and Longitude of the Royal Ohfervatory at Greenwich, i ^ 
Moreover, from the two refractions thus found at the equa- 
tor and pole, the refractions of the circumpolar ftars at their 
palling the meridian above the pole were computed by Dr. 
Bradley, from the hypothecs that the refractions at confi- 
derable altitudes are as the tangents of the zenith diltances ; 
which rule is pretty accurately true with refpeCt to the real refrac- 
tions, and would vary but little from the truth for the appa- 
rent refraCtions, which would be the fum or difference of the 
true refraCtions and the errors of the arc, in cafe the total arc 
erred from the truth by a very {mail quantity, not exceeding 
i o or at mod; 20 feconds. The obferved zenith diltances of 
the ftars above the pole being corrected by the refraCtions thus 
computed, and fubtraCted from the known co-latitude, gave 
their true diltances from the north pole, which added to the co- 
latitude gave their true zenith diltances under the pole ; and 
this diminilhed by the obferved zenith diltance would give the 
refraCtion under the pole, or the fum or difference of the refrac- 
tions and the errors of the inltrument belonging to their refpec- 
tive zenith diltances ; and thus his whole table would exhibit 
the fum or difference of the true refraCtion and error of the 
inltrument. Hence the latitude of Greenwich eltablifhed by 
Dr. Bradley, with his quadrant, as well as the latitudes of 
the Obfervatories at the College of Mazarine and the Cape of 
Good Hope, fettled by the Abbe de la Caille with his fex- 
tant, and the declinations of the ftars and the obliquity of 
the ecliptic found by both will be very near the truth, indepen- 
dent of the juftnefs of the total arcs, although their refpeCtive 
refraCtions may be fuitable only to their own particular inltru- 
ments. But, for the reafons before given, I apprehend, the 
Abbe de la Caille’s refraCtions to be much too large, and 
Dr. Bradley’s to be very near the truth. 
A a 2 
I {hall 
