398. Astronomical and Nautical Collections. 



ference of the paths described by the two systems of undu- 

 lations, or, what is the same in effect, change the signs of the 

 motions of oscillation in one of them, if we wish to calculate 

 the colours which they will exhibit, according to the laws of 

 interference. It is evident that the effects are precisely 

 such as would arise from the combination of forces in the 

 plane of the figure, that is to say, in a direction perpendi- 

 cular to that of the rays, in the planes of polarisation or in 

 the perpendicular planes ; for if two forces, represented by 

 GO and CE', should unite in CS, they would have the same 

 sign ; as the two piencils F„^. and F^^,, which are united in 

 that line of polarisation, have the same sign ; and the two 

 other constituent forces, CT and CT', acting in opposite 

 directions, would be affected by contrary signs. 



The principle of the preservation of living force made it 

 easy to foretel that the two images must be complementary 

 to each other, but it did not indicate which of the two 

 should agree with the simple difference of the paths, and 

 which should require the addition of the half undulation. 

 I have, therefore, referred to the facts, and have deduced 

 the rule here given from the experiments of Mr. Biot. It 

 may also be inferred from the experiment with the two 

 rhomboids. 



This rule explains why two pencils of direct light, which 

 are polarised at right angles, do not exhibit any appearance 

 of mutual influence, when they are brought back to a 

 common plane of polarisation by the action of a pile of glass 

 or a rhomboid of calcarious spar. It is not that they have 

 no power of influencing each other under such circumstances, 

 for, independently of general considerations of a mechanical 

 nature, this supposition would be unsupported by analogy ; 

 but the fact is, that the effects of different systems of undula- 

 tions of direct light compensate each other, and disappear. 

 In fact, we may imagine direct light to be an assemblage, 

 or rather a rapid succession, of an infinity of systems of 

 undulations, polarised in all possible azimuths, in such a 

 manner, that there is always as much light polarised in any 

 given plane as in the plane of the perpendicular to it; now 

 it results from the rule which has been given, that if, for 

 example, we are obliged to add a half undulation to the dif- 



