386 Mr. R. H. M. Bosanquet on the Relation between the 



of air at the orifice of the ear in a unit of time, we may put 



T 



Here a certain proportion of the energy expended traverses, 

 at right angles we suppose, a small plate of air whose mass 

 we will assume constant and equal to unity. Then the air is 

 subjected to a forced vibration, which may be represented by 

 57= « sin nt in the simplest case; and the energy of this vibra- 

 tion is measured by— ^, where wT = 27r; that is to say, — ^— 



measures the energy communicated to the plate of air in a 

 quarter of a vibration. 



It is clear that if we take the expression for the velocity 



where nT=27r, we cannot avoid having the square of the periodic 

 time in the denominator of the vis viva. In a recent paper in 

 the Philosophical Magazine, Mr. Moon has omitted this element. 

 See the determination of the energy of a vibrating string, 

 Donkin^s ^Acoustics,' p. 127, which is to some extent analogous 

 to the present case, except in the difference of the vibrating body. 



If the plate were moving freely, the energy gained as kinetic 

 in the first quarter oscillation would be transformed into the 

 form of potential in the second ; but here we have no potential 

 energy in the plate of air, the movement at every instant depend- 

 ing on what is transmitted from the source of energy. Thus all 

 the elements of work in both directions proceed from the source, 

 and must be reckoned in estimating its action on the air : this 

 observation occurs in Mr. Moon^s paper. 



The work passed through the plate of air in a whole oscilla- 

 tion is then Sir^a'^ 



Hence the following proposition : — In notes whose oscillations 

 are similar, i. e. have the amplitudes proportional to the wave- 

 lengths or periodic times, the work transmitted by one oscilla- 

 tion of each note is the same. 



Since there are - oscillations in a unit of time, 



'^ SttV 



w= — 5—. 



Substituting this for w in the expression for the intensity, we 



I = ^.___, 



whence proceed the following propositions : — 



In notes of different pitch the apparent intensity varies as the 



