and Longitude of the Royal Obfervatory at Greenwich. 155 
fixed ftars, after the manner ufed by Mr. Flamsteed for 
deducing the right afcenfions of the fixed fiars, he found the 
apparent zenith difiance of the equator, which leflened by pa- 
rallax and added to the apparent zenith difiafice of the pole 
gave a fum lefs than 90° by the fum of the two refractions 
belonging to the pole and meridian zenith difiance of the equa- 
tor. But he remarked, that the difference of refractions, be- 
longing to thefe zenith distances, would come out the fame 
within 2 or f' by any of the heft tables then extant* whether 
deduced folely from obfervations, or partly from obfervations 
and partly from theory. The fum and difference of refractions 
anfwering to the pole and equator being thus given, the refrac- 
tions therrifelves are given, the greater of which added to the 
apparent zenith diftance of the equator gives the latitude of 
the place, and the lefs refraCtion added to the apparent zenith 
difiance of the pole gives the co-latitude. 
He afterwards, from the confideration that the refraCtions at 
the pole and equator may be taken without fenfible error as the 
tangents of the zenith difiances, according to Mr. Thomas 
Simpson’s theory of refraCtions in his Mathematical Difierta- 
tions, divided more accurately the fum of the refraCtions at 
the pole and the equator into the jufi parts anfwering to each 
zenith difiance, and thereby found the latitude with more 
exaCtnefs. in this manner he found the latitude of the Royal 
Obfervatory to be 51 0 28' gf'i, and the mean refraCtion at 
45 ° ?>' t0 be Si " 5 tbe barometer fianding at 29,6 inches, and 
the thermometer of Fahrenheit’s fcale at 50°. 
But, not to let a matter of fo much confequence reft on my 
aflertion or memory, when further proof can be given of it, 
I have by me, in the hand-writing of Dr. Baadley, among 
other particulars, his calculations of the latitude of the Obfer- 
X 2 vatory 
