VOL. LXXVII.] PHILOSOPHICAL TRANSACTIONS. 221 



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the apparent zenith distance of the pole, gave a sum less than 90° by tlie sum 

 of the two refractions belonging to the pole and meridian zenith distance of the 

 equator. But he remarked, that the difference of refractions, belonging to these 

 zenith distances, would come out the same within 2 or ^" by any of the best 

 tables then extant, whether deduced solely from observations, or partly from ob- 

 servations and partly from theory. The sum and difference of refractions an^ 

 swering to the pole and equator being thus given, the refractions themselves are 

 given, the greater of which added to the apparent zenith distance of the equator, 

 gives the latitude of the place, and the less refraction added to the apparent, ze- 

 nith distance of the pole, gives the co-latitude. 



He afterwards, from the consideration that the refractions at the pole and 

 equator may be taken without sensible error as the tangents of the zenith dis- 

 tances, according to Mr. Thomas Simpson's theory of refractions in his Mathe- 

 matical Dissertations, divided more accurately the sum of the refractions at the 

 pole and the equator into the just parts answering to each zenith distance, and 

 thereby found the latiti^de with more exactness. In this manner he found the 

 latitude of the Royal Observatory to be 51° 28' SQ^'', and the mean refraction at 

 45° 3' to be 5T'i the barometer standing at 29.6 inches, and the thermometer 

 of Fahrenheit's scale at 50°. But, not to let a matter of so much consequence 

 rest on my assertion or memory, when further proof can be given of it, I have 

 by me, in the hand-writing of Dr. Bradley, among other particulars, his calcu- 

 lations of the latitude of the observatory from his observations, according to the 

 manner above explained; in which he first states it at 51° 28' 38^'', and finally 

 more correctly in these words. " The apparent zenith distance of the equator, 

 by the mean of 20 observations in 1 746-47, 51° 27' 28''''. The mean apparent 

 distance of the pole, by the observations made between 1750-52, 38° 30' 35''''. 

 Sum 89° 58' 3". Sum of refractions 1' 57". Polar refraction A5\". Equatorial 

 refraction l' 1 1\", Latitude 51° 28' 394-". Co-latitude 38'' 31' 20VV' 



The latitude of the observatory being thus settled, as well as the quantity of 

 refractions for all stars passing the meridian between the pole and the equator. 

 Dr. Bradley readily inferred from his observations the true distance of all such 

 stars from the north pole, which, compared with their zenith distances observed 

 below the pole, gave the refractions at those lower altitudes. Finally, by com- 

 paring the refractions together observed in extreme degrees of heat and cold, he 

 deduced the law of their variation as affected by heat and cold; and thus at length 

 he inferred his elegant rule for determining the refraction in all circumstances, 

 that it is to 57'', in the direct compound ratio of the tangent of the apparent 

 zenith distance lessened by 3 times the refraction, to the radius, and of the height 

 of the barometer in inches to 29.6 inches, and in the inverse ratio of the degree 

 of height of Fahrenheit's thermometer increased by 350, to 400» 



