Mr. Ivory on the astronomical refractions. 
4 59 
2 iy -f- 2 i . 4-y — 2 i (l — c~ u ), 
by putting y = ( i — ■/) u -f- 2 / We shall therefore have 
this expression of the refraction, viz. 
r== (1 + ~) .«(i+a)Sin. 0 
'hr— 
Cos. 1 0+22 
due 
-u 
Si -« 
y + 2 2 .—-3/ — 2J^(l — c) 
and by expanding 
r = (i-|- . a. (1 -f ai) Sin. 0 x f duc ' 
* 1 J Cos * 
«(i+«) an. 9 x r—^n T 
J | Cos.* 6 + 2 232 j- 2 
^ —w, — 
du . c (1 — c. ) 
o’ 
} 
v' Cos.® 0 + 2 iy 
- u 
a) Sin. 0 x 11 ' c 
.f Cos.® 0 + 2 23/ 
Let denote the observed height of the mercury in the 
barometer reduced to the fixed temperature of 50° of Fahren- 
heit; r the temperature of the air on the same scale; and 
£ = the expansion for one degree : then, 
•(>+t)=t 
1 ( 1 + t) — * ( 1 + ^( T — so)) 
+ | 3 (t — 50) x 30 
x + Jx = f X _^ = 
I + — 
1 + 2 / 3 (t — 50) x 30- 
consequently, 
^2 T — 50 
2 480 
+80 ( T ~ 5 °) {so-p). 
By substituting these values, we get, 
Jx = - 2 " 
:ing these 
r — (* +“) • *(i+«) Sin. 
du . c 
S/ COS.® 0 + 2 2 2/ 
