228 PHILOSOPHICAL TRANSACTIONS. [aNNO 1787. 



This obliquity 23° 28' &''.5 is deduced in the manner used by Dr. Bradley, and 

 is more to be depended on than the other 13^ 28' 7"'0 deduced from both sol- 

 stices, on account of the less certainty of the lower refractions, from which how- 

 ever it only differs a second and a half. Thus all the observations of the sun and 

 circumpolar stars accord to 1" or 2" with the latitude of the Observatory settled 

 by Dr. Bradley, making use of his refractions. 



I shall now determine the latitude independent of Dr. Bradley's refractions, and 

 infer the higher refractions at the same time, from a comparison of my observa- 

 tions of the apparent zenith distance of the equator before set down, with Dr. 

 Bradley's observations of the apparent zenith distance of the pole, both taken 

 with the same excellent brass mural quadrant, in the same manner as Dr. 

 Bradley deduced them from the apparent zenith distance of the equator observed 

 with the iron quadrant compared with the apparent zenith distance of the pole 

 observed with the brass quadrant, according to the extract from the manuscript 

 in my possession before cited. 



The mean apparent zenith distance of the equator, by my observations of 6 

 years from 17 65 to 1771, was related before 51° 2?' 29".8. The mean apparent 

 zenith distance of the pole was found by Dr. Bradley from 1750 to 1752 to be 

 38" 30' 3d". Their sum 89° 58' 4'^8 taken from 90° leaves l' 55/^2, the sum of 

 the refractions at the two zenith distances. Saying then, as l' 06''. 7 the sum of 

 the refractions by Dr. Bradley's rule, to l' 55''^2 the sum by observation, so are 

 r ll'''.4 and 45''.3 the respective refractions at the two apparent zenith distances 

 of the equator and pole by Dr. Bradley's rule, to l' 10'^5 and 44'.7 th^ two re- 

 fractions at those zenith distances, which added to them give the co-latitude 38° 

 31' 19'^7, and the latitude 51° 28' 40'^3. And as l' 56 .7 : 1' 55/''.8 :: so is 57" 

 the refraction at the apparent zenith distance 45° 3' by Dr. Bradley : 56".27 the 

 true refraction at that zenith distance, or not half a second differing from Dr. 

 Bradley's, but more to be depended on as deduced from observations made with 

 the brass quadrant only, and calculated from a parallax of the sun nearer to the 

 truth. 



But if the apparent zenith distance of the pole be made use of, resulting from 

 a mean of 310 observations made with the brass quadrant, according to Dr. 

 Bradley's manuscript, communicated by Dr. Hornsby, from the whole of his 

 observations from 1750 to 1753, viz. 38° 30' 3&, the sum of this and 51° 27 

 29'''.8, the apparent zenith distance of the equator found by myself with the same 

 instrument, or 89° 58' 5'''8 taken from 90° leaves l' 54".2, the sum of the two 

 refractions at the pole and equator. Whence the refraction at the pole will be 

 found in like manner as before 44''^3, and that at the equator l' 9''''.9, and the 

 latitude 51° 28' 39".7, and the refraction at the apparent zenith distance of 

 45° 3' = 55'^8, which is l".2 less than Dr. Bradley's determination, and 1^.2 

 greater thaia deduced from Mr. Hawksbee's experiment of the refraction of the 



