296 THE PRINCIPLES OF SCIENCE. [CHAP. 



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

 with its loudness establishes an exact law of nature. 1 



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. Melloni 

 applied the same kind of reasoning, in a somewhat 

 different form, to the radiation of heat-rays. 



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 

 once obtained experimental data, there is no further 

 difficulty beyond that of arithmetic or algebraic calcu- 

 lation. 



Gold is reduced by the gold-beater to leaves so thin, 

 that the most powerful microscope would not detect any 

 measurable thickness. If we laid several hundred leaves 

 upon each other to multiply the thickness, we should 

 still have no more than y^th of an inch at the most to 

 measure, and the errors arising in the superposition and 

 measurement would be considerable. But we can readily 

 obtain an exact result through the connected amount of 

 weight. Faraday weighed 2000 leaves of gold, each 

 3 1 inch square, and found them equal to 384 grains. 

 From the known specific gravity of gold it was easy to 

 calculate that the average thickness of the leaves was 



28^000 of an inch - 3 

 We must ascribe to Newton the honour of leading the 



1 Jamin, Cours de Physiqw, vol. i. p. 152. 



2 Faraday. Chemical Researches, p. 393. 



