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the spectrum. Behind the slit, at a distance equal to its focal length, is an achromatic lens of 4 inches focal length. The dispersing portion of the apparatus consists of two prisms of dense flint glass, each having a refracting angle of 60°. The spectrum is viewed through a small achromatic telescope, provided with proper adjustments, and carried about a centre suitably adjusted to the position of the prisms by a fine micrometer screw. This measures to about the th part of the interval between A and H of the solar spectrum. A small mirror attached to the instrument receives the light, which is to be compared directly with the star spectrum, and reflects it upon a small prism placed in front of one half of the slit. This light was usually obtained from the induction-spark taken between electrodes of different metals, raised to incandescence by the passage of an induced electric current.

506. The spectroscope represented in Plate XIII. is a very powerful one, made by Mr. Browning for Mr. Gassiot, and was for some time employed at the Kew Observatory for mapping the solar spectrum. The light enters at a narrow slit in the left-hand collimator, which is furnished with an object-glass at the end next the prism, to render the rays parallel before they enter the prisms. In the passage through the prisms the cylindrical beam of light is made to describe a circular path, widening out as it goes, and in consequence enters the telescope on the right of the drawing.

It is often convenient to employ what is termed a direct-vision spectroscope—that is, one in which the light

FIG. 60.-Path of the ray in the Herschel-Browning spectroscope. enters and leaves the prisms in the same straight line. How this is managed in the Herschel-Browning spectro

scope, one of the best of its kind, may be gathered from Fig. 60.

507. In both telescopic and spectroscopic observations the visible rays of light are used. The presence of the chemical rays, however, enables photographs of the heavenly bodies to be taken, and celestial photography, in the hands of Mr. De la Rue and Mr. Rutherfurd, made its first rapid advance towards its present high state of perfection. The method adopted is to place a sensitive plate in the focus of a reflector or refractor properly corrected for the actinic rays, and then to enlarge this picture to the size required. Mr. De la Rue's pictures of the Moon, some 1 inches in diameter, are of such perfection that they bear subsequent enlargement to 3 feet. Prints of the Sun are now regularly taken at Greenwich and South Kensington; and where the record is interrupted by clouds, it is filled in by pictures obtained on the same plan in the Mauritius and in India. The art promises to be one of the great engines of astronomical research in the future. Already a nebula has been discovered in the Pleiades by the camera, which had never previously been seen with the telescope, and stars down to the sixteenth magnitude can be photographed with such distinctness that the laborious process of charting small stars may be said to be superseded by the comparatively expeditious method of printing them, or rather, letting them print themselves. The absolute truthfulness of celestial photographs gives them a special value as records. Mr. Common's splendid picture of the Orion nebula may reveal to future astronomers changes of wonderful interest in that strange mass of glowing vapours. Tebbutt's comet was the first body of the kind successfully photographed, previous attempts having failed through the extreme chemical feebleness of cometary light. Now, however, not only comets themselves, but their spectra, as well as the spectra of stars, nebulæ, sunspots, and even of the solar chromosphere across the blaze of daylight, stamp their impressions with the utmost delicacy on the sensitive plate.

5214

CHAPTER VII.

DETERMINATION OF THE APPARENT PLACES
OF THE HEAVENLY BODIES.

LESSON XLI.--Geometrical Principles. Circle. Angles. Plane and Spherical Trigonometry. Sextant. Micrometer. The Altazimuth and its Adjustments.

508. That portion of our subject which deals with apparent positions is based upon certain geometrical principles, among which the properties of the circle are the most important.

509. A circle is a figure bounded by a curved line, all the points in which are at the same distance from a point within the circle called the centre. The curved line itself is called the circumference; a line from any part of the circumference to the centre is called a radius; and if we prolong this line to the opposite point of the circumference we get a diameter. Consequently, a diameter is equal to two radii.

510. The circumference of every circle, large or small, is divided into 360 parts, called degrees, which, as we have before stated (Art. 159), are divided into minutes and seconds, marked (′) and ("), to distinguish them from minutes and seconds of time, marked (m) and (3).

511. That part of the circumference intercepted by any lines drawn from it to the centre is called an arc, and the two lines which join at the centre inclose what is called an angle, the angle in each case being measured by the arc of the circumference of the circle intercepted.

512. The arc, and therefore the measured angle, will contain the same number of degrees, however large or small the circle may be —or, in other words, whatever be the diameter. Each degree will, of course, be larger in a large circle than in a small one, but the number of degrees in the whole circumference will always remain the same; and therefore the angle at the centre will subtend the same number of degrees, whatever be the radius of the circle.

513. An angle of 90° is called a right angle, and there are therefore four such angles at the centre of a circle. The two lines which form a right angle are said to be at right angles to each other. If we print a T, for instance, like this, we get two right angles, and the upright stroke is called a perpendicular.

514. When the opening of an angle is expressed by the number of degrees of the arc of a circle it contains, it is called the angular measure of the angle. Another property of the circle is, that whatever be its size, the diameter, and therefore the radius, always bears the same proportion to the circumference. The circumference is a little more than three times the diameter-more exactly expressed in decimals, it is 3.14159 times the diameter; in other words

diam. × 314159=circumference ;

and therefore

circumference÷3*14159=diameter.

For the sake of convenience, this number 3.14159 is expressed by the Greek letter π. When either the radius, diameter, or circumference is known, we can easily find the others.

A

515. We next come to the properties of triangles. triangle is a figure which contains three angles, and it is therefore bounded by three sides. If all three sides are on the same plane, the triangle is called a plane triangle ; but if they lie on the surface of a sphere, it is called a spherical triangle, and the sides, as well as the angles, may be expressed in angular measure; as the angular length of each side is the angle formed by its two ends at the centre of the sphere. For instance, if we on a terrestrial globe draw lines connecting London, Dublin, and Edinburgh, we shall have a spherical triangle, as the Earth is a sphere; and we can express the opening of each angle and the length of each side in degrees. We may treat three stars on the celestial sphere in the same manner. Each angle of a plane triangle is determined as we have already seen; and it is one of the properties of a triangle that the three interior angles taken together are equal to two right angles—that is, 180°. It is clear, therefore, that if we know two of the angles, the third is found by subtracting their sum from 180°.

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Here are two triangles, and they look very unlike; but there is one thing in which we have just seen they exactly resemble each other. The angles a b c in both are together equal to two right angles. Now one is a right-angled triangle, i.e. the angle b is a right angle, or an angle that contains 90°; consequently, we know that the other angles, a and c, are together equal to 90°; and therefore,

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