428 
Mr. Ivory on the astronomical refractions. 
of Gay Lussac gives 174 metres, or 95 fathoms. With these 
several values we shall find — equal to 0.188,0.192, and 
0.177 respectively ; and we may adopt y as an approximation. 
Thus, 
01 _i_ 
e- 5 
Y s (making s = o) = 1 — y = ~. 
5. In one particular case of this problem we are possessed 
of many skilful observations made in the course of the trigo- 
nometrical surveys of England and France. We allude to 
the terrestrial refraction, which regards that part of the tra- 
jectory described by the light in its passage from a terrestrial 
object to the eye of the observer. As this case is immediately 
deduced from the equations that have been investigated, the 
comparison of the result with observations may, in some de- 
gree, instruct us how far the theory will agree with nature. 
We have found this equation, viz. 
~ ( making s = o) = ± ; 
which being accurately true at the surface of the earth, it 
may, without sensible error, be extended to a small height 
above the surface. In the case of the terrestrial refraction 
we thus have, 
*> = ys; 
and, if this value be substituted in the expression of dr, we get, 
dr= a Sin. 6 x 
—ds 
Cos. 
1 0 -1- 2 (t— —a) S 
5 
By integrating 
r = y x -- Sl ^ 6 - x | y/ Cos - 2 6 + 2 (i — j *) sj — Cos. 9 | : 
,_ T“ 
