HOMOGENEOUS FLUIDS BY POLARIZED LIGHT. 55 



plain (what at first appears difficult to conceive) how it happens 

 that the double refraction exerted by particles so irregularly 

 arranged does not give rise to more than two systems of lumi- 

 nous waves in the fluid. 



When it is homogeneous, the effects produced by all the par- 

 ticles are added, and the interval between the two systems of 

 waves ought to be increased in proportion to the length of the 

 passage. When the fluid is composed of two different kinds of 

 particles, the axes of which however are turned in the same 

 manner with relation to the planes of entrance, their effects are 

 added, if in both it is the same refraction that is the most rapid ; 

 and they are subtracted, on the contrary, if the most rapid re- 

 fractions ai'c of opposite natures. The inverse takes place when 

 the particles have their axes turned in contrary directions rela- 

 tively to their planes of entrance. 



It is likewise seen that the mixture of any number of fluids 

 of different kinds, the particles of which are thus constituted, 

 ought to produce the same effect upon Kght as that which it 

 would suffer if it traversed successively these different fluids. 

 Hence the problem, in this general case, may always be reduced 

 to the particular case of a homogeneous fluid. 



In the preceding memoir, in explaining the theory of the ap- 

 paratus which I take here as a model of the constitution of the 

 particles, I showed that the intensity and the position of the 

 diff'erent systems of waves which it produced, united in any plane 

 of polarization whatever, are independent of the azimuth in 

 which the apparatus is directed, and only depend upon the mu- 

 tual inclination of the two extreme planes of polarization. We 

 may then suppose all the particles of the fluid turned in such a 

 manner that their principal sections are parallel to each other : 

 then, if one of these particles is considered as comprised between 

 two others, its plane of entrance is at right angles to the plane 

 of exit of the one which precedes it, and thus causes to disappear 

 the quarter of an undulation difference produced by the latter. 

 In the same manner its plane of exit is at right angles to the 

 plane of entrance of the following particle, which destroys con- 

 sequently the modification which it had communicated to the 

 light. Thus all the intermediate planes of entrance and of exit 

 may be put out of view, reserving only the plane of entrance 

 of the first particle and the plane of exit of the last. It is then 

 evident that the formula which I have calculated for the appa- 



