50 



POLARISATION OF LIGHT, 



Fig. 54. 



to be about three times that of a b,fig. 55, 

 the tints have the form shown in fig. 55. 



Fig. 55. 



In all these cases beautiful complemen- 

 tary systems of fringes are produced by ' 

 causing the plate C, fig. 39, to revolve 

 90 ; but we cannot find room for 

 figures of these phenomena, of the beauty 

 of which it is impossible to form any 

 idea without coloured drawings. When 

 the heat is uniformly distributed over 

 these plates of glass, the colours ah 1 dis- 

 appear. 



The tints in all these phenomena are 

 similar to those polarised by crystallised 

 bodies, and are regulated by the very 

 same laws, mutatis mutandis. 



By comparing the values of the tints 

 with their distances from the central 

 line a b, of the plate in fig. 53, Dr. 

 Brewster found that they were repre- 

 sented by the following formula, founded 

 on the supposition of two series of rect- 

 angular axes. Let d be the distance 

 from a b of the point at which the tint 

 t is required, T the maximum tint in the 

 centre a b of the plate, and D the dis- 

 tance of either of the -black lines M N, 



TV/* 

 OP from ab : then t = T ~. The 



Td 2 

 term = represents the tint which 



would be produced by the principal axis 

 perpendicular to the plate, and passing 

 through its centre ; but as the axis in 

 the plane of the plate would produce an 

 uniform tint, T, in every part of the plate, 

 which acts in opposition to the other tint, 

 the real tint / will be equal to the diff er- 



Td* 

 ence of these, ortoT r ; or, making 



T and D equal to unity, we have 



t = I T- C/ 2 , 



In order to find the tint at any point 

 in terms of the shortest distance of that 

 point from the lines of no double refrac- 

 tion MN, OP, let 3, y be the distances of 

 the point from MN, OP : then since d is 

 the distance of that point from the central 

 line a b, we have S = 1 d, y = 1 d, and 

 ^l' 1 d 2 : that is, the tint t at any point 

 varies as the product of the distances 

 of that point from the lines of no double 

 refraction. Calling v the velocity of 

 the extraordinary ray, and V that of the 



ordinary ray, we shall have v = VV 2 + aW 

 a formula which represents the extra- 

 ordinary refraction in rectangular plates 

 of glass. In circular plates the expres- 

 sion will be v= VV 2 +aB 2 . 



If the plate of glass, highly and 

 uniformly heated, is placed upon a cold 

 piece of iron A B, it will exhibit similar 

 fringes ; but the double refraction between 

 MN, OP, will now be positive, and the 

 extreme fringes negative : and in this 



Analogous effects are produced in 

 plates of rock salt, fluor spar, obsidian, 

 semiopal, rosin, copal, amber, &c. 



As the heat of the hand is sufficient 

 to develope a faint system of fringes in 

 a plate of glass, the number of fringes 

 and tints may be increased indefinitely by 

 increasing the number of plates, and 

 hence the foundation of Dr. Brewster's 

 Chromatic differential Thermometer, by 

 which differences of heat may be mea- 

 sured by the numerical value of the tints 

 produced by a bundle of glass plates. 



3. On the effects of combining and 

 crossing Rectangular Plates of Glass. 

 When two positive or two negative 

 rectangular plates of glass are combined, 

 so that the lines M N, o j>, fig. 53, are 

 parallel, the combination will be positive 

 or negative according to the character 

 of the individual plates, arid the tints will 

 be equal to \vhat would have been pro- 

 duced, by using a plate equal to the sum 

 of their thicknesses ; when a negative 

 and positive plate are similarly com- 

 bined, the effect will be equal to the dif- 

 ference of their action. If their actions 

 are equal, the effect of the combination 

 will be to destroy the double refraction 

 altogether. 



If two negative or t\vo positive rect- 

 angular plates are crossed, as in fig. 56, 

 the tints in the square of intersection 

 are raised where the negative crosses 

 the positive structure, and depressed 

 where the negative crosses the negative, 



