CHAPTER XXV. 



ACCORDANCE OF QUANTITATIVE THEORIES. 



IN the preceding chapter we found that facts may be 

 classed under four heads as regards their connection 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 determine its amount, 

 nearly 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 are 

 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 explain 

 it as related to other quantities, or as governed by kr own 

 quantitative laws. 



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

 retical grounds, and afterwards confirm the prediction by 

 direct measurement. 



(5) We may indirectly determine the quantity of an 

 effect without being able to verify it by experiment. 



These classes of quantitative facts might be illustrated 

 by an immense number of interesting points in the history 



