HOMOGENEOUS FLUIDS BY POLARIZED LIGHT. 53 



of light being divided into two systems of polarized waves, the 

 one parallelly, the other perpendicularly to the plane, the first 

 beipg a quarter of an undulation behind the second. 



Let us consider that part of the incident ray which has been 

 ordinarily refracted in the first particle, and thus polarized in 

 the direction of O O', and let us represent it by O. On leaving 

 the particle it divides itself into two systems of polarized waves, 

 the one parallelly, the other perpendicularly to TT', the intensi- 

 ties of which, as also the relative positions, are represented by 

 the following expressions : 



\/\% \/h 



O . T. O . R. 



In fact, as I observed in the preceding memoir, when a system 

 of waves is thus decomposed into two others, the velocities of 

 the molecules of asther, in their oscillations, are not proportional 

 to the square of the cosine and sine of the angle OCT, but 

 simply to the sine and cosine ; so that it is not the sum of the 

 velocities which is constant, but the sum of the squares of the 

 velocities. This is a consequence of the principle of the con- 

 servation of living forces in the vibrations of elastic bodies. 



By the action of the plane of entrance R, R/ of the second 

 particle, each of these pencils of light divides itself into two other 

 systems of w'aves, making in all four : if the angle OCO, which 

 the principal section of the second particle makes with that of 

 the first, be represented by jo, the intensities of their vibrations 

 will be — 



^^ -.^mp.O^, y/-.cos;).0^, /y/-.cos/).Oi, /y/l.sin/j.O. 



O.T.Ri. O.T.Tj. O.R.R,. O.R.T/. 



In virtue of the double refraction of this particle, each of these 

 pencils divides itself again into two, polarized, parallelly and 

 perpendicularly to the plane O, O/. The intensities of the sy- 

 stems of waves ordinarily refracted in the second particle will be 

 represented by the following expressions : 



+ -sinjo.Oi, +-cosp.O^, +-cosi?.Oi, --siny^.O. 

 O.T.R,.0,. O.T.T,.0,. O.R.R,.0,. O.R.T/.O/. 

 Adding the expressions which have the same characteristic. 



