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represented by the monthly means of the four close circumpolars Polaris, Cephei 51, 8 Ursa Minoris, and λ Ursa Minoris for the years 1880-1891. The observations are taken from the N.P.D. ledgers of the volumes of Greenwich Observations, are reduced with Bessel's Refractions, and to the co-latitude value of 21"'90, and are not corrected for flexure or R-D: that is, where they have been corrected for flexure they have been recorrected to make the flexure = 'oo. For discussions on the subject of the value of the correction for flexure as derived from the observations on the collimators, reference should be made to papers on Greenwich North Polar distances by Mr. Christie in Memoirs R.A.S., vol. xlv., and by Professor Newcomb, in vol. ii. of the Astronomical Papers of the American N. A. office. The mean monthly values have been reduced to the epoch 1885. The precessions corresponding to the R.A. of each star at the middle of each year have been taken from Folie's Tables, and added together to reduce the results of the several years to the epoch 1885. The proper motions were taken from the Ten-Year Catalogue.

The differences between the monthly means thus reduced to 1885 and the adopted place for 1885 were then formed by taking monthly mean minus adopted place, both for above and below pole observations, and were combined with weights according to the number of observations.

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The adopted places for 1885 were as follows:

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As these stars are all close to the pole, any correction as now applied for R-D or flexure will be practically the same for all of them, and as the R-D variable term is found to be practically constant for these years, will only affect the zero line. Any error in the adopted places will, however, affect the form of the curve unless the above and below pole observations in any month are equal. Separate curves were also formed including and excluding the daylight observations of Polaris and Polaris s. p., from which it was evident that there was no systematic error due to the daylight observations.

These differences, the same as were published in the first paper in November, were finally smoothed by taking the means of every three. It may be remarked that from the end of 1885 to the beginning of 1889 Mr. Chandler appears to have had no observations under investigation. The general accordance between all three curves is wonderfully good, and therefore the divergence of the Greenwich Observations at the beginning of 1881 is to be scanned with the more critical eye.

Mr. Chandler's curves representing theory and the twentydays' groups of observations have been copied direct from his paper. It was occasionally found a little difficult to follow the latter.

2. The vindication of the correctness of the Greenwich

Transit Circle observations in general, and those for 1851-1865 in particular.

On page 86, No. 251 of the Astronomical Journal, Mr. Chandler makes remarks to the following effect:-That the Greenwich observations with the Transit Circle for 1851-65, complicated with instrumental error and large accidental errors of observation, seem to frustrate efforts to get any pertinent results. We at Greenwich have noticed for some time a disposition among foreign astronomers to disparage the Greenwich observations. Scattered up and down foreign astronomical literature remarks such as the following may be found far too frequently :-The results are not accordant; the instrumental errors are complicated; the accidental errors are large and abundant; the observations have been rejected. To such I would remark that uniformity is not synonymous with truth, and that systematic errors are oftentimes the penalty of close agreement; it is to discordant and not to accordant observations that astronomy owes its most brilliant discoveries. In the volume of Greenwich Observations every step in the reductions is clearly set down, and the details of all instrumental errors carefully published. A discordant observation at Greenwich has never been rejected simply because it was discordant; but all results have been published, so that anybody using the observations can exercise his own discretion in retaining or rejecting such observations. The fact that Mr. Chandler has, after careful consideration, rejected sixteen years of observations with the Greenwich Transit Circle in such an important investigation as that on which he is engaged, and prefers to use the results of the Reflex Zenith Tube, is so striking that it becomes imperative to closely inquire into the subject. For this purpose I have taken the observations of the four close circumpolars as the representatives of the Greenwich Transit Circle observations.

The observations now under discussion comprise the rest of the series of the Greenwich Transit Circle observationsthat is, from 1851-1879. The same stars have been used, the same method of reduction adopted, Bessel's Refractions, colatitude 21"90, and no correction for flexure or R-D. The observations from 1851-1867 have all been reduced to the epoch 1860, and the observations from 1868-1879 to the epoch 1875. The precessions have been found in the same way, and the results found in an exactly similar manner, and compared with Mr. Chandler's curves representing his latest theory (that is law of eq. 15, A. J., No. 277), and the twenty-day groups of observations on which his theory is based. The following are the adopted places of the stars at the two epochs ::

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