343 
on Atmospherical Refraction, 
the second table, that 0 Persei at 88° i' requires but a small 
equation { — 2", 41) when computed from my former numbers; 
and at 88° both these formulae will coincide. I had therefore, 
in my former paper, determined too hastily, that the formula 
proposed would agree with observation so far as 88°; not 
having then discovered the discrepancies between 80° and 88% 
which are corrected by the present formula. 
In order to facilitate the computation of the true refraction, 
it is required to form a table of mean refractions from certain 
formulae. This may appear difficult at the first view ; since 
every refraction must become equal to, tang. % — yr x x ; and 
unless r is assumed very nearly, several operations may be 
necessary before the differences will vanish. However, pro- 
ceeding in small arcs of 10' to 70°, of 5' to 86% of 4' to 88% 
of 3' to 89°, and of 2' thence to the horizon, the second dif- 
ferences of the variation of these arcs may always be taken 
by inspection : and the resulting refraction will be equal to that 
assumed, in one operation. The correction for the barometer 
and thermometer will be the sum of the two factors in the 
annexed tables, into the mean refraction : and the product 
added thereto, according to the algebraic sign of their sum, 
will give the true refraction. This method is more expeditious, 
than by logarithms ; no other tables of reference being re- 
quired : and the computation will be effected with a small 
number of figures ; which is an object I have constantly had 
in view\ 
S. GROOMBRIDGE. 
Blackheath, 31 January, 1814. 
