When the sun's centre passes over a meridian, it is apparent noon there. The mean time of the apparent noon for a given day at any place being deducible from the Nautical Almanac, it is clear, that this time compared with the observed time of the transit of the sun's centre as deduced above, will obviously furnish the error of the Chronometer.

Again, the difference of the errors of the Chronometer on two successive days will be its rate.

EXAMPLE.

Computation of the observations made on the sun at Kaliana, G. T. Station, in Lat. 29° 30′ 49′′ and Long. 77° 41′ 52".

Circumstances, however, will sometimes happen, which will prevent the sun from being observed. In this case, it will be necessary to resort to the transit of a star, which may be taken in the following manner:-The theodolite being duly adjusted in the plane of the meridian, the telescope may be fixed to the altitude of the star. When the star appears in the field of the telescope, it must be brought to the middle thereof, as in the case of the sun, by the motion of the vertical tangent screw only. This done, note the Chronometer time of the star's passage over the vertical wire, which will be the observed time of the transit.

It is always convenient to select a Nautical Almanac star for such observations, because its apparent right ascension being given, the computation of its transit will present little or no difficulty. For this reason we will suppose that a Nautical Almanac star has been taken. Now, the siderial time of its transit is known, it being the star's apparent right ascension at that instant, an element which is furnished by the Nautical Almanac. Again, the same work gives the siderial time of the mean noon for every day in the year. For any given day therefore take the siderial time of the mean noon corrected for the longitude of the place of observation, and deduct it from the star's apparent right ascension, the difference will be the siderial interval between the mean noon and the star's transit; which interval converted to mean solar time, will be the mean time of the transit in question.*

The mean time of the star's transit being computed, it may be compared with the observed time, and the error and rate of the Chronometer determined in the same way as in the case of an observation on the sun.

EXAMPLE.

Computation of Transit observations made on 15 Argus at Noh, G. T. Station, in Lat. 27° 50′ 44′′ and Long. 77° 41′ 13′′.

Such is the way in which the error and rate of a Chronometer are computed upon the mean solar time. If the error and rate are required upon the siderial time, however, the

* The method of converting a siderial interval into a mean solar interval and vice versâ is explained in the Nautical Almanac, (pages 554 to 557.)

procedure to be followed is exactly similar to that just described. For instance, suppose a transit of the sun or that of a star has been taken, the apparent right ascension of the object observed, compared with the time of observation will furnish the error of the Chronometer upon siderial time. Again the comparison of two errors determined in this way on two consecutive days, will give the required rate.

As an example of this computation, take the same observations made on the sun at Kaliana, in October 1836.

Deduction of the Siderial error and rate of a Chronometer.
Kaliana Station of observation.

In the preceding computation, it is assumed, that the true azimuth of the referring mark is given, and that the theodolite has been exactly placed in the plane of the meridian. It is evident, that these are conditions, which cannot be readily fulfilled in practice. For instance, it may happen that only an approximate azimuth of the referring mark is forthcoming; or that if the true azimuth is known, the theodolite has not been truly adjusted thereto. In either case, therefore, there will be an error in the setting of the instrument, and when that error is known, the observed time of the sun's or the star's transit, will require to be reduced to the meridian, which may be done in the following manner:

To the logarithm of the azimuthal-deviation of the theodolite from the meridian taken in seconds, add the log. sine of the zenith distance of the object observed, the log. secant of

its declination, and the arithmetical complement of the logarithm of 15, the natural number answering to the sum, will be the required correction in seconds of time, positive if the transit observation were made to the East, and negative if it were taken to the West of the meridian.

When this correction is applied to the observed time of the transit, the resulting element will be the true Chronometer time of the meridional passage of the sun or the star observed.

EXAMPLE.

At G. T. Station Noh, the Theodolite was placed 3". 835 to the west of the meridian on the 6th April 1837, and the transit of 15 Argus observed. The correction to the transit time for this Azimuthal deviation may be computed as follows:

m

S

-0.22 Log.T-34107

Now, the observed time of the transit was 9h. 29. 45.20, which being diminished by this correction will furnish 9. 29. 448.98, as the Chronometer time of the star's passage over the meridian. Accordingly this corrected time has been made use of in computing the Chronometer errors at p. 668.

CHAPTER IV.

ON THE DETERMINATION OF THE ERROR OF A CHRONOMETER FROM OBSERVATIOMS ON A HIGH AND LOW STAR.

THERE is a method of ascertaining the error and rate of a Chronometer, which only requires an approximate knowledge of the azimuth of the referring mark. The method consists in taking the transits of a high and low star* with a theodolite placed as nearly as possible in the plane of the meridian. The only precaution, to be attended to in taking these observations, is that when the instrument is once set to the meridian, it must not be moved in azimuth, until both the required transits are taken.

The transits of a high and low star, taken as directed above, furnish two results at once; namely, 1st, the deviation of the instrument from the plane of the meridian, and 2nd, the

"In general, the two stars suitable for this purpose, ought to have opposite declinations, one North and the other South, having nearly the same right ascension, and being removed from each other by not less than forty degrees." -Pearson's Astronomy, Vol. 2nd, p. 331.