CHAPTER XXV. 



ACCORDANCE OF QUANTITATIVE THEORIES AND 

 EXPERIMENTS. 



IN the preceding chapter we found that facts may be 

 classed under four heads as regards their connexion with 

 theory, and our powers of explanation or prediction. The 

 facts hitherto considered were generally of a qualitative 

 rather than a quantitative nature ; but when we look 

 exclusively to the quantity of a phenomenon, and the 

 various modes in which we may estimate or establish its 

 amount, almost the same system of classification will hold 

 good. There will, however, be five possible cases : 



(1) We may directly and empirically measure a phe- 

 nomenon, without being able to explain why it should 

 have any particular quantity, or to connect it by theory 

 with other quantities. 



(2) In a considerable number of cases we can theo- 

 retically predict the existence of a phenomenon, but may 

 be unable to assign its amount, except by direct measure- 

 ment, or to explain the amount theoretically when thus 

 ascertained. 



(3) We may measure a quantity, and afterwards ex- 

 plain it as related to other quantities, or as governed by 

 known quantitative laws. 



(4) We may predict the quantity of an effect on theo- 

 retical grounds, and afterwards confirm the prediction by 

 direct measurement. 



