Various natural as well as artificial reflecting surfaces have been made by mechanical arrangements, to afford the means of obtaining double angles: such as pouring water, oil, treacle, or other fluid substances into a shallow vessel; and to prevent the wind giving a tremulous motion to its surface, a piece of thin gauze, talc, or plate-glass, whose surfaces are perfectly plane and parallel, may be placed over it, when used for observation. But the most accurate kind of artificial horizon is that in which fluid quicksilver forms the reflecting surface, the containing vessel being placed on a solid basis, and protected from the influence of the wind. The adjoining figure represents an instrument of this kind. The mercury is contained in an oblong wooden trough, placed under the roof A, in which are fixed two plates of glass whose surfaces are plane and parallel to each other. This

roof effectually screens the surface of the metal from being agitated by the wind, and when it has its position reversed at a second observation, any error occasioned by undue refraction at either plate of glass will be corrected.

Another and more portable contrivance for an artificial horizon, is represented in the following figure, which consists of a circular plate of black glass about two inches diameter, mounted on a brass stand, half an inch deep, with three foot-screws, a, b, c, to set the plane horizontal; the horizontality being determined thus by the aid of a short spiritlevel, d, having under the tube a face ground plane on which it lies in contact with the reflecting surface; place the level on the glass in a direction parallel to the

line joining two of the three foot-screws, as a and b, then move one of these screws till the bubble remains in the middle of the tube in both the reversed positions of the level, and the plate will be horizontal in that direction; then place the level

at right angles to its former position, and turn the third footscrew back or forwards till the bubble again settles in the middle of its tube, the former levelling remaining undisturbed, and the plane will then be horizontal. This instrument, from its portability, is extremely convenient for travellers, as when packed in its case, it can be carried in the pocket without being any incumbrance.

When an artificial horizon is used, the observer must place himself at such a distance that he may see the reflected object as well as the real one; then having the sextant properly adjusted, the upper or lower limb of the sun's image (supposing that the object) reflected from the index-glass, must be brought into contact with the opposite limb of the image reflected from the artificial horizon, observing that when the inverting telescope is used, the upper limb will appear as the lower, and vice versâ ;* the angle shown on the instrument, when corrected for the index error, will be double the altitude of the sun's limb above the horizontal plane; to the half of which, if the semi-diameter, refraction, and parallax be applied, the result will be the true altitude of the centre.

True alt. of Sun's centre,........... 61 28

2,98

*When the contact is formed at the lower limb, the images will separate shortly after the contact has been made, if the altitude be increasing; but if the altitude be decreasing, they will begin to overlap ; but when the contact is formed at the upper limb, the reverse takes place. An observer, if in doubt as to which limb he has been observing, should watch the object for a short time after he has made the observation.

W

We will conclude this Chapter with an illustration of the method of observing altitudes with an artificial horizon; and a few lines explanatory of Parallax and Refraction:

Let AB represent

the surface of the quicksilver contained in a wooden trough, whose plane is continued to C; DEF, the roof, in which are fixed two plates of glass, DE and EF, whose surfaces are plane and parallel

to each other: and

O the sun at S,

whose altitude is required. Now the ray SH, proceeding from the sun's lower limb to the surface of the quicksilver, will be reflected thence to the eye in the direction HG, and the upper limb of the sun's image, reflected from the quicksilver, will appear in the line GH, continued to R; and it is a well known principle in catoptrics, that the angle of incidence, SHA or SHC, is equal to the angle of reflection, GHB; and as the angle AHR, or CHR, is the opposite angle of GHB, it is, therefore, equal to it, and to the angle SHC, the altitude of the sun's lower limb above the horizontal plane: so that, if we suppose the angle SHR, measured by a sextant, to be 80°, the altitude of the sun's lower limb will be 40°, subject to the corrections, as above.

In the example given of observing an altitude of the sun, its semi-diameter is added. The apparent diameter of the sun, moon, &c., is the angle under which they appear to an observer situated on the earth; the amount of which depends upon the real magnitude of the object, and its distance from the observer. The sun's semi-diameter is given in the Nautical Almanac. Its mean semi-diameter is 16', which is the quantity used in

common practice, as it never varies more than half a minute from that amount.

The situation of a celestial body, when viewed from the surface of the earth, is called its apparent place, and that part of the heavens where it would be seen, if observed at the same time from the centre of the earth, is called its true place. The difference between the true and apparent places is termed the Parallax of the object. The parallax of an object is greatest at the horizon, and gradually diminishes as the body rises above the horizon, until it comes to the zenith, where the parallax vanishes. It is evident that the altitude of an object seen from the earth's surface, is less than it would be if seen from the centre: hence, the parallax is to be added to the apparent altitude, in order to obtain the true altitude. The sun's mean horizontal parallax is 83".

The third correction for an altitude of the sun, is on account of Refraction. The rays of light which proceed from a celestial body, on entering the atmosphere in an oblique direction are bent out of their rectilinear course, and incline more and more towards the centre of the earth as they pass deeper into the atmosphere, and hence enter the eye of an observer in a different direction from that of the object, and make it appear higher than its real place. And the difference between the real and apparent places of the heavenly bodies, as affected by the passage of the rays of light through the atmosphere, is called the Refraction of the object. The more obliquely the rays enter the atmosphere, the more they will be bent out of their rectilinear course, and hence the greater the refraction: consequently, refraction is greatest at the horizon, and ceases at the zenith. Refraction is always to be subtracted from the apparent altitude of an object, because the effect of refraction is to cause bodies to appear higher than they really are; so much so, that the sun, stars, &c. may actually be below the horizon, when they appear above it. Tables of refraction are given in the Appendix.

CHAPTER V.

THE SPIRIT LEVEL.

CERTAIN parts of the capital instruments used in surveying and in astronomical observations, require to be adjusted in truly horizontal positions; and, to arrive at this adjustment, one or more subsidiary instruments, called spirit levels, are attached to such principal instruments. The spirit level, attached to a good telescope, furnished with a compass, and such means of correct adjustment, as we shall presently describe, becomes also itself a capital instrument, being used in that department of surveying, termed levelling, which consists in measuring the vertical distances between various stations.

The spirit level consists of a glass tube, differing from the cylindrical form by having its diameter largest in the middle, and decreasing slightly and with great regularity from the middle to the ends. The tube is nearly but not quite filled with spirits of wine, thus leaving in it a bubble of air, which rises to the highest part of the tube, so as to have its two ends equally distant from the middle, when the instrument is in adjustment. The tube is generally fitted into another tube of metal, and attached to a frame terminating in angular bearings, by which the level can either be suspended from, or else be stood upon, cylindrical pivots. When, however, the level forms a permanent part of any instrument, the manner of attaching it is modified to suit the particular form of the instrument to which it is attached. A small and accurately divided scale is attached to the best instruments, or otherwise a scale is scratched upon the glass tube itself.