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July 28.

July 31.

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Micrometer-reading, 27039; Circle-reading, 128 20 35.82,
128 25 15:18;

18.325;

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Taking the mean of all the preceding values (including the rather exceptional value on July 31), we find for the definitive value, 32" 079.

The value used throughout the year is that found by Mr. Carrington, namely 32" 050.

The following observations were made for the determination of the flexure of the telescope, the collimators having been accurately set on each other. Six of the eight microscopes were read; that is, all except the vertical pair.

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The effect, therefore, of the flexure of the telescope is that on July 26, the angle measured has been on July 26, 180° 0′ 4′′·•58; and on July 28, 180° o' 5"24; and the mean value of the flexure 5" 24 + 4" 58 2":46. As this value is considerably larger than was anticipated, it was verified by two sets of observations made on January 19 and February 4 of 1863, which gave for the mean value, 2" 59; so that no doubt whatever exists of its correctness, and the correction + 2"5 x Sin south zenith distance has been added to all circle-readings throughout the year.

The examination of the divisions of the graduated circle was made early in the year 1863, on January 2 and 3; the eight microscopes of the circle having been read for positions at intervals of 5° round the whole circle.

The usual process was used for deducing the error of the diameters under the microscopes; namely, by first subtracting the mean of the sums of all the opposite pairs from the sum of each pair taken separately, and then subtracting the mean of all these differences for each diameter from the separate differences. The remainders are considered to be errors of the sum of readings for each diameter under the microscopes, arising from error of division. As each error recurs

eight times, one reading of the circle gives a result of considerable

accuracy.

The following table exhibits the results, the argument being the Pointer Reading for the diameter under the pair of horizontal microscopes (A, C) :

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As the four new microscopes (placed diagonally on the pier with regard to the original ones) were always used for observation after they were mounted, it will be necessary to deduce from the preceding table the actual corrections to be applied to the mean of the readings. Calling the original microscopes (horizontal and vertical) A, B, C, D, in circular order, beginning with the north horizontal microscope, and the new microscopes a, b, c, d (a being next to A); then, for any given pointer-reading, the divisions under a − c will be at a part of the circle having a less reading by 45° than those under AC, and the divisions under bd, will have a less reading by 135°. The proper correction, then, for any pointer-reading will be, on the mean of the four microscopes, one-fourth of the sum of the errors (with signs changed), at readings less than the pointer-readings above by 45° and 135° respectively. The following table has thus been formed from that preceding, and exhibits the errors actually to be applied to the observations:

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No correction has been applied for errors of division in the year 1862.

I will now proceed with the explanation of the computations for the reduction of the observations of zenith distance.

As previously explained, the observations in the early part of the year were made with the use of the two horizontal microscopes A, C, and, after that, by the use of the four new microscopes a, b, c, d. The runs were observed in the course of the observations by reading for a certain number of objects both the preceding and the following division of the circle, and the corrections for runs have been scrupulously applied.

For stars observed at a small distance from the central wire, (generally at one of the side wires,) the correction for curvature has been computed by the usual formula and applied to the circle-reading.

A correction is also applied for the want of horizontality of the wire. By means of 16 readings of the micrometer at the 1st and 7th wires made between April 23 and May 23, it was found that the excess of reading at the 7th wire above that at the 1st, was o''066, and the correction 1"06, additive before meridian transit and subtractive after, was applied for observations of objects made at these wires till June 4. After that time, owing to a readjustment of the

eyepiece, the correction was found to be o"-64, subtractive before meridian passage. In the case of planets or the moon the correction for motion in the interval has also been applied. It has been the practice, as at Greenwich, to make several bisections of the moon's limb as it is passing the vertical wires, and the observation for each bisection has been accurately reduced to the meridian by a formula similar to that used at Greenwich. The readings of the telescope-micrometer have then been reduced to arc, assuming the value of a revolution to be 32" 05, and the resulting numbers, being added to the corrected circle-readings, form the concluded Meridional Circle Reading.

For the determination of the zenith-point it has been the practice to observe, whenever it is possible, one star north of the zenith and one star south of the zenith by reflexion and direct vision, in addition to the observation of the reflected image of the wire, and to combine all the observations, giving twice the weight to an observation of a star, to prevent too great preponderance being given to the nadir position of the telescope. In the year 1862 the number of reflexionobservations of stars is rather scanty; first on account of the preliminary arrangements being incomplete at the beginning of the year, and secondly from want of practice of the observers at the commence

ment.

The following Table gives the values of the runs of microscopes on an arc of 5', which have been used throughout the year, together with the observed zenith-points, and the limits of their use.

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RADCLIFFE OBSERVATIONS, 1862.

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