1813.] Imperial Institute of France. 233 



on the light, or diminishes it, according to regular laws, which 

 may be calculated. These M. Biot has deduced from experi- 

 ment, and he developes them in detail. This holds with plates 

 of mica regularly crystallized; and this simultaneous action of 

 three axes is the cause of all the anomalies which that substance 

 presents when it is exposed under different incidences to a polar- 

 ized ray. 



To imitate this opposition of two rectangular axes of which 

 these actions are composed, M. Biot, in a fourth memoir, places 

 above each other two plates of sulphate of lime, so that their 

 axes are rectangular, and exposes them in that manner to the 

 polarized ray, beginning at first with very thin plates, and passing 

 successively to those of greater and greater thickness. The 

 colour polarized in this case is always that which agrees with the 

 difference of the thickness ; but the variations of these colours 

 by changes of incidence are a great deal more extensive than in 

 simple plates, because they depend upon the sum of the thick- 

 ne^es. 



This result being verified for the whole series of colours con- 

 tained in the table of Newton, from the smallest degree of 

 thickness in the plates to the greatest capable of producing 

 colour, it was probable that the same property would extend to 

 any thickness whatever. This is in reality the case. If we take two 

 plates of sulphate of lime, whose thicknesses are e^ and place 

 them above each other in such a manner that their axes cross at 

 right angles, the colour polarized will be that which corresponds 

 to a single plate of the thickness — e. If the quantity e' — e 

 be within the Hmits of thickness which give colour, then colours 

 will he produced; but if — e be beyond these limits, we shall 

 have two white images, li e^ — e is o, the colour polarized by 

 the system is o also, and the second plate destroys what the first 

 produced. 



In this manner colours may be produced with plates of any 

 thickness whatever. It is not even necessary that the plates be of 

 the same nature, provided the difference of their actions on light 

 be of the order of that which alone would give coloured images. 

 Thus we may cross a plate of rock crystal with a plate of sul- 

 phate of lime, of mica, or of sulphate of barytes ; but the 

 thicknesses which must be given to each of these crystals are 

 different, according to the intensity of their action. A plate of 

 sulphate of lime, of a millimetre in thickness, is sufficient to 

 produce colours with a plate of ice several centimetres thick.* 

 We have only to cross their axes at right angles. This takes 

 place equally, whether the plates touch, or be separated to some 

 distance from each other. 



* A rairjuetreis 0*03937 inch, a centimetre 0'S93T inch. 

 I 



