HOMOGENEOUS FLUIDS BY POLARIZED LIGHT. CI 



the interval e — o comprised between the two systems of waves. 

 When r is equal to zero, on the contrary, the tint corresponds 

 exactly to the interval e — o ; it is this which may be called the 

 fundamental tint. The formula then becomes — 



V[ 



+ — cos 2 i . cos 2 TT (e — o) 



this is precisely the general expression for the intensity of the 

 luminous rays in the ordinary image, for the particular case of 

 a crystalline lamina, the axis of which is placed in an azimuth 

 of 45°, with respect to the plane of primitive polarization. 



If the double refraction exerted by oil of turpentine upon the 

 different kinds of rays was sensibly constant, as in crystals, it 

 would follow that we could always exactly compensate the effect 

 ■which it produces upon polarized white light with a crystallized 

 lamina of proper thickness, by turning the parallelopiped in 

 such a manner as to make the plane of double I'eflexion parallel 

 to the plane of primitive polarization. But we have seen that 

 this is not the case, and that it follows from the changes of the 

 fundamental tint, that the double refraction of the oil of turpen- 

 tine varies, on the contrary, very much with the length of the 

 luminous waves. We may even conceive that the law of these 

 variations may be such as to render impossible an exact compen- 

 sation in the case of white light. 



To conceive clearly the necessary conditions of this compen- 

 sation, instead of referring the intervals comprised between the 

 two systems of waves in the oil of turpentine and in the crystal- 

 line lamina to the same unit of length, let us suppose them ex- 

 pressed, for each kind of luminous undulation, in a function of 

 the length of that undulation. It is clear that, if the diffei'ences 

 between the numbers which express these relations for the tube 

 filled with oil of turpentine are equal to the differences between 

 the corresponding numbers of the crystalline lamina, exact com- 

 pensation is possible ; for it results from this hypothesis that 

 the numbers of the crystalline lamina are equal to the numbers 

 of the tube, plus a common number, which is generally a fraction. 

 Now we may suppress all the integer numbers, and consider 

 only the remaining fraction, the only quantity which is opposed 

 to the exact compensation. But, from the formula — 



F . i/ — -f- — cos 2 (i — r) cos [2r — 2n{e — o)]. 



