12 THE PRINCIPLES OF SCIENCE. 



staff, string, or other kind of measure may be employed 

 to represent the length of one object, and according as it 

 agrees or not with the other, so must the two objects 

 agree or differ. In this case the proxy or sample repre 

 sents length ; but the fact that lengths can be added and 

 multiplied renders it unnecessary that the proxy should 

 always be as large as the object. Any standard of con 

 venient length, such as a common foot-rule, may be made 

 the medium of comparison. The height of a church in 

 one town may be carried to that in another, and objects 

 existing immoveably at opposite sides of the earth may be 

 vicariously measured against each other. We obviously 

 employ the rule that whatever is true of a thing as 

 regards its length, is true of its equal. 



To every other simple phenomenon in nature the same 

 principle of substitution is applicable. We may compare 

 weights or densities or degrees of hardness, and all other 

 qualities, in like manner. To ascertain whether two 

 sounds are in unison we need not compare them directly, 

 but a third sound may be the go-between. If a tuning- 

 fork is in unison with the middle C of York Minster 

 organ, and we afterwards find it to be in unison with the 

 same note of the organ in Westminster Abbey, then it 

 follows that the two organs are tuned in unison. The 

 rule of inference now is that what is true, as regards 

 pitch, of the tuning-fork, is true of any sound in unison 

 with it. 



The skilful employment of this substitutive process 

 enables us to make measurements beyond the powers of 

 our senses. No one can count the vibrations, for instance, 

 of an organ pipe. But we can construct an instrument 

 called the syren, so that while producing a sound of any 

 pitch it shall register the number of vibrations consti 

 tuting the sound. Adjusting the sound of the syren in 

 unison with an organ pipe, we measure indirectly the 



