24 THE PRINCIPLES OF SCIENCE. 



The Propagating Power of Identity. 



The relation of identity or sameness in all its degrees 

 is reciprocal. So far as things are alike, either may be 

 substituted for the other ; and this may perhaps be con- 

 sidered the very meaning of the relation. But it is well 

 worth notice that there is in identity a peculiar power of 

 extending itself among ah 1 the things which are identical. 

 To render a number of things similar to each other we 

 need only render them similar to one standard object. 

 Each coin struck from a pair of dies not only exactly 

 resembles the matrix or original pattern from which the 

 dies were struck, but exactly resembles every other coin 

 manufactured from the same original pattern. Among a 

 million such coins there are not less than 499,999,500,000 

 of pairs of coins exactly resembling each other. Similars 

 to the same are similars to all. It is one great advantage 

 of printing that all copies of a document taken from the 

 same type are necessarily identical each with each, and 

 whatever is true of one copy will be true of every copy. 

 Similarly, if fifty rows of pipes in an organ be tuned in 

 perfect unison with one row, usually the Principal, they 

 must be in unison with each other. Identity can also 

 reproduce or propagate itself ad injinitum ; for if a 

 number of tuning-forks be adjusted in perfect unison 

 with one standard fork, all instruments tuned to any one 

 fork will agree with any instrument tuned to any other 

 fork. Standard measures of length, capacity, or weight, 

 or any other measureable quality, are propagated in the 

 same manner. So far as copies of the original standard, 

 or copies of copies, or copies again of those copies, are 

 accurately executed, they must all agree each with every 

 other. 



It is the power of mutual substitution which gives 



