To take a Transit.

With the latitude of the place and the declination of the object, compute its meridian altitude.

When it is known to approach the meridian, elevate the telescope to the given altitude by the circle attached to the end of the axis, or in some instruments, by one of the circles attached to the eye-end of the telescope. Now, because the telescope inverts objects, the object will appear to come into the field of view from the west, and move towards the east.

Mark the time of transit over each wire, using a dark glass to save the eye when the sun is observed.

FROM THE GREENWICH OBSERVATIONS.

51m 29.451m 48.6 14h 52m 78.552m 26.752m 46.7 8th 53 45.054 4.314 54 23.454 42.5 55 1.6

Sun's 2 L.

Sun's 1 L.

Suppose the observation had been made with one wire, as the

The error of the clock may readily be determined from the stars, if one of those whose true places are given in the Nautical Almanac is observed. Otherwise the corrections must be applied from appropriate tables.

Observed the transit on 3d

21h 55m 38.30

21 56 24.35

46.05

49.20

3.15

0.67

TO BRING A TRANSIT INSTRUMENT INTO THE MERIDIAN.

To perform this problem, the time should be accurately determined by an altitude near the prime vertical, or still better by equal altitudes, as already explained. Bring the telescope to any celestial object when nearly passing the meridian, and, by turning the horizontal screw, make the middle wire bisect the object at the instant of its transit, then is the instrument in the meridian.

Should the object be the sun, as it cannot be accurately bisected, either limb must be observed when on the meridian, and by allowing for the time his semidiameter takes to pass the meridian, that of the centre becomes known. This is found most accurately in the Nautical Almanac, or, if it is not at hand, from Table XV.

To find the Time that any Star takes to pass from one Wire to another in a Transit Instrument, that of the Equinoctial being known. Rule. To the cosine of the star's declination add the proportional logarithm of the time at the equinoctial, the sum is the proportional logarithm of the time by the given star.

Ex-On the 10th of April, 1826, by a transit telescope which gave 25.4 for the passage of a star of the equinoctial from wire to wire; what would be the time by Antares, having 26° 2′ S. declination ?

Or this would be more readily performed by considering the seconds minutes, and converting the decimals into thirds to be estimated seconds, then the answer will come out in minutes and seconds to be estimated seconds and thirds.

Hence the star's expected time of approach to the other wires becomes known after its contact with the first is observed.

One of the most convenient methods of fixing the transit telescope in the meridian in mean northern latitudes is by means of Polaris. It is required to set a transit instrument by Polaris, on the 1st of March, 1826, at Edinburgh, in latitude 55° 57′ 21′′ N. By a reference to the Nautical Almanac, its altitude at its superior transit will be 57° 34', and at its inferior 54o 21'; and its R. A. is 0h 58m 12$ 20. It must therefore pass the meridian about 2h 8m, and 14h 8m at the altitudes stated above, which serve as a guide to advertise the observer to be prepared.

Now let the clock be regulated to sidereal time, and when it shows 0h 58m 12.2, make the middle wire bisect Polaris, then will the instrument be in the meridian. If, however, the first time assumed was not known with sufficient accuracy, the error of the clock can now be found very nearly by the transit of the sun or a star. By repeatedly observing Polaris, and correcting in this manner, the instrument will at last be truly in the meridian. This may be verified

in several ways. One of the most general methods is by observing that the semirevolutions of circumpolar stars are equal, supposing the rate of the clock to be uniform.

Rule. Let a circumpolar star be observed by the transit above and below the pole. If the difference of these times is exactly half a revolution of the earth round its axis, found from observations of the fixed stars by the clock, the transit is truly in the plane of the meridian.. If the difference between these times is not equal to half a revolution, take the difference between the interval of the times of the two passages, and half a revolution, and to the constant logarithm 0.30103, add the proportional logarithm of this difference, the log cotangent of the star's polar distance, and the log, cosine of the latitude of the place, the sum, rejecting tens in the index, will be the prop. log of the angle which the transit makes with the true meridian. Then if the star, when above the pole, comes later to the meridian wires of the transit than half a revolution after it passed it when below the pole, the transit lies to the east of the true south meridian.

Again, to the prop. log of the error in azimuth just found, add the log secant of the star's altitude, and the log sine of its polar distance, the sum, rejecting tens in the index, is the prop. log of the error of the transit in time from the true meridian at that altitude.

Ex.-At Cambridge, in latitude 52° 12′ N., longitude 30 E., by a clock that loses 3m 10 a day on mean solar time, Capella was observed to pass the meridian wire below the pole, at 6h 0m 0 in the evening, and the next morning to pass it at 5h 56m 213.

The time it would have passed if the transit had been

5 58 25

exactly in the meridian.

But it passed it at

5 56 21

To find the error in the transit below the pole. Deviation in azimuth P. L.

2.03971

The difference of these times is 11h 58m 25, being exactly half a revolution of the fixed star, as shown by the clock. If it is only necessary to find the error of the transit at the altitude when the star passes the meridian either above or below the pole, add together the constant logarithm 0.30103, the proportional logarithm of the difference between the interval of the two observations and half a revolution, the log cosine of the star's polar distance, the log cosine of the latitude, and the log secant of the star's altitude, the sum, rejecting tens in the index, will be the prop. log of the error of observation for the time of the true passage over the meridian.

Should the observer not choose to trust to the uniformity of the going of the clock, he may select two circumpolar stars whose right ascensions differ nearly 12h, as it requires in this case only a few minutes' perfect regularity in the clock. Take the difference between the transits of circumpolar stars by the clock, which are nearly in the same azimuth, the one above, the other below the pole; repeat the operation 12 hours after successively, when the stars have reversed their positions, and if there be a variation in their differences, it shows a deviation in the instrument, which may be corrected by substituting half the difference for the error, and repeating the trial by approxi mation till the adjustment is complete.

α

If some of those stars whose apparent places are given in the Nautical Almanac be selected, the operation will be comparatively easy. These in pairs are; 1, a Cassiopeia and Ursa Majoris; 2, Polaris and Ursa Majoris; 3, Polaris ora Arietis and a Draconis ; 4, Capella and a Herculis; 5, 6 Tauri and ẞ Draconis; 6, ß Auriga and Draconis; 7, Pollux and y Aquila. No doubt some of these can only be so observed in very high northern latitudes; and, there

fore, recourse must be had in some instances to other tables, such as those of Dr Pearson.*

It sometimes happens that an observer has not a command of the whole meridian, especially if he has not an observatory properly adapted to the purpose, yet may find it necessary to take transits for the regulations of clocks or chronometers. In this case recourse must be had to the sun, and to pairs of high and low stars having nearly the same right ascension. Having, by the sun and a good watch or chronometer, placed the instrument nearly in the meridian, observe the transits of two stars having nearly the same right ascension, but differing at least 30° or 40° of declination. Now if the interval between their passing the meridian in sidereal time, be exactly equal to their difference of right ascension, the instrument is truly placed; if not, it wants correction.

If, when the latitude is N. and the stars S. of the zenith, the highest star come first to the meridian, and the interval between the transits be too great, it deviates towards the west; if too small, towards the east.

But if the lowest star come first to the meridian, and the interval between the transits be too great, it deviates towards the east; if too small, towards the west. In either case there is required a correction, which may be computed in the following manner:

Rule. To the secant of the star's declination add the sine of the difference of the latitude and declination, if they are of the same name, or the sine of their sum, if they are of different names; of the sum of which find the natural numbers. To the logarithm of the sum of these add the arithmetical complement of the logarithm of their difference, and the logarithm of the difference between the excess of the right ascension of one star above that of the other, and the observed interval of time between the transits, the sum will be the logarithm of an arc in time.

Half the sum of the excess of the right ascension of the one star above the other and the forgoing arc will be the deviation at the lowest star, and half the difference between these will be the deviation at the highest.

The deviation in time at each star being now known, the instrument may be easily rectified by either or both of them on the following night, or still more readily by a third star on the same evening; or, if the telescope is sufficiently powerful to show stars in the day, all the corrections may be performed at any time in a few successive hours. For the deviation of one star being known, that at another may be computed by the following

Rule. To the logarithm of the given deviation add the cosine of the corresponding star's declination, the secant of the declination of the third star, the cosecant of the sum of the latitude and declination of the first star if they are of different names, or of their difference if they are of the same name, and the sine of the sum of the latitude and declination of the third star if they are of different names, or of their difference if they are of the same name; the sum of these will

* Perhaps the catalogue in the Nautical Almanac might be extended, and the selection more judicious. For example, the places of some of the smaller stars in Orion might be properly exchanged for either circumpolar or high and low stars. An accurate catalogue of the principal stars is given among the tables in this work.