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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 SS'. 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 fringes 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 194, pp. 191, 221. 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. 2nd ring: Dark purple, or rather violet, blue, a very imperfect yellow green, vivid yellow, crimson red.

3rd 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 become 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.

Fig. 59.

NOTE 195, p. 193. The absolute thickness of the film of air between the glasses is found as follows:-Let AFBC, fig. 59, be the section of a lens 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 CE, then BD or C F is the thickness of the air producing it. EC is a known quantity, and when A B, the diameter, is measured with compasses, BD or FC can be computed. Newton found that the length of BD corresponding to the darkest part of the first ring, is the 98000th part of an inch when the 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 suc




cession 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 196, p. 194. The focal length or distance of a lens is the distance from its centre to the point F, fig. 60, in which the refracted rays meet. Let LL' be a lens of very short focal distance fixed in the windowshutter 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 pin-hole 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 6 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.

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

3rd order: Purple, indigo, blue, greenish blue, brilliant green, yellow green, red.

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

5th order: Dull green, faint bluish white, faint red.
6th order: Very faint green, very faint red.
7th order: A trace of green and red.

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NOTE 197, p. 195. Let LL', fig. 61, be the section of a lens placed in a windowshutter, 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, rr, &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.


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NOTE 198, p. 198. Fig. 43 represents the phenomena in question, where S S 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 199, p. 201. Fig. 62 represents a prismatic crystal of tourmaline, whose axis is A X. The slices that are used for polarising light are cut parallel to A X.

NOTE 200, p. 203. 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

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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 O o, E o, 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 184), and the rays Rr, rO, Oo, are all in the same plane. The pencil rE, 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 rO 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 rI; and when the crystal is turned round, the image E revolves about O, which remains stationary.

NOTE 201, p. 204. Both of the parallel rays Oo 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, E o. 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 202, p. 204. 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. 63, 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 203, p. 206. If I C, fig. 48, be the incident and C S the reflected rays, then the particles of polarised light make their vibrations at right angles to the plane of the paper.

NOTE 204, p. 206. Let A B, fig. 48, be the surface of the reflector, I C the incident and CS the reflected rays; then, when the angle SCB is 57°, and consequently the angle P C S equal to 33°, the black spot will be seen at C by an eye at S.

NOTE 205, p. 207. Let A B, fig. 48, be a reflecting surface, I C the incident and C S the reflected rays; then, if the surface be plate-glass, the angle SC B must be 57°, in order that C S may be polarised. If the surface be crown-glass or water, the angle SC B must be 56° 55′ for the first, and 53° 11' for the second, in order to give a polarised ray. 1

NOTE 206, p. 209. A polarising apparatus is represented in fig. 64, where R is a ray of light falling on a piece of glass r at an angle of 57°, the re

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flected ray r s is then polarised, and may be viewed through a piece of tourmaline in 8, or it may be received on another plate of glass, B, whose surface is at right angles to the surface of r. The ray rs is again reflected in s, and comes to the eye in the direction & E. The plate of mica, M I, or of any substance that is to be examined, is placed between the points r and s.

NOTE 207, p. 211. In order to see these figures, the polarised ray rs, fig. 64, must pass through the optic axis of the crystal, whch must be held as near as possible to 8, on one side, and the eye placed as near as possible to s on the

other. Fig. 65 shows the image formed by a crystal of Iceland spar which has one optic axis, The colours in the rings are exactly the same with those of Newton's rings given in Note 194, and the cross is black. If the spar be turned round its axis, the rings suffer no change; but if the tourmaline through which it is viewed, or the plate of glass, B, be turned round, this figure will be seen at the angles 0°, 90°, 180°, and 270° of its revolution. But in the intermediate points, that is, at the angles 45°, 135°, 225°, and 315°, another system will appear, such as represented in fig. 66, where all the colours of the rings are complementary to those of fig. 65, and the cross is white. The two systems of rings, if superposed, would produce white light.

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NOTE 208, p. 208. Saltpetre, or nitre, crystallises in six-sided prisms having

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