hence, taking the successive differences, we get for the value of a revolution, 31" 65, 31'93, and 32" 12, respectively.

Similarly, on May 31, Mr. Quirling found the value of a revolution to be 31" 94.

On June 30 and July 14, Mr. Lucas found, by a similar process, the values to be 32′′ 320 and 32" 50.

The mean of these values is 32" 07, which agrees very closely with Mr. Carrington's values. The latter, namely 32"03, has been adopted for use.

The Error of Collimation was determined by the use of the collimators on every evening except Sundays, at each observation the collimators being set accurately on each other, by means of the micrometer-screw of the south collimator, and the reading of the micrometer being taken. The reading of the telescope-micrometer for coincidence with the north and south collimators successively was then taken six times, and the mean of all was taken as the reading for the line of collimation. The difference between this reading and the actual setting of the micrometer for observation, .when reduced to are and corrected for the diurnal aberration, is the error of collimation.

As Mr. Quirling and Mr. Lucas differed somewhat in their results for collimation, it has been thought best to use the value deduced on every evening of observation without combination with other values, so that the values of the instrumental-errors of each observer might be quite independent of the other. This difference between the observers, (which has been the source of much embarrassment,) seems to be due to a difference of estimation of the accurate position of the point where the wires cross each other; and it may be stated that Mr. Lucas's estimation agrees well with my own. It may also be stated that Mr. Quirling, on account of short-sightedness, is obliged to push in the eyepiece much closer to the wires than either Mr. Lucas or myself.

The Error of Level (determined every evening at the same time as the error of collimation) was found by taking the readings of the transit telescope-micrometer for coincidence of the direct and reflected images of the central wire as viewed with a Bohnenberger's eyepiece, and comparing the mean of the readRADCLIFFE OBSERVATIONS, 1862.

0

ings (six in number) with the mean of the readings for the line of
collimation.

As the value of the Error of Level depends, therefore, on that
for the line of collimation, the results of each observer are used
for his own observations; a fresh value being, in general, used every
evening.

Error of Azimuth.-This error is determined by consecutive transits of Polaris, whenever such have been observed; but generally, in defect of this, by transits of two circumpolar stars differing in R. A. by nearly 12h, (of which a list has been prepared carefully,) compared with the Apparent Right Ascensions accurately computed from the Radcliffe Catalogue of Stars, or the Radcliffe Observations; or, finally, by the transit of a circumpolar star and a south star.

The following is the list of those employed in the year 1862 :—

:

Assumed Mean Right Ascensions and Approximate N.P.D.'s of Stars used in 1862 for the Determination of Azimuthal Error, with the Authorities for Right Ascension.

Radcliffe 3523 16 5 784

Radcliffe 3522 16 6 399
Antares

5 59
a Capricorni. 20 10 23.70 102 58
16 20 5703 116 7 Greenwh List. Radcliffe 4980 20 38 55°09

16 51 8.23 80 24

2 30 R. O., vol. xvi.

B Aquila.

19 44 297 19 48 3203 A Ursa Min. .20 2 117

81 30 Greenwh List.

83 56

a2

K Ophiuchi

Sin Z. D.

38 30 Rad. Cat.
3 24 Greenwh List. Groomb. 4101 23 27 49'91

I

In the computation of the corrections to Apparent R. A. of the circumpolar stars given above, the terms depending upon 2) have been taken into account. The method of deducing the amount of azimuthal-error needs scarcely any explanation. Two tables of factors for the errors of collimation, level, and azimuth have been formed Cos Z. D. (that is, tabulated values of -, and 15 Sin N. P. D.' 15 Sin N. P. D.' 15 Sin N. P. D.), the one for the list of stars above given, and for all stars used in deducing clock-error, and the other for small intervals of N. P. D., and thus in any particular case the factor for azimuth can be taken out at sight. In the case, then, of two consecutive observations of Polaris, above and below Pole, the times of the observed transits, (the latter corrected for clock-rate and change of R. A. in twelve hours,) are affected by these factors multiplied into the required azimuthal-error z. These times ought to be equal, if the instrument has remained steady during the interval of the observations, and, by equating them, z is determined. If three consecutive transits be observed, the process is essentially the same, excepting that the mean of the successive differences of the seconds of transits will give the effect of the error of azimuth without correction for clock-rate and change of right ascension. Finally, in the case of two circumpolar stars, or of one circumpolar and one south star, each transit being affected by z multiplied into its proper factor, and compared

with the right ascension of the star, will give a clock-error; and the two clock-errors thus deduced, when corrected for clock-rate in the interval, should be equal; and hence z is found.

The following table gives the values of the errors of collimation, level, and azimuth which have been used throughout the year 1862, with the days of observation annexed:

Instrumental Errors used in the Reduction of the Transit Observations,