantitative evidence from natural science; for all quantitative evi- 

 dence, depends, in ultimate analysis, upon the agreement between 

 some theoretical formula connecting variables and the relationship 

 between these variables which is actually observed, but un- 

 questionably the experimental relations could invariably be repre- 

 sented, within the order of accuracy of the observations, by other 

 and quite different formulae. Thus, to quote a familiar example, 

 Rudolphi's and van't Hof fs equations for the dependence of the 

 dissociation of strong electrolytes upon their dilution are very diffe- 



a 4 



rent from one another, Rudolphi's being- ^-^7- = K where a 



(1 -- a) 2 V 



is the degree of ionisation and V the volume in which one gramme- 

 molecule of the substance is dissolved, while van't Hoff's equation 



a 3 



is ' = K 1 , where a and V have the same meaning as in 



(1 a ) V 



Rudolphi's equation. Yet these equations yield equally good con- 

 stants w T hen applied to the same experimental determinations; 

 which equation, therefore, should we prefer? At present there is 

 no evident theoretical foundation for either equation, they are 

 empirical" formulae. But if it should transpire that one of these 

 formulae could be anticipated upon theoretical grounds, that is 

 unquestionably the formula which we would prefer. To quote 

 another example, when the experimental relation between the amount 

 of material transformed ( x) and the time (= t) in a chemical 



o 



reaction obeys the formula log - - = Kt, where a and K are 



a x 



constants, we conclude that only one molecule is undergoing trans- 

 formation, because that is the relation which would be theoreti- 

 cally anticipated if only one molecule were engaged in the reaction; 

 but, arguing from Enriques' standpoint, physical chemists have 

 been mistaken in drawing this inference, because the experimental 

 relations could certainly also be represented by the formula x = a 



_|_ bt -|- ct' 2 -\- dt 3 -f- , and there is no reason, or Enriques 



percieves no reason, for assigning preference to the one formula 

 rather than to the other. Or, to quote yet another example, a 

 limited portion of the curve y = log x can be represented by the 

 formula x a -j- bx -f- ex 2 -|- dx 3 , and a still larger portion of the 

 curve by the formula y = a -{- bx -f- ex 2 -f- dx 3 -j- ex 4 and so on, 

 from which we should conclude, following Enriques' type of 

 argument, that we are not justified in assuming that a table of 

 logarithms is really and truly a table of logarithms. 



When a certain relation, subsisting between experimentally 

 determinate variables, is deduced from theoretical considerations, 



