VOL. LXXVII.] PHILOSOPHICAL TRANSACTIONS. 235 



latitude of the College of Mazarine, gives the latitude of Gottingen 51° 31' 

 54".g, or only 2". 3 more than I have deduced above from M. Mayer's observa- 

 tions of the pole star rightly corrected, and only C.Q less than is set down in 

 M. Mayer's tables, which he expressly says, p. 48 of the precepts to his solar 

 and lunar tables, published by myself for the Commissioners of Longitude in 

 1770, was deduced from his own observations. 



I have before, when I showed the Abbe de la Caille's refractions to be con- 

 siderably too great, at the same time vindicated them as fit for his instrument, 

 because he deduced them in a manner which gave him the apparent elevation of 

 objects above their true place by the sum of refraction and the error of his instru- 

 ment, if his instrument measured the zenith distances too small, as I had con- 

 cluded it did. The like remark may be applied to Dr. Bradley's table; for his 

 refractions at the pole and equator, having been determined with one and the 

 same quadrant, at one time turned to the north to observe the apparent zenith 

 distance of the pole by means of the polar star and other circumpolar stars, and 

 afterwards to the south to observe the apparent zenith distance of the equator, in 

 the manner before explained, must necessarily be the true refractions, if the 

 instrument measured the true angle; and the sum or difference of the true re- 

 fractions and the errors of the instrument for these zenith distances, in case the 

 instrument did not measure the true angle; and therefore equally proper to cor- 

 rect his observations, whether the total arc was just or not. 



Further, from the two refractions thus found at the equator and pole, the 

 refractions of the circumpolar stars at their passing the meridian above the pole 

 were computed by Dr. Bradley, from the hypothesis that the refractions at con- 

 siderable altitudes are as the tangent of the zenith distances; which rule is pretty 

 accurately true with respect to thereal'refractions, and would vary but little from 

 the truth for the apparent refractions, which would be the sum or difference of 

 the true refractions and the errors of the arc, in case the total arc erred from 

 the truth by a very small quantity, not exceeding 10 or at most 20 seconds. 

 The observed zenith distances of the stars above the pole being corrected by the 

 refractions thus computed, and subtracted from the known co-latitude, gave 

 their true distances from the north pole; which added to the co-latitude gave 

 their true zenith distances under the pole; and this diminished by the observed 

 zenith distance would give the refraction under the pole, or the sum or difference 

 of the refractions and the errors of the instrument belonging to their respective 

 zenith distances; and thus his whole table would exhibit the sum or difference of 

 the true refraction and error of the instrument. Hence the latitude of Green- 

 wich established by Dr. Bradley, with his quadrant, as well as the latitudes of 

 the observatories at the College of Mazarine and the Cape of Good Hope, 

 settled by the Abbe de la Caille with his sextant, and the declinations of the 



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