refraction is unequal in different parts of the lens, rays from a point cannot be converged to a point, but either the more or the less converging will be spread out.

There is also a difficulty in refracting telescopes, owing to the differing refractions of the different colored rays. Violet rays, being the most refrangible, come to a focus sooner than those of any other color. Red rays, being less so, will have a longer focus. Any image formed in the focus of violet rays will be violet colored, and images may be formed between this and the focus of red rays of each color of the spectrum. Therefore no white image can be formed, for there is no one spot in which all the colored rays will be present.

§ 47. If the dispersive powers of different media were in proportion to their refractive powers, it would be impossible to correct this chromatic aberration. But fortunately different media produce spectra of different lengths when the mean refraction is the same. Let us compare two prisms, one of crown glass, the other of flint glass, with such a refracting angle that the light shall enter and quit them at equal angles, the mean ray of each will have the same refraction. But the spectrum produced by the flint glass will be longer than that produced by the crown prism. Thus flint glass is said to have a greater dispersive power than crown glass, because at the same angle of mean refraction it separates farther the extreme rays of the spectrum. Diamond has a refraction nearly three. times that of glass, while its dispersive power is less than that of glass.

§ 48. Now if different media produce different bands of color with the same focal length, it follows that they may produce equal bands of color with different focal lengths. A concave lens may be used with a convex lens of equal dispersive power, but a higher refractive power, and the excess of the refractive power, will be the available power of the lens, and white light will be refracted to the focus. Such a lens is called an achromatic lens, and the image formed by it would be perfect were there not in equal spectra formed by different media a difference which prevents their entirely neutralising one another's refrac

tion. The bands of the same color in the two spectra are not of equal breadth, and therefore the images seen through such a lens are bordered on one side with a purple, on the other with a green fringe.

A telescope which is free from dispersion is called achromatic; one which is free from aberration also is called aplanatic, or free from all errors.

Reflecting telescopes are perfectly free from color. For compound light is reflected, though not refracted, entire, all the colors following the same law of equal angles of incidence and reflection.

CHAPTER III.

ASTRONOMICAL INSTRUMENTS.

Difficulties in the construction of Telescopes. Telescope Stands. Transit Instrument. Graduated Circle and Vernier. Mural Circle. Polar and Horizontal Point. Transit Circle. The Equatorial. The Altitude and Azimuth Instrument. Theodolite. Sextant. Difficulties in Observing. Personal Equation. Lord Rosse's Reflectors.

§ 49. Though the theory of the construction of telescopes is attended with many difficulties, those which occur in practice are as numerous, perhaps some of them are insuperable. For a reflector, a perfectly uniform metal is required, free from all microscopic pores, not liable to tarnish, not so hard as to be incapable of taking a good figure and an exquisite polish, not so soft as to be easily scratched. Various compositions of metals are employed, consisting chiefly of copper and tin, with a little zinc, arsenic or silver. After casting they must be ground and polished with the utmost care. Lenses also require the greatest nicety in composition, casting, grinding, polishing, and centering. To ascertain if the shape is perfect, an opaque back is placed behind the lens, the lens is made to revolve, and a lighted candle is brought before it, whose reflected

image is attentively watched. If this image has any motion, the lens is not perfect in its adjustment.

§ 50. After an instrument is completed the next desideratum is a steady and immovable stand, free from vibration. The instrument should be supported at both ends to give steadiness, and to prevent its being affected by the wind; for every vibration will be increased in the same ratio as the amplification of the instrument, and produce a tremulous or dancing motion in the objects. Thus a superior telescope badly supported may be inferior to a common one on an immovable stand.

The materials of which stands are composed shou'd be capable of transmitting as little vibration as possible; the vibration of a frame of cast iron in one piece, though otherwise perfectly steady, would be sufficient to destroy distinct vision. The difficulty of preventing vibrations in reflecting telescopes greatly impairs their value, as they are more affected by such disturbance than refractors. Ä telescope, which taken from its stand and placed on a lump of soft clay would enable a person to read a bill placed at a distance of 900 feet, would on its stand make it distinct only at a distance of 650 fect, although no tremor would be discerned on the stand.

§ 51. A difficulty in placing an instrument arises from the absence of natural indications, other than those afforded by astronomical observations themselves, whether an instrument has or has not its true position with respect to the horizon and its cardinal points, the axis of the earth, or to other principal astronomical lines and circles. For instance, to place a transit instrument correctly, we must know the direction of our meridian, but we must first learn this meridian approximately by observing the shadow cast by the sun at noon.

The transit instrument consists of an astronomical telescope with wires and a micrometer, and is mounted on a nicely formed axis at right angles to itself. This axis remaining always horizontal and directed to the east and west points of the horizon rests at its extremities in two sockets perfectly even, and set in two blocks of stone of a size and weight sufficient to prevent all agitation. The

smooth extremities of the axis are capable of nice adjustment by screws, both in a vertical and horizontal direction. By placing a spirit level on the points, the axis can be made perfectly horizontal. Whether the axis lies precisely east and west can only be nicely ascertained by observations made with the instrument itself. When it is perfectly well adjusted the central line of the telescope will not quit the plane of the meridian when the instrument is turned round on its axis. The transit instrument is used to note the passage of bodies over the meridian, to note the right ascension of the fixed stars, the upper and lower culminations of the circumpolar stars, and for various problems in time and longitude.

§ 52. In the focus of the eye-piece and at right angles to the length of the telescope is placed the system of wires. This consists of one horizontal and five equidistant vertical threads or wires, which always appear in the field of view when properly illuminated, by day by the light of the sky, by night by that of a lamp. The horizontal wire is fixed, the middle vertical wire is brought to bisect the axis of the telescope, and thus to coincide with and represent that portion of the celestial meridian which appears in the field of view. When a star crosses this wire it culminates, or passes the celestial meridian. The instant of this event is noted by a clock or chronometer, an indispensable accompaniment of the transit instrument. For greater precision, the moment of crossing each of the five or seven vertical threads is noted and a mean taken between the times thus obtained, the threads being equidistant; this tends to subdivide and destroy the errors.

An important observation of its correctness consists in reversing the ends of the axis, or turning it east for west. If this be done, and it gives the same results, we may be sure that the line of collimation of the telescope is at right angles to its axis, and marks out in the heavens a great circle.

§ 53. To measure any small angular distance with a micrometer, as the diameter of a planet, two parallel wires are made to approach to or recede from each other till the body to be measured is exactly inclosed by them. Having accurately measured the planet by the two cross

wires, we must next ascertain their distance asunder. The wires are moved by screws. The very slow motion which may be imparted to the end of a screw by a very considerable motion in the power, makes it very useful in the measurement of minute motions and spaces. Suppose a screw cut so as to have fifty threads in an inch, each revolution of the screw will advance its point through the fiftieth part of an inch. Now suppose the head of the screw to be a circle whose diameter is one inch, the circumference of the head will be 3.14 inches. This may easily be divided into a hundred equal parts distinctly visible. If a fixed index be presented to this graduated circumference, the hundredth part of a revolution of the screw may be observed by noting the passage of one division of the head under the index. Since one entire revolution of the head moves the point through the fiftieth of an inch, one division will correspond to the five thousandth part of an inch.

Micrometer threads are made of spiders' webs, Indiarubber and glass threads, hair and wires. By thickly coating a fine platina wire with silver and drawing it out as fine as possible, and then dissolving the silver but not the platina, a very fine wire is obtained.

$54. The angular intervals measured by means of the clock and transit instrument, are arcs of the equinoctial intercepted between the hour circles passing through the objects observed. Their measurement is performed by no artificial graduation of circles, but by the help of the earth's diurnal motion, which carries equal arcs of the equinoctial across the meridian, in equal times, at the rate of 15° per sidereal hour.

In all other cases, when angular intervals are to be measured, circles or portions of circles are referred to, others constructed of metal, and mechanically subdivided into equal parts, such as degrees, minutes, &c. The instrument is sometimes movable upon the circle, sometimes both revolve together on an axis concentric with the circle, and forming one piece with it. As the telescope and circle revolve through any angle, the part of the limb of the latter, which by such revolution is carried past the index,