475 
Mr. Ivory on the astronomical refractions. 
tute the numerical values already found in the expressions 
investigated in No. 12 : thus, 
d* 8 
d r 
dU 
dp 
— TVT^- x W x Sin ' 6 x 41 x {° ' 3,846 ' 
4" o . 49442 . e 
+ o . 432 62 . e 6 
+ o . 26447 • 
4- o . 12831 . e 10 
+ 0 . 05260 . e 12 
4- o . 01815 . e 14 
4- o . 00807 . e 16 
Lost. * x —1— = o . 2288628. 
& 2 v i 480 
_ a_ (l + a ) Sill. 5 x £ x f o . 125 . e 2 
2 Vi 3° l 
-j- o . 23437 • e* 
+ o . 25072 . e 6 
+ 0 . 19446 . e % 
o . 12109 . e'° 
4- o . 06385 . e 12 
+ o . 02945 • e 14 
4- o . 01214 • c 1 
Log. a x — = o . 7736018. 
By means of the foregoing formulae the table annexed to 
this paper was computed. In the first column are placed the 
distances from the zenith : the second contains the values of 
$ 6 , or the mean refractions at the temperature of 50° of 
Fahrenheit and the barometric pressure 30 English inches: 
the third contains the logarithms of the refractions : and, 
when the zenith distance is greater than 75 0 , the values of 
and are added in two other columns. 
dr dp 
