[ 38 ] 



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

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

 Queen's College, Cambridge*. 



MR. BOSANQUET appears to think f that in my paper in 

 the Philosophical Magazine for October last, I have 

 fallen into an error in estimating the vis viva. 



In point of fact I never attempted to estimate the vis viva. 

 Adopting the definition of intensity propounded by three out of 

 the five writers to whom I referred, viz. that the intensity is 

 measured by the square of the amplitude, I pointed out that, 

 admitting the square of the amplitude properly to represent 

 the effect on the eye or ear of a single undulation, we must 

 divide that quantity by the time — or, as Mr. Bosanquet would 

 express it, we must multiply it by the number of undulations 

 incident on the organ in a unit of time — in order to arrive at 

 the true measure of intensity of the ray or note. 



I must plead guilty, however, to having overlooked the con- 

 trariety exhibited by the definitions cited in my paper, — Sir 

 John Herschel, Dr. Lloyd, and Mr. Airy taking the square 

 of the amplitude as the measure of intensity, while Prof. 

 Tyndall and Dr. Helmholtz (herein following Fresnel) adhere 

 to the square of the maximum velocity as the measure ; which 

 latter, as Mr. Bosanquet points out, will have the square of the 

 periodic time in the denominator, assuming the vibration to 

 be correctly represented by the formula ordinarily employed for 

 that purposej. Having always worked with the former defini- 

 tion, and never having heard that there was any dispute about 

 the matter, I took for granted without inquiry the identity of 

 the definitions, although the slightest examination would have 

 shown them to be irreconcilable§. 



* Communicated by the Author. 



t See Phil. Mag. S. 4. vol. xliv. p. 386. 



X That in some important particulars the formula completely misrepre- 

 sents the vibration is certain. I do not dwell upon this, however, as the 

 want of correspondence between the two definitions is abundantly obvious. 



§ Sir John Herschel adopts both definitions, apparently without any 

 consciousness of their incongruity; for, while in the passage I have 

 quoted from his ' Treatise on Light' (No. 563) he speaks of the amplitude 

 as determining the intensity both of light and sound, in his ' Treatise on 

 Sound' (No. 126) he gives the following: — 



" In the theory of sound, as in that of light, the intensity of the impres- 

 sion made on our organs is estimated by the shock, impetus, or vis viva of 

 the impinging molecules, which is as the square of their velocity — and not 

 by their inertia, which is as the velocity simply." 



I may remark that the notion of the intensity of our sensations being 

 measured by the " shock " of the " impinging molecules," which Sir John 

 Herschel here adopts from Fresnel, is founded on a complete misappre- 



