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equal to the transmitted light; at 26° 38' it is equal to, the variation, according to Arago, being as the square of the cosine.

NOTE 189, p. 154. Atmospheric refraction. Let a b, a b, &c., fig. 49, be strata, or extremely thin layers, of the atmosphere, which increase in

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density towards m n, the surface of the earth. A ray coming from a star meeting the surface of the atmosphere at S would be refracted at the surface of each layer, and would consequently move in the curved line S v v v A ; and as an object is seen in the direction of the ray that meets the eye, the star, which really is in the direction A S, would seem to a person at A to be in s. So that refraction, which always acts in a vertical direction, raises objects above their true place. For that reason, a body at S', below the horizon H A O, would be raised, and would be seen in s'. The sun is frequently visible by refraction after he is set, or before he is risen. There is no refraction in the zenith at Z. It increases all the way to the horizon, where it is greatest, the variation being proportional to the tangent of the angles Z A S, ZAS', the distances of the bodies S S' from the zenith. The more obliquely the rays fall, the greater the refraction.

Fig. 50.

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NOTE 190, p. 154. Bradley's method of ascertaining the amount of refraction. Let Z, fig. 50, be the zenith or point immediately above an observer at A; let HO be his horizon, and P the pole of the equinoctial A Q. Hence PAQ is a right angle. A star as near to the pole as s would appear to revolve about it, in consequence of the rotation of the earth. At noon, for example, it would be at s above the pole, and at midnight it would be in s' below it. The sum of the true zenith distances, Z As, Z As', is equal

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to twice the angle ZA P. Again, S and S' being the sun at his greatest distances from the equinoctial AQ when in the solstices, the sum of his true zenith distances, Z AS, ZAS', is equal to twice the angle ZAQ. Consequently, the four true zenith distances, when added together, are equal to twice the right angle QAP; that is, they are equal to 180°. But the observed or apparent zenith distances are less than the true on account of refraction; therefore the sum of the four apparent zenith distances is less than 1800 by the whole amount of the four refractions.

NOTE 191, p. 155.

Terrestrial refraction. Let C, fig. 51, be the centre of the earth, A an observer at its surface, A H his horizon, and B

Fig. 51.

H

D

some distant point, as the top of a hill. Let the arc B A be the path of a ray coming from B to A; EB, EA, tangents to its extremities; and AG, BF, perpendicular to CB. However high the hill B may be, it is nothing when compared with CA, the radius of the earth; consequently, A B differs so little from A D that the angles A E B and ACB are supplementary to one another; that is, the two taken together are equal to 1800. ACB is called the horizontal angle. Now BAH is the real height of B, and EAH its apparent height; hence refraction raises the object B, by the angle EA B, above its real place. Again, the real depression of A, when viewed from B, is FBA, whereas its apparent depression is FBE, so EBA is due to refraction. The angle FBA is equal to the sum of the angles BA H and A CB; that is, the true elevation is equal to the true depression and the horizontal angle. But the true elevation is equal to the apparent elevation diminished by the refraction; and the true depression is equal to the apparent depression increased by refraction. Hence twice the refraction is equal to the horizontal angle augmented by the difference between the apparent elevation and the apparent depression.

NOTE 192, p. 155. Fig. 52 represents the phenomenon in question. SP is the real ship, with its inverted and direct images seen in the air. Were there no refraction, the rays would come from the ship SP to the eye E in the direction of the straight lines; but, on account of the variable density of the inferior strata of the atmosphere, the rays are bent in the curved lines Pc E, Pd E, Sm E, Sn E. Since an object is seen in the direction of the tangent to that point of the ray which meets the eye, the point P of the real ship is seen at p and p', and the point S seems to be in s and s'; and, as all the other points are transferred in the same manner, direct and inverted images of the ship are formed in the air above it.

S

Fig. 52.

E

NOTE 193, p. 156. Fig. 53 represents the section of a poker, with the refraction produced by the hot air surrounding it.

NOTE 194, p. 156.

The solar spectrum. A ray from the sun at S, fig. 54, admitted into a dark room, through a small round hole H in a

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window-shutter, proceeds in a straight line to a screen D, on which it forms a bright circular spot of white light, of nearly the same diameter with the hole H. But when the refracting angle BAC of a glass prism is interposed, so that the sunbeam falls on AC the first surface of the prism, and emerges from the second surface A B at equal angles, it causes the rays to deviate from the straight path SD, and bends them to the screen M N, where they form a coloured image V R of the sun, of the same breadth with the diameter of the hole H, but much longer. The space VR consists of seven colours-violet, indigo, blue, green, yellow, orange, and red. The violet and red, being the most and least refrangible rays, are at the extremities, and the green occupy the middle part at G. The angle Dg G is called the mean deviation, and the spreading of the coloured rays over the angle Vg R the dispersion. The deviation and dispersion vary with the refracting angle B A C of the prism, and with the substance of which it is made.

NOTE 195, pp. 159, 164. Under the same circumstances, and where the refracting angles of the two prisms are equal, the angles Dg G and V g R, fig. 54, 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 neutralize each other's effects, and refract a beam 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. NOTE 196, p. 165. The object glass of the achromatic telescope consists of a convex lens A B, fig. 55, of crown-glass placed on the Fig. 55. outside, towards the object, and of a concave-convex 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 CD be so constructed that their focal lengths are in the same proportion as their dispersive powers, they will refract rays of light without colour.

A C

NOTE 197, p. 165. If the mean refracting angle of the prism Dg G, fig. 54, were the same for all substances, then the difference Dg V-Dg R would be the dispersion. But the angle of the prism being the same, all these angles are different in each substance, so that in order to obtain the dispersion of any substance the angle DgV-Dg R must be divided by the angle Dg G or its excess above unity, to which the mean refraction is always proportional. According to Mr. Fraunhofer the refraction of the extreme violet and red rays in crownglass is 1.5466 and 1.5258; so Dg V-Dg R=1.5466 — 1·5258 = '0208, and half the sum of the excess of each above unity is 5362; consequently

BD

DgVDgR_0208

⚫5362

=

=0.03879; for diamond

DgG

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so that the dispersive power of diamond is a little less than that of crownglass; hence the splendid refracted colours which distinguish diamond from every other precious stone are not owing to its high dispersive power, but to its great mean refraction.-SIR DAVID BREWSTER.

NOTE 198, p. 168. When a sunbeam, after having passed through a coloured glass V V', fig. 56, enters a dark room by two small slits O O' 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 When a hair, or a small slip of

a card, and received on a screen SS'.

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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 199, pp. 171, 200. 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 blueish green, pale yellowish pink, red.

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