396 Astronomical and Nautical Collections, 



when the difference of their paths is so small, that we should 

 expect them to produce very bright colours in white light. 

 It must be recollected that a small difference in the routes is 

 necessary, in order that the different effects that it occasions 

 in the different kinds of undulations may produce sensible 

 colours, as in the case of fringes produced by mirrors, and 

 of reflected rings. 



It is not sufficient that the rays which have been polarised 

 at right angles should be brought back to a common plane 

 of polarisation, in order that they should be able to influence 

 each other ; they must have been originally polarised on the 

 same plane: hence arises the necessity of employing light 

 previously polarised, when we wish to exhibit colours in 

 crystallized plates. 



We have seen by the experiment with the combined rhom- 

 boids, that when two luminous pencils, originally polarised 

 in the same plane, are then polarised at right angles, they 

 produce two complementary images in passing through a 

 new rhomboid, which brings them back to a common plane 

 of polarisation ; for when the central stripe, for example, 

 was black in the extraordinary image, it was at its greatest 

 brightness in the ordinary image, and the same opposition 

 was observable in all the bright and dark stripes of the two 

 images. The two images exhibited by the polarised light, 

 transmitted by a thin crystallized plate, must also be com- 

 plementary to each other. It follows of necessity, that if 

 one of them corresponds to the difference of the routes of 

 two systems of transmitted undulations, the other must cor- 

 respond to the same difference, augmented or diminished by 

 half an undulation, because there is a perfect agreement in 

 the one and discordance in the other. 



In order to know which of the two differences must be so 

 augmented or diminished, we must observe the following 

 general rule. The image, of which the tint agrees precisely 

 with the difference of the paths described, is that for which 

 the planes of polarisation of the constituent pencil, after 

 having been separated from each other, are brought back by 

 a contrary motion to be reunited; while the planes of polari- 

 sation of the two pe7icils, constituting the complementary 

 image ^ continue to separate from each other, as considered 



