10 THE PRINCIPLES OF SCIENCE. [CHAP. 



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 represents 

 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 

 convenient size, 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 immovably at opposite sides of the earth may be 

 vicariously measured against each other. We obviously 

 employ the axiom 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, densities, degrees of hardness, and degrees of 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 of the tuning- 

 fork as regards the tone or pitch of its sound, 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 siren, 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 siren in 

 unison with an organ-pipe, we measure indirectly the 

 number of vibrations belonging to a sound of that pitch. 

 To measure a sound of the same pitch is as good as to 

 measure the sound itself. 



Sir David Brewster, in a somewhat similar manner, 

 succeeded in measuring the refractive indices of irregular 

 fragments of transparent minerals. It was a troublesome, 

 and sometimes impracticable work to grind the minerals 



