to shew twenty-four hours during the rotation of the concave surface, and commence its reckoning when the first point of Aries is on the meridian, it will shew the right ascension of all the points of the concave surface on the meridian at any time; and all that is necessary to ascertain the right ascension of any object, is to observe the time shewn by the clock when that object passes the meridian. This time is the right ascension, and being multiplied by 15, gives the right ascension in degrees, &c.

The instrument by which the time of the transit over the meridian is accurately observed, and the manner of observing it, will be presently explained.

178. The intersection of the ecliptic and equator not being marked on the concave surface, we must, for regulating the clock, make use of some fixed star, the right ascension of which is known: the clock may be put nearly to sidereal time, and the exact time being noted when a star, the right ascension of which is known, passes the meridian, the error of the clock will be known. Thus if the clock shew 1h 15m 14s, when a star, the right ascension of which, is 1h 15m 10s, passes, the error of the clock will be 4s, and every right ascension observed must be corrected by this quantity.

179. It is evident then, that the right ascension of some one star being known, the right ascensions of the rest may be obtained with much facility. The method which follows, has been used by Mr. Flamstead, and by astronomers in general, to obtain the right ascension of a Aquila.

When the sun between the vernal and autumnal equinoxes has equal declinations, its distances in each case, from the respective equinoxes, are equal. We can ascertain when the sun has equal declinations, by observing the zenith distances for two or three days, soon after the vernal equinox, and for two or three days about the same distance of time before the autumnal,

and then, by proportion, ascertain the precise time when the declinations are equal: at these times also we can ascertain, by proportion, the differences of the right ascension of the sun and some star, by observing the differences at noon for two or three days. Let

E the right ascension of the sun, soon after the vernal equinox, then 180°-E the right ascension before the autumnal, when it has equal declination.

=

A the right ascension of the star in the former instance.
A+p the right ascension in the latter.

We obtain by help of observations A – E and (180— E) -(Ap). Let these differences of right ascension be D and D', that is,

and (180-E) — (A + p) = D'. From which we can determine E and A. For, adding these equations 180°-2E-1 -p 180o — (D + D′)—P and thence A = D =D + D'or E =

2

+ E is known. The value of p arises from the change of right ascension of the star in the interval between the times of equal declinations, and is therefore known from the tables of precession and aberration, &c.

This kind of observation may be repeated many times for the same star between two successive equinoxes, and likewise in different years; and, by taking a mean of many results, great precision will be obtained.

The advantage of this method is, that the sun's zenith distance being the same at the two times of observation, probably, any error in the instrument will equally affect each zenith distance; and therefore we can exactly find when the declinations are the same, although we were not able to observe the declination itself with the greatest accuracy.

180. The construction of clocks for astronomical purposes

has arrived at such a degree of perfection, that, for many months together, their rate of going can be depended on, to less than a second in twenty-four hours. This accuracy has been obtained by the nice execution of the parts, in consequence of which the errors from friction are almost entirely avoided, and, by using rubies for the sockets, and pallets, where the action is most incessant, the effect of wear is almost entirely obviated. But the principal source of accuracy is the construction of the pendulums, which are so contrived, that even in the extremes of heat and cold they remain of the same length. This is generally effected by a combination of rods of two different metals, differing considerably in their expansive powers. They are so placed as to counteract each other's effects on the length of the pendulum. Formerly brass and steel were used, the former expanding much more by heat than the latter. In this construction nine rods or bars were placed by the side of each other, and the pendulum, from its appearance, was called a gridiron pendulum. A composition of zinc and silver is now frequently applied instead of brass, on account of its greater expansion, by which five bars are made to serve. Other constructions are also used, for preserving the same length in the pendulum, but not so commonly.

181. A clock of this description is absolutely necessary for an observatory. It is regulated to sidereal time, and the hours are continued to twenty-four, beginning when the vernal intersection of the ecliptic and equator is on the meridian; and not like common clocks, at noon. But however well executed the clock may be, it is depended on only for short intervals; the time it shews being examined by the transit of fixed stars, the right ascensions of which have been accurately settled. For this purpose the right ascensions of thirty-six principal stars were determined with great exactness by Dr. Maskelyne. Several of these may be observed every day, each observation

pointing out the error of the clock; and the mean of the errors will give the error more exactly. Nothing more then is necessary for determining the right ascension of a celestial object, than to observe the sidereal time of its transit by the clock: that time, being corrected, if necessary, by observations of the standard stars, is the right ascension.

CHAPTER XI.

METHODS OF ASCERTAINING MINUTE PORTIONS OF CIRCULAR ARCHES -ASTRONOMICAL QUADRANT-ZENITH SECTOR-CIRCLE-AND TRANSIT INSTRUMENT-METHODS OF FINDING THE MERIDIAN.

182. As the arches or limbs, as they are called, of astronomical instruments, are seldom divided nearer than to every five minutes, it is necessary briefly to explain the methods by which smaller portions may be ascertained: there are three methods now principally used, 1. by a vernier; 2. by a micrometer screw; 3. by a microscope.

183. The first method is of more general use than the other two, and is applied to a great variety of philosophical instruments. It is named after its inventor. It will be easily understood by an instance. Let the arch lt (Fig. 25) be divided into equal parts, lh, hm, mn, np, &c. each 20', and let it be required to ascertain smaller portions, for instance, the distance of P from pA. Let another circular-arch, called the vernier, 7° long, slide upon the arch lt, and let it be divided into twenty equal 7 × 60

parts, that is, each part =

20

= 21'. If these parts be bc,

cd, de, &c. then the division d coinciding with the division m, the division c will be (21' —20') or 1' beyond the division n; the division b 2' beyond the division p, &c. So that in this way we can ascertain portions of 1', 2', &c., although the arches themselves are divided only into portions of 20'. To apply this, suppose it were required to ascertain the distance of P from pA: