and Longitude of the Royal Obfervatcry at Greenwich. 173 
ferved a great many refractions of ftars under the pole, with 
the ftate of the thermometer, and fometimes of the barometer 
alfo, as recorded in his Hiftoire Celefte. Thefe I calculated for- 
merly, and found the refraCtions obferved in very hot and very 
cold weather, compared together, to follow the fame rate of 
increafe and decreafe, according to the changes of temperature, 
as Dr. Bradley hasaffigned; and, reducing the obferved re- 
fractions to the mean temperature, I found them agree nearly 
with Dr. Bradley’s. 5. The refraCtive power of the air 
about its mean temperature was carefully obferved by Mr. 
Hawksbee, as related in his Phyfico-Mechanical Experiments^ 
and the ratio of the fine of incidence to that of refraCtion out 
of air into a vacuum found to be as 999736 to icooooo. Hence 
the aftronomical refraCtion at the altitude of 45 0 fhould be 
54/', 6 , only 2^,4 lefs than Dr. Bradley’s, and 2" lefs than 
the fame when his higher refraCtions are new calculated with 
the true parallax of the fun, and i", 2 lefs than I have before fhewn 
to refult from my obfervations of the apparent zenith diftance of 
the equator compared with Dr. Bradley’s of the apparent ze- 
nith diftance of the pole, both taken with the fame brafs mural 
quadrant, but 12" lefs than the Abbe de la Caille’s. 
From all thefe faCts, I think, I may be allowed to conclude,, 
that the Abbe de la Caille’s refraCtions are not juft, but 
confiderably too large ; and, confequently, as there can be 
110 doubt of the care or diligence ufed by this aftronomer in his 
obfervations and calculations, that the total arc of his inftru- 
ment is too large for the radius, and, as I (hall ftiew prefen tly, 
gires the meafures of the zenith diftances too fmall. 
But it may alked, are then all the obfervations of t his great 
aftronomer, with their refults, the fruit of fo much labour and 
pains, to be confidered as uncertain or lowered in their value in 
proportion to the error of his inftrument ? I am happy to 
anfvver y 
