452 Mr. Ivory on the astronomical refractions. 
near coincidence of the refractions in so many different cases 
with the observed quantities. In order to examine this point, 
we may take the case of Gay Lussac’s ascent ; the data ob- 
tained by observation, as they are given by Ramond,* being 
as follows, viz. 
Log. P= — 1.6361109 
t= 30 0 . 8 
r = — 9.5. 
With these numbers, by means of the formula P = 
x ( 1 — u ) , we get, 
1 u — 0.5004? 
which may be reckoned the density by observation ; and we 
must now compare it with the result of the theory. 
Now whenw = 4,/=o; and we have these equations, 
viz. 
consequently, 
r, 4 
1 — u == P 5 : 
and, by substituting the foregoing value of P, we find, 
1 — w = 0.5115, 
which is greater than the value deduced from observation by 
about — of the whole. 
5° 
Again, we have generally, 
1 — u> = (1 — z ) m 
P =(!-/) (>-s)” +, + 2/( 1 -z) 2 ” ! : 
wherefore, 
1 
p= ( 1 -/) (*-») + '” + 2/(i— a )'; 
* Memoires sur la For mule Barometrique, 1811. Examples at the end. 
