228 



Proceedings of Philosophical Societies. [Marcfi^ 



reflection from a second glass, we have only to consider a as 

 representing the dihedral angle which the plane of incidence of 

 the ray upon that glass forms with the primitive plane of polari- 

 zation : then the value of will express the intensity and the 

 colour of the reflected ray. 



All the particular consequences that may be deduced from 

 these formulas, in giving different values to i and «, are realized 

 by experiment, as may be seen in the memoirs of which we are 

 giving an account. For example, we may determine all the 

 positions of the plate and of the crystal or glass in which one of 

 the two images disappears. We find, likewise, all those in which 

 the two images can be white, and equal or unequal in intensity, 

 and those in which they are equal in intensity without being 

 white. We see, also, by these formulas, that the plate will not 

 give colours if the incident ray is composed of two white equal 

 pencils, polarized at right angles, or if it is formed of an mfi- 

 nite number of white pencils polarized in every direction like 

 direct light. 



Nothing remains indeterminate in these formulas, but the kind 

 of the two colours O and E ; or rather of one of them, since 

 both together compose white : but experiment shows that the 

 colour E depends upon the thickness of the plate, and the nature 

 of the substance. By measuring with the greatest exactness the 

 thickness of a great number of plates, by means of a very accu- 

 rate instrument contrived by M. Cauchois, a skilful optician, M. 

 Biot found that in the same crystal very pure and homogeneous, 

 the thicknesses which polarize such and such a colour are pro- 

 portional to the thickness of the thin plates of the same substance, 

 which would reflect the same colour in the phenomenon of co- 

 loured rings. But Newton has given in his Optics a table of 

 these thicknesses, calculated from very exact experiments. We 

 may then, by means of that table, determine all the colours 

 which will be polarized by the plates of a given crystal, provided 

 we have measured the thickness of a single one, and observed 

 the colour which it polarizes. It is sufficient to refer the thick- 

 nesses of these plates to the scale of Newton by the simple rule 

 of proportion. We suppose here tbat the plates are cut parallel 

 to the axis of crystallization. The factor by which they must be 

 multiplied varies with the nature of the crystal; and even in 

 crystals whose chemical composition is similar, it undergoes 

 sometimes changes, depending upon the contexture of the 

 crystal, and its more or less perfect crystallization. But its value 

 is constant for every homogeneous crystal. In very pure sulphate 

 of lime, of the trapezian variety, the mean value of the factor is 

 about that is to say, that if we express the thickness of the 

 plates in millionth parts of millimetres, and take the ^th of it, 

 the result compared with the third column of the table of 

 Newton will give us the colour E, which eacli of these plates 



