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XXXV. On the Definition of Intensity in the Theories of Light 

 and Sound. By Robert Moon, M.A.^ Honorary Fellow of 

 Queen's College, Cambridge^. 



IT is clear that the loudness of a note must depend on the 

 amount of motion which it produces in the nerves of the 

 ear. Bat a note may be prolonged indefinitely, in which case 

 the amount of motion of the nerves of the ear will be prolonged 

 indefinitely, without producing any increase in the loudness of 

 the note. 



If a note be prolonged through a definite interval of time with- 

 out undergoing any change of character, either as to intensity or 

 otherwise, the amount of motion in the nerves of the ear pro- 

 duced by it will obviously be proportional to the length of the 

 interval during which the note continues ; whence it is clear 

 that the true measure of the loudness of a sound must be the 

 amount of motion of the nerves of the ear which it occasions, 

 divided by the time during which it operates. 



And since the only test we are ever likely to get of the 

 amount of motion of the nerves of the ear in any given case is 

 the amount of motion of the aerial particles through the inter- 

 vention of which the nerves are stimulated, it follows that we 

 must take for oar test of the loudness of a sound the ratio of the 

 aggregate amount of motion of the particles producing it to the 

 time of its continuance. 



In estimating the aggregate amount of motion above spoken 

 of, it is to be observed that it is not the algebraical sum of the 

 expressions for the motion during each semiexcursion of the mo- 

 lecules, but the entire space travelled over by the particles in the 

 given interval, without reference to the direction in which such 

 motion takes place, that is to be taken into account — since it is 

 obvious that the efi'ect of the aerial particles in stimulating the 

 nerves of the ear does not depend on the fact of the motion of the 

 latter taking place in any one direction rather than in its opposite. 



Hence, denoting by 2a the amplitude of excursion of the par- 

 ticles, and by n the number of excursions to and fro in a given 

 time t, if we represent by a^ the eflPect on the nerves of the ear 

 of a single complete vibration of the particles, the aggregate 

 effect on the nerves of the ear during the time t will be repre- 

 sented by na^ ; and the loudness of the sound will be represented 



nci , t 



by — - ; that is, since - denotes the time of vibration, the inteji- 

 I n 



sity of a sound varies as the square of the amplitude directly, and 



as the time of vibration inversely j. 



* Communicated by the Author. 



t Not wishing to encumber the argument of this paper with a separate 



