Zenith 
dist. 
Mr. Ivory on the Theory of the Astronomical Refractions, 99 
which may be shortly denoted hy f' x x been com- 
puted by means of the equivalent series, for every half de- 
gree between 85° and 88°, the results being as follows : 
& 
/' xxi^) 
85° 
it 
/' X 1-5 
S5i 
/' X 2-0 
86 
/' X 3-3 
86i 
/' X 4-9 
87 
/' X 7-4 
87-1- 
/' X 11-2 
88 
/' X 17-0 
From this view it appears that f',, although considerably less 
2 
than f or may still have some influence on the refractions 
at very low altitudes. The mean refraction in Bessel’s table, 
and in the new table, can hardly be supposed to differ 2^' 
from the true quantity, which would limit f' to be less than 
. It is a matter of some importance to obtain a near 
value of f ^ : and it is probable that this can be accomplished 
in no other way but by searching out such values of f andy’' 
as will best represent many good observed refractions at alti- 
tudes less than 5°. If such values were found, our knowledge 
of the decrease of heat in ascending in the atmosphere would 
be improved, and the measurement of heights by the baro- 
meter would be made more perfect. 
April 25, 1838. 
Table I. 
Mean Refractions for the Temperature 50° Fahrenheit, and 
the barometric Pressure 30 inches. 
'IS. 
// 
1-02 
2-04 
3*06 
4-08 
5*11 
6- 14 
7- 17 
Log S S. 
0-0085 
0-3097 
0-4860 
0-6112 
0-7086 
0-7882 
0-8557 
DifF. 
3012 
1763 
1252 
974 
796 
675 
-a 
^ 
T. 
C. 
'5 
'^S. 
Log 1 6. 
Diff. 
T. 
C, 
o 
7 
8 
9 
10 
11 
12 
13 
0 7*17 
8*21 
9-25 
10- 30 
11- 35 
12- 42 
13- 49 
0-8557 
0-9144 
0- 9663 
1- 0129 
1-0553 
1-0941 
1-1300 
587 
519 
466 
424 
388 
359 
H2 
