414 PROFESSOR STOKES, ON THE COMPOSITION AND RESOLUTION OF 



limit continually decreases, and the inferior increases, and consequently the fringes become 

 fainter and fainter. 



21. It is a well-known law of interference that if two rays of common light from the same 

 source be polarized in rectangular planes, and afterwards be brought to the same plane of polari- 

 zation, or in other words, analyzed so as to retain only light polarized in a particular plane, they 

 ,will not interfere, but if the light be primitively polarized in one plane they will interfere. 

 This law seems to have presented a difficulty to some, because, it would be argued, the 

 most general kind of vibrations are elliptic, so that we must suppose the vibrations of the 

 ether in the case of common light to be of this kind ; and yet the phenomena of inter- 

 ference are exhibited perfectly well if the light be at first elliptically polarized instead of 

 plane-polarized. For my own part, I never could see the difficulty, but on the other hand it 

 seems to me that it would be an immense difficulty were the law anything else than what it is. 

 For, if we consider the rectangular components of the vibrations which make up common light, 

 these components being measured along any two rectangular axes perpendicular to the ray, we 

 must suppose them to be independent of each other, or at least to have no fixed relation to 

 each other so far as regards the changes in the mode of vibration, which we must suppose to be 

 taking place continually, though slowly, it may be, in comparison with the time of a luminous 

 vibration. To suppose otherwise would be contrary to the idea of common light, in which it is 

 implied that on the average whatever we can say of one plane passing through the ray, we can 

 say of another : whatever we can say of the direction one way round we can say of the other 

 way round. 



At the end of his excellent Tract on the Undulatory Theory, Mr Airy has shewn how the 

 simple, supposition of the existence, in common light, of successive series of undulations, in 

 which the vibrations of one series have no relation to those of another, would account at the 

 same time for the interference of common light and the non-interference of the pencils, polarized 

 in rectangular planes, into which common light may be conceived to be decomposed. But he 

 has, I think, introduced a gratuitous difficulty into the subject, by asserting that it is neces- 

 sary to suppose the transition from one series into another to be abrupt, and that a gradual 

 change in the nature of the vibrations is inadmissible. This assertion, which seems to have 

 led others to conceive that there was here a difficulty with which the undulatory theory had to 

 contend, seems to have resulted from an investigation from which it appeared that common 

 light could not be represented by an indefinite series of elliptic vibrations, in which the major 

 axis of the ellipse was supposed to revolve uniformly, rapidly, with regard to the duration of 

 impressions on the retina, though slowly with regard to the time of a luminous vibration. I 

 have elsewhere pointed out on what grounds I conceive that the instance of the revolving ellipse 

 is not a case in point, namely, that it is not a fair representation of common light, because it 

 gives a preponderance on the average to one direction of revolution over the contrary, which is 

 contrary to the idea of common light*. Let us now apply the general formula? (16) and (17) 

 to this case. 



Let c cos (4, c sin /3 be the semi-axes of the ellipse, a the azimuth of the first axis at a given 



* Report of the meeting of the British Association at Swansea in 1848. Transactions of the Sections, p. 5. 



