POLARISATION OF LIGHT. 



Fig. 56. 



or the positive the positive structure. 

 By determining the tint at any given 

 }x>int in each plate by the preceding 

 formula, and combining these tints ac- 

 cording to the rules already given, it 

 will be found that the lines of equal tint, 

 which we may call the isochromatic lines 

 in the square of intersection ABCD, 

 are hyperbolas, which will be equilateral 

 when the breadths of the two plates and 

 their maximum tints are the same*. The 

 beauty of this combination surpasses 

 all description. 



When a positive rectangular plate 

 crosses a negative rectangular plate, it 

 will be found, by the same method, that 

 the isochromatic lines in the rectangle 

 of intersection are perfect circles when 

 the breadth of the plate and the tints 

 in each are the same : this effect is shewn 

 mfig. 57. But when the breadth of the 

 plates is different, the isochromatic lines 

 will be ellipses. 



Fig. 57. 



4. On the distribution of the doubly 

 refracting force in spheres, spheroids, 

 and tubes of glass. If we take a cold 



* See Edin. Transactions, voL viii. p. 35?. 



51 



sphere of glass and immerse it in a 

 trough of hot oil placed in the polarising 

 apparatus fig. 39, we shall observe, 

 when the heat has reached its centre, 

 a black cross with four sectors of polar- 

 ised light like the inner circle of fig. 25. 

 The maximum tint is not at the edge, 

 but nearly half way between the centre 

 and the circumference of the sphere. If 

 in this state the sphere is turned round 

 in the trough, it will exhibit in every po- 

 sition the very same figure. If we now 

 suppose the trough to be filled with 

 such spheres, they will exhibit the same 

 phenomena in whatever direction the 

 polarised light is transmitted through 

 the fringes, and even if the spheres 

 were in a state of motion in the 

 trough. A fluid composed of such 

 spherical particles would exhibit the 

 same polarising structure in every pos- 

 sible direction, and even if it were in a 

 state of rapid gyration. If the particles 

 possessed the" structure that produces 

 circular polarisation, the fluid would de- 

 velope the phenomena exhibited by oil 

 of turpentine and the other fluids already 

 mentioned in Chapter XII, p. 5. 



If a spheroid is used in place of a 

 sphere, the structure will be symmetri- 

 cal only round its axis of revolution, 

 viz., the shorter axis, if it is oblate, and 

 the longer axis, if it is prolate. If the 

 polarised ray A G,fig. 39, passes along 

 any of these axes, we shall observe a 

 black rectangular cross, and four lumi- 

 nous sectors, which will remain unal 

 tered during the motion of the spheroids 

 round the axis of revolution. But if 

 this axis is inclined to A C, the sym- 

 metry of the figure is deranged, and the 

 black cross will sometimes open at the 

 centre. If an equatorial diameter of 

 the spheroid is parallel to A C, then the 

 black cross will be complete when the 

 plane of the equator is parallel or per- 

 pendicular to the plane of primitive po- 

 larisation, but it will open at the centre, 

 in other positions, like the system of 

 rings in crystals with two axes. 



if heat is applied to the circumference, 

 A C BD, fig. 58, of a glass tube, whose 

 diameter is AB, and the diameter of 

 whose bore is ab, the black cross AB, 

 C D, will be seen, and there will be 

 observed a dark circle, mnop, of no 

 double refraction, having in the outside 

 the positive doubly refracting structure, 

 and in the inside the negative doubly 

 refracting structure. The breadth of 

 the negative annulus is less than that 

 E 2 



