Mr. Groombrigde’s Observations 
vation, will produce a table of refractions, nearly the same as 
Dr. Bradley’s, though the latter is effected by a more simple 
formula. M. Piazzi has shewn from his observations, that 
the actual refractions, so far as 8o° from the zenith, are greater 
than those assumed by Dr. Bradley ; and thence to the horizon, 
the formula of the latter produces an excess, therefore re- 
quires a reduction in the quantity. The ninth and tenth 
columns of the above fifty stars, will show the same result as 
that of M. Piazzi ; viz. that below 8o° the assumed refraction 
is greater than will be given from observation : and the mean 
correction required for the four last stars, from 87° to 89°, 
will be — 0,027, which he determines — 0,029. Those stars 
from the zenith to 8o°, I have already corrected, by assuming 
a greater constant quantity ; whence it follows, that all those 
equations will be plus, as compared with Dr. Bradley ; but this 
will not happen with those at lower altitudes, since his for- 
mula thence fails: and it is the correction thereof, which I 
shall next proceed to investigate. 
This problem of the mean refractions, so important to prac- 
tical astronomy, which has occupied the attention of many 
mathematicians, has always had in view, to reconcile the 
known laws of the refraction of a ray of light passing through 
different media, with the actual quantity deduced from observa- 
tion. The investigations of various authors are given in the first 
volume of Mr. Vince’s Astronomy ; and that of Mr. Simpson, 
in his Mathematical Dissertations. It has been proved, that 
the refractions vary nearly as the tangents of zenith distance, 
into a constant quantity ; and assuming the variation directly 
as the tangents, the approximation will not be sensibly affected 
so far as 60 6 ; but comparing these, with those at lower alti- 
