216 Mr. R. H. M. Bosanquet on the Measure of Intensity 



which the principal plane of the crystal makes with the original 

 plane of polarization. The verification is stated to have been 

 made photometrically by Arago ; but it is easy to obtain a veri- 

 fication for one's self. If the ray that has passed through a Nicol 

 fall through a hole on a crystal of Iceland spar of suitable thick- 

 ness so that the emerging rays overlap, it is quite easy to recog- 

 nize that, as the crystal is turned round, the intensity of the 

 overlapping part is constant. Now the amplitudes of the po- 

 larized pencils will be 



a cos a and a sin a, 



if a be the amplitude of the original ray, and a the inclination of 

 the principal plane of the prism to the plane of polarization of the 

 Nicol. But if these amplitudes were the measures of the inten- 

 sities, the intensity of the overlapping part would be represented 

 by a (sin a + cos a), and would vary with a. The question is here 

 submitted to direct experiment ; and we see that it is only by 

 taking the intensity to be measured by the square of the ampli- 

 tude that the experimental result can be accounted for ; we have 

 then, of course, « 2 (sin 2 a + cos 2 a) =a 2 . 



In the case of sound, the law of Topfer, which is quoted in 

 my paper in the Philosophical Magazine, November 1872, shows 

 that in organ-pipes of equal intensity the wind consumed is pro- 

 portional to the wave-length. As I have remarked, this is equi- 

 valent to saying that the work done is proportional to the wave- 

 length. Topfer' s law is beyond dispute. It might well have 

 been left to rest on his authority, except that, for once, he gives 

 no measures or evidence for it; but he is generally so accurate 

 that his enunciation of the law carries weight. The evidence in 

 the case of sound does not at present amount to actual proof of 

 the representation of intensity by mechanical energy, but to a 

 high degree of probability. I have devised a better method of 

 observation, which requires special arrangements, and hope to 

 throw some additional light on the subject when I have an op- 

 portunity of carrying this out. 



As one of Mr. Moon's suggestions is sometimes felt as a diffi- 

 culty by learners, I will just touch upon it. It seems specious 

 to say that, if we superpose two luminous or sonorous vibrations 



2?r 

 of the type ^ = «sin— (vt—x) 3 the amplitude of the resulting 



vibration will be 2#, and the intensity four times that of either 

 vibration. But if we draw from this the conclusion that from 

 twice the energy proportional to a 2 we obtain energy propor- 

 tional to 4a 2 , we clearly make a mistake. In the first place, if 

 the two vibrations are to be superposed they must be in the same 

 phase ; this requirement prevents the occurrence of the super- 



