are greater for flint glass than for crown glass. But as they vary with the angle of the prism, it is only necessary to augment the refracting angle of the crown glass prism by a certain quantity, to produce nearly the same deviation and dispersion with the flint glass prism. Hence, when the two prisms are placed with their refracting angles in opposite directions, as in fig. 54., they nearly neutralise each other's effects, and refract a ray of light without resolving it into its elementary coloured rays. Sir David Brewster has come to the conclusion, that there may be refraction without colour by means of two prisms, or two lenses, when properly adjusted, even though they be made of the same kind of glass.

Fig. 55.
A C

NOTE 190. p. 194. The object glass of the achromatic telescope consists of a convex lens A B, fig. 55., of crown glass placed on the outside towards the object, and of a concavoconvex lens CD of flint glass placed towards the eye. The focal length of a lens is the distance of its centre from the point in which the rays converge, as F, fig. 60. If, then, the lenses A B and C D be so constructed that their focal lengths are in the same proportion as their dispersive powers, they will refract rays of light without colour.

BD

NOTE 191. p. 198. When a sun-beam, after having passed through a coloured glass V V', fig. 56., enters a dark room by two small slits O0' in a card, or piece of tin, they produce alternate bright and black bands on a screen SS' at a little distance. When either one or other of the slits O or O' is stopped, the dark bands vanish, and the screen is illuminated by a uniform light, proving that the dark bands are produced by the interference of the two sets of rays. Again, let Hm, fig. 57., be a beam of white light passing through a hole at H, made with a fine needle in a piece of lead or a card, and received on a screen S S'. When a hair, or a small slip of card hh' about the 30th of an inch in breadth, is held in the beam, the rays bend round on each side of it, and, arriving at the screen in different states of vibration, interfere and form a series of coloured fringe on each side of a central white band m. When a piece of card is interposed at C, so as to intercept the light which passes on one side of the hair, the coloured fringes vanish. When homogeneous light is used, the fringes are broadest in red, and become narrower for each colour of the spectrum progressively to the violet, which gives the narrowest and most crowded fringes. These very elegant experiments are due to Dr. Thomas Young.

Fig. 58.

NOTE 192. pp. 202. 237. Fig. 58. shows Newton's rings, of which there are seven, formed by screwing two lenses of glass together. Provided the incident light be white, they always succeed each other in the following order:

1st ring, or 1st order of colours: Black, very faint blue, brilliant white, yellow, orange, red. L 2d ring: Dark purple, or rather violet, blue, a very imperfect yellow green, vivid yellow, crimson red.

3d ring: Purple, blue, rich grass green, fine yellow, pink, crimson.

4th ring: Dull bluish green, pale yellowish pink, red.

5th ring: Pale bluish green, white, pink.

6th ring: Pale blue-green, pale pink.

7th ring: Very pale bluish green, very pale pink.

After the seventh order, the colours became too faint to be distinguished. The rings decrease in breadth, and the colours become more crowded together, as they recede from the centre. When the light is homogeneous, the rings are broadest in the red, and decrease in breadth with every successive colour of the spectrum to the violet.

NOTE 193. p. 204. The absolute thickness of the film of air between the glasses is found as follows:- Let A FBC, fig. 59., be the section of a lens

Fig. 59.

E

lying on a plane surface or plate of glass P P', seen edgewise, and let EC be the diameter of the sphere of which the lens is a segment. If A B be the diameter of any one of Newton's rings, and BD parallel to C E, then BD or CF is the thickness of the air producing it. EC is a known quantity, and when AB the diameter is measured with compasses, BD or FC can be computed. Newton found that the length of B D, corresponding to the darkest part of the first ring, is the 98000th part of an inch when Pthe rays. fall perpendicularly on the lens, and from this he deduced the thickness corresponding to each colour in the system of rings. By passing each colour of the solar spectrum in succession over the lenses, Newton also determined the thickness of the film of air corresponding to each colour from the breadth of the rings, which are always of the same colour with the homogeneous light.

NOTE 194. p. 206. There are seven rings, and not three, as stated in the text. Let LL', fig. 60., be a lens of very short focus fixed in the window shutter of a dark room. A sunbeam SLL passing through the lens, will be brought to a focus in F, whence it will diverge in lines FC, FD, and will form a circular image of light on the opposite wall. Suppose a sheet of lead, having a small pin-hole pierced through it, to be placed in this beam; when the pinhole is viewed from behind with a lens at E, it is surrounded with a series of coloured rings, which vary in appearance with the relative positions of the pin-hole and eye with regard to the point F. When the hole is the 30th of an inch in diameter and at the distance of 63 feet from F, when viewed at the distance of 24 inches, there are seven rings of the following colours :

1st order: White, pale yellow, yellow, orange dull red.

2d order: Violet, blue, whitish, greenish yellow, fine yellow, orange red.

3d order: Purple, indigo blue, greenish blue, bril. liant green, yellow green, red.

4th order; Good green, bluish white, red.

5th order: Dull green, faint bluish white, faint red.

B

C

D

Fig. 60.
S

H

6th order: Very faint green, very faint red. 7th order: A trace of green and red.

NOTE 195. p. 207. Let LL', fig. 61., be the section of a lens placed in a window shutter,through which a very small beam of light SLL' passes into a dark room, and comes to a focus in F. If the edge of a knife KN be held in the beam, the rays bend away from it in hyperbolic curves Kr, Kr', &c. instead of coming directly to the screen in the straight line KE, which is the boundary of the shadow. As these bending rays arrive at the screen in different states of undulation, they interfere, and form a series of coloured fringes, r r', &c. along the edge of the shadow KESN of the knife. The fringes vary in breadth with the relative distances of the knife edge and screen from F.

NOTE 196. p. 210. Fig. 43. represents the phenomenon in question, where SS is the surface, and I the centre of incident waves. The reflected waves are the dark lines returning towards I, which are the same as if they had originated in C on the other side of the surface.

Fig. 62.

NOTE 197. p. 213. Fig. 62. represents a prismatic piece of tourmaline, whose axis is A X. The slices that are used for polarsing light are cut parallel to A X.

X

NOTE 198. p. 215. Double refraction. If a pencil of light Rr, fig. 63., falls upon a rhombohedron of Iceland spar A B X C, it is separated into two equal pencils of light at r, which are refracted in the directions r O, r E: when these arrive at O and E they are again refracted, and pass into

the air in the directions Oo, Eo, parallel to one another and to the incident ray Rr. The ray r O is refracted according to the ordinary law, which is,

that the sines of the angles of incidence and refraction bear a constant ratio to one another (see Note 182.), and the rays R r, r O, O o, are all in the same plane. The pencil r E, on the contrary, is bent aside out of that plane, and its refraction does not follow the constant ratio of the sines: r E is therefore called the extraordinary ray, and r O the ordinary ray. In consequence of this bisection of the light, a spot of ink at O is seen double at O and E, when viewed from r; and when the crystal is turned round, the image E revolves about O, which remains stationary.

NOTE 199. p. 216. Both of the parallel rays O o and E o, fig. 63., are polarised on leaving the doubly refracting crystal, and in both the particles of light make their vibrations at right angles to the lines Oo, Eo. In the one, however, these vibrations lie, for example, in the plane of the horizon, while the vibrations of the other lie in the vertical plane perpendicular to the horizon.

NOTE 200. p. 217. If light be made to fall in various directions on the natural faces of a crystal of Iceland spar, or on faces cut and polished artificially, one direction A X, fig. 60., will be found, along which the light passes without being separated into two pencils. A X is the optic axis. In some substances there are two optic axes forming an angle with each other. The optic axis is not a fixed line, it only has a fixed direction; for if a crystal of Iceland spar be divided into smaller crystals, each will have its optic axis; but if all these pieces be put together again, their optic axes will be parallel to A X. Every line, therefore, within the crystal parallel to A X is an optic axis; but as these lines have all the same direction, the crystal is still said to have but one optic axis.

NOTE 201. p. 219. If IC, fig. 48., be the incident, and CS, the reflected rays, then the particles of polarised light make their vibrations at righ angles to the plane of the paper.

NOTE 202. p. 219. Let A B, fig. 48., be the surface of the reflector, IC