Mr. Ivory on the Theory of the Astronomical Refractions* 95 
«+ J , 1. - _ T . (,_50) - J (SO - 
The first term of this expression is the mean refraction cor- 
rected in the. manner usually practised by astronomers. If 
we assume that the temperature of the mercury in the baro- 
meter is the same with that of the air, this term will be equal 
to 
1 1 1 P 
— 50)'. T —50 * ^ 1+c(t-50) ’ 30’ 
^ 10000 
c = *002183, 
the new factor being added to compensate the expansion 
of the mercury. Two subsidiary tables are given for com- 
puting this part: Table II. contains the logarithms of 
for 30° on either side of the mean temperature 
1+c(t— 50) ^ 
50°, negative indices being avoided by substituting the arith- 
metical complements ; and Table III. contains the logarithms, 
or the arithmetical complements, for all values of p from 31 
to 28. 
The coefficients, T and b, of the other two terms vary with 
the distance from the zenith ; and they can be computed in 
no other way than by reducing them to series of the powers 
of e. By substituting for X Qj, the equivalent series already 
known, we immediately obtain 
b = l.|B 3 e 3 +B,.^ + B,c’+ &c.| . 
Further, by expanding S and its differential, the expression 
of T will take this form, 
T = sine. ^ + Gye’’ + Gg^+&c. ; 
and we shall have 
G 3 = A, -A 3 + 2 Bg = 0-24.36 
G 5 = — Ai + 3 A 3-2 A 5 + 2 Bj = 0-4523 
G; = A ,— 3 A 3 + SA 5 — 3 A 7 + 2 B 7 =0-4705 
Gg = -Ai + 3A3-5A5 + 7A,-4A9 + 2Bg = 0-3502 
G,i = Ai -3 Ag + 5 A 5-7 A 7 + 9 Ag - 5 A„ + 2 B,i = 0-2092 
Gj 3 = — A, + 3 Ag— SAj + 7 Af — 9Ag+ *' A,i — 6 A,g+2Bi3 
= 0-1050. 
The series for T and b being now known, the coefficients of 
