Definition of Intensity in the Theories of Light and Sound. 305 



The definition of intensity in the theory of light must of 

 course be precisely similar. 



It may be useful to compare the definition at which we have 

 thus arrived with that ordinarily given in approved text-books 

 on the theory of undulations. Of these I shall give four ex- 

 amples. 



"As in the doctrine of sound, the frequency of the aerial pulses, 

 or the number of excursions to and fro from its point of rest 

 made by each molecule of the air, determines the pitch or note, 

 so, in the theory of light the frequency of the pulses, or number 

 of impulses made on our nerves in a given time by the asthereal 

 molecules next in contact with them, determines the colour of 

 the light ; and .... as the absolute extent of the motion to and 

 fro of the particles of air determine the loudness of the sound, so 

 the amplitude, or extent of the excursions of the sethereal mole- 

 cules from their points of rest, determine the brightness or in- 

 tensity of the light.''— ^Aicyc. Met.^vi. "Light,''No.563(1830). 



" In the aerial pulses the amplitude of the vibration deter- 

 mines the loudness of the sound; and the frequency of the 

 pulses, or the time of vibration, determines its note. In like 

 manner, the amplitude of the cethereal vibrations determines the 

 intensity of the light ; and their frequency, or the period of vi- 

 bration, determines its colour,'^ — Lloyd's ' Wave Theory,' p. 14 

 (1857). 



" When in our final results we have found the expression 



c.sm 



r27r ^ , ^ 27r n 



for the displacement of the particles touching a screen or touch- 

 ing the eye, we shall assume the intensity of the light to be 

 represented by c"^. We shall suppose that the colour of light 

 depends on the value of \." — Airy, ' On the Undulatory Theory 

 of Optics,' p. 20 (1866). 



"At a certain point of its excursion, the velocity of the 

 particle is a maximum. The intensity of the sound is propor- 

 tional to the square of this maximum velocity." — Tyndall, ' On 

 Sound,' p. 11 (1867). 



The contrast of the definition of intensity thus enunciated 

 with that which I have propounded is sufficiently striking. 

 That the latter is correct, I apprehend, there can be no manner 

 of doubt. 



A Cambridge mathematician, whose views are apt to exercise 



controversy, I content myself with recording here my conviction that the 

 effect of a single complete vibration on the nerves of the ear is properly 

 represented by the simple power, and not by the square of the amplitude — 

 and consequently that the intensity of light should be dejined as varying with 

 the amplitude directly and with the time of vibration inversely, 

 Phil. Mag. S. 4. Vol. 44. No. 293. Oct. 1872. X 



