be the logarithm of the deviation in seconds of time at the third star. Ex-On the 1st of March, 1826, at the observatory of Edinburgh, in latitude 55° 57′ 20′′ N., I observed the transits of Capella and Rigel, on the same evening, about a quarter past 6, and found the interval between the two transits 2.5 less than the difference between their true apparent right ascensions, as given in the Nautical Almanac; required the deviation of the instrument at either star, and also at a third, as Sirius? Latitude 55° 57' N. 55° 57' N. Dec. of Capella 45 48 N. sec. 0.156664 Rig. 8 25 S. sec. 0.004703 Now since the highest star comes first to the meridian, and the interval between the transits is too short, the deviations are easterly. If the stars had been between the zenith and the north pole, the deviations would have been westerly. Since it has been found necessary to fix the instrument as soon as possible, we shall proceed to compute the deviation at the third star, which can be easily done, as we have an hour and three quarters nearly to perform the calculations and complete the arrangements; thus: After having corrected the instrument by means of Sirius, I observed the transits of Castor and Procyon, and again those of Procyon and Pollux, and found the interval of time to agree with their difference in right ascension, from which I concluded, that in the space of about three hours I had placed my transit instrument exactly in the meridian. As it is rather a difficult operation to fix a transit instrument ac curately in the meridian, these operations should be repeated a considerable number of times to ensure the utmost possible accuracy. After the observations prove satisfactory, a meridian-mark may be put up in a horizontal direction at a considerable distance, with which the central wire may be frequently examined and rectified previous to any very nice observation. This mark may be of various constructions, such as a copper-plate with a hole in it, so as a small segment of light may be seen on each side of the vertical middle wire, or a small notch in a building, or even a post at some distance. A thin slip of brass or copper painted black, with white lines or divisions at every inch, and numbered throughout, will also be found very convenient, and by knowing its distance, the deviation upon it may be computed.* The transit instrument being now properly rectified, it will be found the most accurate of all for determining the error and rate of a clock or chronometer, by taking the transit of the sun or stars daily, and marking the difference regularly in a column prepared for that purpose. If a star be observed, sidereal time must be reduced to mean solar time by Table XXXI. when necessary. Ex. 1.-The observed times of the sun's passing the meridian of the observatory were as follows:-What was the original error on the last day of observation and the daily rate? Obs. Time Mean Time. 1826. Sun's Transit. App. Noon. Chronometer Daily Rate. Mar. 10h 25m 27.10h 12m 40.70h 12m 463.4 Bar. Ther. 29.87 52° 29.90 53 29.86 51 29.88 50 29.85 52 29.84 54 29.87 52 Mean daily rate is therefore 1826, is 57.8 +1.56 And the original error at noon, on the 6th of March, Hence its error, supposing the rate to remain uniform, may, at any moderately distant future time, be determined. Ex. 2.-On the same evenings the star Rigel passed the meridian as follows:-Required the daily rate and the original error on the sixth at the time of observation, about 6 o'clock in the evening? Hor. deviation sec. alt. x cos. dec. x obs. diff. of time x 15, to radius 1. On Captain Kater's plan, by contracting the diameter of the object-glass by some contrivance for that purpose, the meridian-mark may be only a few feet distant.— See his paper on the Floating Collimator. 6 10 27.8 Time of transit by chronometer on the 6th 6 23 25.0 Error of chronometer, fast by star, Mean error at 6h fast : 0 12 54.2 0 12 54.4 + 1.57 The barometer being at 29.86, and thermometer, 49.5° Fah. As opportunities may not occur daily for celestial observations, it is in that case necessary to compare a chronometer with a good clock, the rate of which can be depended on, and is occasionally ascertained by the heavenly bodies. Ex. 3.-Given the daily difference between a chronometer and a clock, the rate of the clock being occasionally determined by celestial observations; to find the error and rate of the chronometer? Hence the error of the chronometer may be found at any moderate distance of time, so far as its steady rate can be depended on. The clock was examined by celestial observation, only where the asterisks are placed, or on the 1st, 4th, and 6th, and these are sufficient to ascertain, with the requisite precision, the rate of the chronometer when the clock is good. It is in a somewhat smilar manner that the prize-chronometers are tried at Greenwich. Table of the variations of the sun's R. A. and dec. in 1' for every month in the year. This table will be useful when the change of the sun's R. A. or D. for a few seconds only is wanted. Summary of Directions for making a Series of Observations with the Transit. 1. Place the transit instrument as nearly in the meridian as possible, and select or place substantial meridian-marks at a considerable distance both to the north and south. 2. The clock must be set to sidereal time, and its daily rate ascertained. 3. Observations of pairs of high and low Greenwich stars must be made each evening, along with others whose right ascensions are required. 4. The apparent right ascensions of the Greenwich stars must be computed for the time of observation, or taken from the Nautical Almanac. 5. The azimuthal error must be found by several of these pairs of stars. 6. The error of the clock must be deduced at the time of transit of one of the Greenwich stars. 7. This error must be reckoned constant to every observation made during the same night. 8. The azimuthal error must be considered to have a contrary sign between the zenith and the pole to that on the opposite side of the zenith. 9. A proportional part of the daily rate of the clock must be applied to every observation from the first. 10. The error of each star from the true meridian must be computed from tables prepared for the purpose. 11. To the time of transit of each star add the error of the clock (6), the proportional part of the daily rate (9), and the error from the meridian (10), the respective sums will give the true apparent right ascension required. 12. Compute the sum of the corrections for precession, aberration, lunar and solar nutation, for every star at the time of culmination or observation, and apply each sum with a contrary algebraic sign to each true apparent right ascension, the result will give the mean right ascension for the beginning of the year. 13. Let series of these for each star be registered, and the mean of each series may be expected to give the mean right ascension at the beginning of the year with considerable accuracy. |