THE GENESIS OF SCIENCE. 



ties of observation to disentangle them. Whence it ap- 

 pears not only that in projDortion as knowledge becomes 

 quantitative do its previsions become complete as well as 

 certain, but that until its assumption of a quantitative char- 

 acter it is necessarily confined to the most elementary rela- 

 tions. 



Moreover it is to be remarked that while, on the one 

 hand, we can discover the laws of the greater proportion 

 of phenomena only by investigating them quantitativelj' ; 

 on the other hand we can extend the range of our quanti- 

 tative previsions only as fast as we detect the laws of the 

 results we predict. For clearly the ability to specify the 

 magnitude of a result inaccessible to direct measurement, 

 implies knowledge of its mode of dependence on something 

 which can be measured — implies that we know the particu- 

 lar fact dealt with to be an instance of some more general 

 fact. Thus the extent to which our quantitative previsions 

 have been carried in any direction, indicates the depth to 

 which our knowledge reaches in that direction. And here, 

 as another aspect of the same fact, we may further observe 

 that as we pass from qualitative to quantitative prevision, 

 we pass fi'om inductive science to deductive science. Sci- 

 ence while purely inductive is purely qualitative : when in- 

 accurately quantitative it usually consists of part induction, 

 part deduction: and it becomes accurately quantitative only 

 when wholly deductive. TVe do not mean that the deduct- 

 ive and the quantitative are coextensive ; for there is mani- 

 festly much deduction that is qualitative only. We mean 

 that all quantitative prevision is reached deductively ; and 

 that induction can achieve only qualitative prevision. 



Still, however, it must not be supposed that these dis- 

 tinctions enable us to separate ordinary knowledge from 

 science ; much as they seem to do so. While they show in 

 what consists the broad contrast between the extreme forms 

 of the two, they yet lead us to recognise their essential iden- 



