on Atmospherical Refraction , &c. 201 
where the atmosphere is not so charged with vapours, as that 
of this country. 
I have, in the Table IV. shewn the mean refractions, ac- 
cording to various authors ; the first column contains those of 
Mr. Simpson, from the observations of Dr. Bevis; the second, 
those of Dr. Bradley, by his formula, tang, z — gr x 57" ; but 
this quantity having been found, from later observations, to 
have been too small ; the third column contains the same 
formula, into 58", 107; yet the refractions, at low altitudes, 
will be found too great, and this excess has been corrected 
by M. Piazzi, using arbitrary equations, which will bring 
them nearer to the truth, as shown in the fourth column. 
The more uniform correction of the whole will be, as I have 
proposed in the above theorem, by increasing the coefficient 
of r; a corollary from which will be drawn, that the incre- 
ment of the tangents near the horizon will cause the equa- 
tions of M. Piazzi to vanish. The fifth column contains the 
refractions of the French tables ; and the sixth, my own ; viz. 
tang. » — 3,3625 rx 5S" 3 ng^. 
On inspection of this table, it will appear, that the refrac- 
tions by different formula do not vary considerably, so far as 
8o°; and thence to 87°, my deductions are rather in excess 
of the French tables ; below which, mine are gather less. 
Whether this arises from the defect of the formula, I cannot 
determine ; since the wall of Greenwich park being above 
my horizon, I cannot observe lower than 88^-° : however, so 
far as 88°, the formula I have proposed, agrees with obser- 
vation. 
S. GROOMBRIDGE. 
Blackheath, 22 Jan. 1810. 
