20 THE PKINCIPLES OF SCIENCE. [chap. 



The Propagating Fuiver of Similarity. 



The relation of similarity in all its degrees is reciprocal. 

 So far as things are alike, either may be sul)stitutecl for the 

 other ; and this may perha]3S be considered the very 

 meaning of the relation, iiut it is well worth notice that 

 there is in similarity a pecnliar power of extending itself 

 among all the things which are similar. To render a 

 nnmber of things similar to eacli 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 tlie 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 witli 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 tlie Principal, they must be in unison with eacii 

 otlier. 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 instiiiment 

 tuned to any other fork. Standard measures of length, 

 capacity, weight, or any other measurable quality, are 

 propagatetl 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 whicli gives 

 such great value to the modern methods of meclianical 

 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- 

 cliangealde system, so that anv part of any riile can be 

 substituted for the same part of another. A bullet fitting 

 one rifle will iit all others of the same bore. Sir J. 



