THE PEINCIPLES OF SCIENCE. [CHAP. 



The Propagating Power of Similarity. 



The relation of similarity in all its degrees is reciprocal. 

 So far as things are alike, either may be substituted for the 

 other; and this may perhaps be considered the very 

 meaning of the relation. But it is well worth notice that 

 there isin similarity a peculiar power of extending itself 

 among all the things which are similar. 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 resembles the matrix 

 or original pattern from which the dies were struck, but 

 resembles every other coin manufactured from the same 

 original pattern. Among a million such coins there are 

 not less than 499,999,500,000 pairs of coins resembling 

 each other. Similars to the same are similars to all. It 

 is one great advantage of printing that all copies of a 

 document struck 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. Similarity can also reproduce or propagate itself 

 ad infinitum : 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, weight, or any other measurable 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 capability of mutual substitution which gives 

 such great value to the modern methods of mechanical 

 construction, according to which all the parts of a machine 

 are exact facsimiles of a fixed pattern. The rifles used in 

 the British army are constructed on the American inter- 

 changeable system, so that any part of any rifle can be 

 substituted for the same part of another. A bullet fitting 

 one rifle will fit all others of the same bora Sir J. 



