Definition of Intensity in the Theories of Light and Sound. 361 



at which the sound should no longer be audible ought to be 100 

 feet only if the square of the amplitude be the measure of its 

 intensity, or at 141 feet if the amplitude simply be the correct 

 indicator of intensity \ or if the amplitude of the second wave 

 were one third of an inch only, then the distances (according 

 to the two hypotheses) would be about 67 feet and 115 feet 

 respectively. 



Henry Hudson. 



P.S.— In such an experiment we have the advantage of deal- 

 ing with a single wave. 



XLV. On the Definition of Intensity in the Theories of Light and 

 Sound, By Robert Moon, M.A., Honorary Fellow of Queen 3 s 

 College \ Cambridge*. 



IN a note upon the subject of this paper, contained in the 

 March Number of the Philosophical Magazine, Mr. Bo- 

 sanquet expresses himself as follows : — 



" Mr. Moon has not offered any answer to the remark made 

 at the end of my paper of last November, although, if he under- 

 stood it, it is conclusive in the case of light." 



There are some truths so obvious, some arguments which 

 appear so decisive, that one is apt to suppose that the mere state- 

 ment of them will suffice to carry conviction to the mind even of 

 an opponent. The argument I offered to Mr. Bosanquet ap- 

 peared to me precisely of that character. As he, however, 

 regards it in a different light, I am ready to meet him upon his 

 own ground. 



I have no intention to contest the substantial approximate 

 truth of an experimental law so long established, so a priori all 

 but certain, as Malus's rule of cosines ; but I demur in toto to 

 Mr. Bosanquet's conclusion that the adoption of the simple power 

 of the amplitude as the measure of intensity in plane-polarized 

 rays involves the assumption that a (sin a+ cos a) measures the 

 intensity of the overlapping beams in the experiment which 

 he discusses. So far is this from being the fact, that the latter 

 assumption contradicts the former, as can readily be shown. 

 For, suppose that at a particular point where the beams overlap, 

 the oppositely polarized rays happen to be in the same phase, as 

 they may be ; they will then give rise to a single plane-polarized 

 ray, whose intensity would be a according to the measure which 

 I have proposed, and not a (sin u+ cos a), as the measure which 

 Mr. Bosanquet thus gratuitously seeks to fix upon me would 

 indicate. 



The inconsistency of this proposed extension of my definition 

 * Communicated by the Author. 



