the possibility of any error arising from a change in the rate of the time-keeper. And, as the apparent places of one hundred principal stars are now given in the Nautical Almanac, for every tenth day, it will be better to select two stars from that work. The principle upon which this third method is grounded, is, that a high star is less affected by a deviation of the instrument from the plane of the meridian, than a low star; hence it is evident that if the observed differences of the transits, reduced to sideral time, be exactly equal to the difference of the computed right ascensions, the instrument will be correctly placed in the plane of the meridian; if not, by repeated operations, by methods similar to those before explained, the adjustments must be completed. The restricted limits of this article do not allow us to go into many minute details which are used in large observatories. What we have here given will be sufficient for all the purposes to which a portable transit instrument is usually applied.

To observe the transit of any heavenly body over the meridian.

Having, by means of the previous adjustments, made the line of collimation describe a great circle, passing through the zenith of the place, and the north and south points of the horizon, the instrument will be in a fit state for making the observations. We have said that the telescope contains five vertical and two horizontal wires, placed a short distance from each other. These last are intended to guide the observer in bringing the object to pass across the middle wire of the field, by moving the telescope till it appear between them. The central vertical wire is in the meridian, and the instant of passing this wire will be the time of the passage on the meridian by that star: but as, in noting the time, it will not often happen that an exact second will be shown by the clock, when the star is bisected by the wire, but it will pass the wire in the interval between two successive seconds; the observer must, therefore, whilst watching the star, listen to the beats of his clock, and count the seconds as they elapse: he will then be able to notice the space passed over by the star in every second, and, consequently, its distance from the wire at the second before it arrives at, and the next second after it has passed, the wire; and, with a little practice, he will be able to estimate the fraction of a second at which the star was on the wire, to be added to the previous second. Thus, if the observation of passing the wire was midway between the 7th and 8th seconds, the time of the transit would be 7.5; but if it appeared more distant on the one side than on the other, it would be 7.3, or 7.7, &c., according to its apparent relative distance from the wire.

This kind of observation must be taken at each of the five wires, and a mean of the whole taken, which will represent the time of the star's passage over the mean or meridional wire. The utility of having five wires, instead of the central one only, will be readily understood from the consideration that a mean result of several observations is deserving of more confidence than a single one.

In observing the sun, the times of passing of both the first and second limbs over the wires, are to be observed and set down as distinct observations; the mean of both observations gives the time of the passing of the centre across the meridian. The wires of the instrument are generally placed, by the maker, at such a distance from each other, that the first limb of the sun passes all of them before the second limb arrives at the first wire, and the observer can thus take the observations without hurry or confusion.

The round limb only of the moon can be observed, except within an hour or two of the full moon. In observing the larger planets, the first and second limb may be observed alternately over the five wires; that is, the first limb must be observed at the 1st, 3d, and 5th wires, and the second limb at the 2d and 4th wires; and, by reducing these observations in the same manner as those of the sun, we obtain the meridional passage of the centre. When an observation at one or more of the wires has been lost, it is impossible to take the mean in the same way as in a perfect observation. If the centre wire is the one that is deficient, the mean of the other four may be taken as the time of the meridional passage; or the mean of any two, equally distant on each side of the centre, supposing the intervals of the wires to be equal. But when any of the side, wires are lost, and, indeed, under any circumstances of deficiency in the observation, the most correct method of proceeding is as follows:-Find, by a considerable number of careful observations, over all the wires, the equatorial interval between each side wire, and the central one. These intervals are to be set down for future use. Then, when part of the wires only are observed, each wire is to be reduced to the mean, by adding to, or subtracting from, the time of observation, as the case may be, the equatorial interval between that wire and the centre wire, multiplied by the

We shall hereafter show the use of the transit instrument in regulating a chronometer; and for determining the longitude, by means of the observations of the transits of the moon and moon-culminating stars.

TABLE A.

Correction, in seconds of time, to be applied to one fourth part of the difference of the two intervals, supposing the whole difference to be 1000 of time.

This correction is subtractive from the quarter interval, at the upper transit; additive to the quarter interval at the lower transit.

The difference of the two intervals actually observed, is to be multiplied by the number given by this table, and the product divided by 1000 (which is the same as to cross off the three right-hand figures); the quotient is the correction to be applied to one fourth part of the difference of the intervals.

135

173

146

187

158

TABLE B.

Correction of the azimuth, in minutes and tenths of a minute of space, corresponding to a difference in the two intervals of 1000 seconds in time.

6.42

7.09
7.23

5.29 11.02 16.47 22.47
5.34 11.13 17.03 23.10
5.50 11.46 17.52 24.16
6.20 12.46 19.23 26.20
13.29 20.30 27.51 35.40
14.25 21.55 29.46 38.09
14.52 22.36 30.42 39.19

"1 29.13 36.11 43.53 29.40 36.44 44.33 53.23 31.06 38.30 46.42 .57.16 33.45 41.47 50.40 60.43 44.10 53.34 64.11 47.14 57.17 68.38 48.41 59.03 70.45 7.37 15.22 23.21 31.42 40.37 50.18 61.00 7.54 15.54 24.10 32.50 42.04 52.05 8.12 16.31 25.06 34.05 43.40 54.04

52.35

63.10

65.35

TABLE C.

Correction, in seconds of time, for 1000 seconds of space of deviation in azimuth from the plane of the meridian, to be applied to the time of the transit of the star observed by the transit instrument.