122 THE GENESIS OF SCIENCE. 



ties of observation to disentangle them. Whence it ap 

 pears not only that in proportion 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 quantitatively ; 

 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. Tims 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 from 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. We 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 forma 

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



