error and rate of the Chronometer.

The former of these articles having been treated of in sufficient detail in a former part of the work (pages 175, 176) it need not again occupy our attention at this place; the latter, however, is the especial subject of this chapter, and to that accordingly we will direct the attention of the reader.

The problem of determining times from the transits of a high and low star, may be divided into two cases: 1st, when the high star is observed above the pole, and 2nd, when it is taken below the pole. Each of these cases may again be subdivided into two others, with reference to the North or South position of the low star with respect to the equator.

The separate consideration of the several cases is necessary to the due understanding of the formulæ, which will be given presently.

We will suppose that the stars selected for observation are those of the Nautical Almanac, and use the following symbols to designate the computed and observed elements, appertaining

TO COMPUTE ts.

Take the difference between the right ascensions of the two stars, and convert it to Chronometer time; compute likewise the difference between the observed times of their transits; subtract one difference from the other, and call the resulting quantity ts, which will require to be taken in seconds and in decimals thereof.

The fundamental quantity is being computed, the corrections dp and op' may be deduced by the following formulæ :

Case I.-When the high star is observed above the pole, the low star having north declination.

Table exhibiting the signs of corrections dp & dp'.

Conditions.

Signs of correction.

бр

бр

When the low star transits after the high star, or t'> t.

When the high star transits after the low star, or t>ť.

Case II.-When the high star is observed below the pole, the low star having north declination.

Table exhibiting the signs of corrections dp & dp'.

Conditions.

Signs of correction.

dp

dp'

When the low star transits after the high star, or t> t.

When the high star transits after the low star, or t> t.

+1 1+

Of the four heads under which the formula of computation are given, the intelligent Surveyor will take that which will suit his case, and proceed with his arithmetical deductions accordingly.

When op and Sp' are computed, and proper signs affixed thereto, they may be applied, the former to t, and the latter to t'; the resulting elements will be the times of the meridional passages of the stars observed; whereby the error and the rate of the Chronometer may be easily determined.

EXAMPLE.

Table exhibiting the results of the transit observations taken at Sora, Karara Series Station,

It is necessary to remark that the Chronometer errors and rates deduced in this example, are upon siderial time, and if they are required in terms of the mean time, the necessary reduction may be easily made by a reference to the following Chapter.