396 FOURTH REPORT — 1834. 



nation of the plate to the polarized heam. When the plate is 

 perpendicular to the transmitted pencil, and then turned round 

 in its own plane, the tint does not change, but only varies in 

 intensity, — being a maximum when the principal section of the 

 crystal is inclined at an angle of 45° to the plane of primitive 

 polarization, and vanishing altogether when it coincides with 

 that plane, or is perpendicular to it. On the other hand, when 

 the crystal is fixed, and the analysing plate turned so as to 

 vary the inclination of the plane of the second reflexion to that 

 of the first, the colours change in the most striking manner j 

 and it is found that the colour reflected, in any one position of 

 the plane of the second reflexion, is always complementary to 

 that i-eflected in the perpendicular position. The colours dis- 

 appear altogether when the thickness of the crystalline plate is 

 reduced below a certain limit *. 



The experimental laws of these phenomena were investigated 

 with unwearied zeal by M. Biotf. When the light was inci- 

 dent perpendicularly on plates of the same substance, of differ- 

 ent thicknesses, the tints were observed to follow the same law 

 as the colours of thin plates; the thicknesses of the crystal at 

 which each tint was developed in perfection being proportional 

 to the thicknesses of the plate of air which gave the same tint in 

 Newton's scale. These thicknesses vary with the nature of the 

 crystal 3 and are always much greater than the corresponding 

 thicknesses of the imcrystallized plate which exhibit the same 

 tint. Pursuing the same inquiry, afterwards, for oblique inci- 

 dences, M. Biot found that, in uniaxal crystals, the tint de- 

 veloped was determined by the length of the path traversed by 

 the light within the crystal, and by the square of the sine of 

 the angle which its direction made with the optic axis, jointly. 

 From this law it followed, that if a crystalline plate of moderate 

 thickness be cut perpendicularljf to the axis, and a converging 

 or diverging pencil transmitted through it, the lines of equal 

 tint,— or the isochromatic lines, as they are sometimes called, — 

 will be disposed in concentric circles similar to Newton's rings. 

 This phenomenon was observed, under different circumstances, 

 by Sir David Brewster, Dr. WoUaston, M. Biot, and M. See- 

 beck. 



The researches of M. Biot were followed by those of Sir 

 David Brewster. In investigating the law of the tints in biaxal 

 crystals. Sir David Brewster considers the optic axes as the re- 

 sultants of others which he denominates polarizi7ig axes. The 

 tint developed by a single axis is taken as the measure of its 



• M6m. Inst. 1811. t ^f>id. 1812. 



