THE FOUR EXPERIMENTAL METHODS. 477 



acting cause might develop itself; either a new agent, 

 or a new property of the agents concerned, which lies 

 dormant in the circumstances we are able to observe. 

 This is an element of uncertainty which enters largely 

 into all our predictions of effects ; but it is not pecu- 

 liarly applicable to the Method of Concomitant Varia- 

 tions. The uncertainty, however, of which I am 

 about to speak, is characteristic of that method ; 

 especially in the cases in which the extreme limits of 

 our observation are very narrow, in comparison with 

 the possible variations in the quantities of the pheno- 

 mena. Any one who has the slightest acquaintance 

 with mathematics, is aware that very different laws of 

 variation may produce numerical results which differ 

 but slightly from one another within narrow limits; 

 and it is often only when the absolute amounts of 

 variation are considerable, that the difference between 

 the results given by one law and by another, becomes 

 appreciable. When, therefore, such variations in the 

 quantity of the antecedents as we have the means of 

 observing, are but small in comparison with the total 

 quantities, there is much danger lest we should mis- 

 take the numerical law, and be led quite to miscal- 

 culate the variations which would take place beyond 

 the limits ; a miscalculation which would vitiate any 

 conclusion respecting the dependence of the effect 

 upon the cause, which could be founded upon those 

 variations. Examples are not wanting of such mis- 

 takes. " The formulae," says Sir John Herschel*, 

 " which have been empirically deduced for the elasti- 

 city of steam (till very recently), and those for the 

 resistance of fluids, and other similar subjects," when 

 relied on beyond the limits of the observations from 



* Discourse on the Study of Natural Philosophy, p. 179. 



