THE EXACT MEASUREMENT OF PHENOMENA. 345 



established by a simple acoustical observation. When 

 a rod or tongue of metal fixed at one end is set in 

 vibration, the pitch of the sound may be observed to 

 be exactly the same, whether the vibrations be small or 

 great ; hence the oscillations are isochronous, or equally 

 rapid, independently of their magnitude. On the ground 

 of theory, it can be shown that such a result only 

 happens when the flexure is proportional to the deflecting 

 force. Thus the simple observation that the pitch of 

 the sound of a harmonium, for instance, does not change 

 with its loudness, establishes an exact law of nature e . 



A closely similar instance is found in the proof that the 

 intensity of light or heat rays varies inversely as the 

 square of the distance increases. For the apparent mag- 

 nitude certainly varies according to this law; hence, if the 

 intensity of light varied according to any other law, the 

 brightness of an object would be different at different 

 distances, which is not observed to be the case. Mellon i 

 applied the same kind of reasoning, in a somewhat dif- 

 ferent form, to the radiation of heat-rays f . 



Modes of Indirect Measurement. 



Some of the most conspicuously beautiful experiments 

 in the whole range of science, have been devised for the 

 purpose of indirectly measuring quantities, which in their 

 extreme greatness or smallness surpass the powers of 

 sense. All that we need to do, is to discover some 

 other conveniently measurable phenomenon, which is re- 

 lated in a known ratio or according to a known law, 

 however complicated, with that to be measured. Having 



e Jamin, 'Cours de Physique,' vol. i. p. 152. 



f Balfour Stewart's, ' Elementary Treatise on Heat,' ist edit. pp. 164, 

 165. 



