47 6 
Mr. Ivory on the astronomical refractions. 
The use of this table will be clear, from the subjoined for- 
mula for computing by it the true refraction, supposing that 
t is the temperature by Fahrenheit's thermometer, and p 
the height of the barometer in English inches. 
x^xJS+ — (r-so)— w 
I + 0 (t — 50) 30 
(t — SO) 
( 30 — p ) 
The first term is the mean refraction corrected for the ob- 
served temperature and pressure in the same manner usually 
practised by astronomers. When the zenith distance does 
not exceed 75 0 , the two remaining terms are to be accounted 
as evanescent ; and, even when the zenith distance is 8o° or 
a little more, the same terms may, on most occasions, be 
omitted : otherwise the two terms, amounting generally to 
some seconds, are to be added to the first term with their 
proper signs. 
Three subsidiary Tables are added for facilitating the cor- 
rections for the barometer and thermometer. Table II. con- 
tains the logarithms of — —rf = — for 40° on 
& 1 + /3 (t — 50) t t— ; o 
480 
either side of the mean temperature 50° ; negative indices 
being avoided by substituting the arithmetical complements. 
Table III. contains the logarithms, or the arithmetical com- 
plements, of for the values of p between 31 and 27^. 
Table IV. contains the small corrections, positive or negative, 
to be applied to the numbers in Table III. in order to reduce 
the observed length of the barometric column to the mean 
temperature of 50°. The numbers of this Table are the 
logarithms of ■ t '_ ;o ; equal t0 _ x . 434 . 
IOOOO 
14. Instead of applying the new Tables to particular in- 
