ORIGIN OF THE IDEA OF MEASURE. 201 



ensure commencing with the same length of beat on a fu&amp;lt; 

 ture occasion ; and hence, lastly, the fact, that of all magni 

 tudes, those of linear extension are those of which the 

 equality is most accurately ascertain able, and those to 

 which by consequence all others have to be reduced. For 

 it is the peculiarity of linear extension that it alone allows 

 its magnitudes to be placed in absolute juxtaposition, or, 

 rather, in coincident position ; it alone can test the equality 

 of two magnitudes by observing whether they will coalesce, 

 as two equal mathematical lines do, when placed between 

 the same points ; it alone can test equality by trying wheth 

 er it will become identity. Hence, then, the fact, that all 

 exact science is reducible, by an ultimate analysis, to results 

 measured in equal units of linear extension. 



-StilLit^emains to be noticed in what manner this deter- 

 -mination of equality by comparison of linear magnitudes 

 originated. Once more may we perceive that surrounding 

 natural objects supplied the needful lessons. From the be 

 ginning there must have beeu a constant experience of like 

 things placed side by side men standing and walking to 

 gether ; animals from the same herd ; fish from the same 

 shoal. And the ceaseless repetition of these experiences 

 could not fail to suggest the observation, that the nearer 

 together any objects were, the more visible became any in 

 equality between them. Hence the obvious device of put 

 ting in apposition, things of which it was desired to ascer 

 tain the relative magnitudes. Hence the idea of measure. 

 And here we suddenly come upon a group of facts which 

 afford a solid basis to the remainder of our argument; while 

 they also furnish strong evidence in support of the forego 

 ing speculations. Those who look sceptically on this at 

 tempted rehabilitation of the earliest epochs of mental de 

 velopment, and who more especially think that the derivation 

 of so many primary notions from organic forms is somewhat 

 strai ed, will perhaps see more probability in the several 



