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Zenith Points and Corrections for Runs of the Mean of Microscope-readings used in the Reduction of the Zenith Distance Observations of 1862.

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The zenith points given in the Table above having been subtracted from the concluded circle readings, the south zenith distances of all the objects observed are obtained, and these are converted into true zenith distances from the astronomical zenith by the application of the refractions. The latter are calculated from Bessel's Tables as given in the Appendix to the Greenwich Observations for 1853, but diminished in the proportion of 1: 0.9967, in order to make the results identical

with those of the Tables in Bessel's Fundamenta Astronomia, as these were found to be more consistent with the Radcliffe Observations than those of the Tabula Regiomontana. (See Radcliffe Observations, vol. XV. p. xxiv, &c.) The Barometer used for recording the pressure of the air is by Newman, and is used as a standard. (See Meteorological Observations, page [1].) The thermometers have been in use since 1840, and were originally compared and found to agree with those formerly at the Royal Society. (Radcliffe Observations, vol. I. p. xix.)

Parallax and Semi-Diameter.-For the moon, the horizontal equatorial parallax and the semi-diameter are interpolated by second differences for the time of Oxford transit from the numbers given in the Nautical Almanac without alteration. The parallax applied to the observations is computed from the formula

Sine Parallax = Sine Equ. Hor. Par*. × Sine Distance from Geocentric Zenith, where log. r 11′ 10′′.13, as computed from the ellipticity of the earth

9'99911, and the angle of the vertical is assumed to be

I

300

For the sun, where only one limb has been observed, and for the moon and Mercury, the semi-diameters given in the Nautical Almanac have been applied. The correction deduced for the semi-diameter of Venus has already been given. Whenever one limb only of Mars has been observed in R. A. or N.P.D., the correction + os 12 in R. A. and +1"-8 in N.P.D. has been applied to the Nautical Almanac semidiameter for reduction to the centre of the planet. The corrections for defect of illumination have been computed and applied for the planets Mercury, Venus, and Mars, wherever they are needed.

In all interpolations from the Nautical Almanac, the longitude of the Observatory has been assumed to be 5m 28-6 west of Greenwich ; this being the result of a very careful chronometrical determination made in 1842, by the late Rev. Richard Sheepshanks.

It may be mentioned, to prevent misapprehension, that no change of longitude has been occasioned by the use of the transit-circle, of which the telescope occupies exactly the same position as did the transit-instrument previously in use.

SECTION IV.-Separate Results for Mean R. A. of Stars observed in the Year 1862.-Pages 2 to 27.

In all which has preceded it has been attempted to give an adequate explanation of the various processes employed in the reduction of the observations, together with a description of the Transit Circle, and of its adjustments. The reader will thus be enabled to judge of the degree of care which has been taken to insure accuracy, though the observations themselves are not printed. In what follows reference will be made to the sections of the printed tabular matter.

The Separate Results for Mean R.A. need little explanation. They are taken without any alteration from the sheets in which the reductions have been performed, and the nomenclature of the stars has been previously explained.

I will merely remark on one or two circumstances which occurred to me during the rigorous examinations to which the observations were subjected.

With regard to the observations of Polaris, of which an extensive series has been made, the mean result is greater than that obtained at Greenwich in the same year by 1.70. Thus,

For Greenwich, Seconds of Mean R. A.
Oxford

8.

= 40'52 (67 observations),
= 42 22 (72 observations).

In the year 1863, from observations not yet published, (taking the value given for 1862 in the Greenwich List of Fundamental Stars previously referred to,) we have for Polaris

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It is not, therefore, an accidental circumstance but a substantiated fact, that in estimating the time of transit of Polaris and other circumpolars there is a personal equation between the Oxford observers and the mean of all the Greenwich observers, amounting to more than a second of time. Assuming the difference to be 134, this would amount, when expressed in are, to o"51.

It is therefore very desirable that at each Observatory an independent value of the Right Ascension of Polaris, and of the three other fundamental circumpolar stars, should be obtained by transits above and below pole, and used for the determination of azimuthalerror when only a single transit has been obtained.

My second remark is that the agreement of the separate results (as exhibited principally for the clock-stars which were observed several times), is not so close as could be desired, or as might have been expected from the known care and skill of the observers. This is chiefly observable in the observations of Mr. Lucas, and may perhaps arise from the circumstance that, during his previous employment at this Observatory under Mr. Johnson, he observed, almost

exclusively, zenith-distances with the Meridian Circle. Something also may be due to the difficulties always experienced in bringing into use a new instrument. As far as the observations of 1863 have been reduced, the results of all sorts seem to be much more satisfactory.

The notes which follow the Separate Results in R.A. are necessary for enabling a judgment to be formed of the effect which atmospheric and accidental circumstances may have had on the quality of the observations. A note is also given for every case wherein a star has been observed over a smaller number of wires than five.

SECTION V.-Separate Results for Mean N. P. D. of Stars observed in the Year 1862.

The results are copied without alteration from the sheets in which the reduction of the Circle observations to Mean N. P. D. are performed. The same colatitude has been used as in former years, namely 38° 14′ 24′′8; and, for its correction, use has been made of all suitable observations of stars observed above and below pole in the year 1862. A Table, exhibiting the results of this investigation, will be given in the sequel.

For the purpose of discovering whether, with regard to the observations made by reflexion, there is any difference following a law between the reflexion-results and the direct-results, the following Table has been drawn out, which exhibits the stars in the order of North Polar Distance, and the separate values of the seconds of reflexion-results (R) and of direct-results (D):—

Excess of Reflexion-Results above Direct-Results for Observations of Zenith Distance with the Transit Circle, 1862.

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