Mr. Ivory on the astronomical refractions. 45 3 
and, when m is infinite, /= 
+ — »)*• 
By solving this equation with the given value of P, we get, 
i — u = 0.4951, 
which is less than the true quantity by about of the whole. 
It is remarkable that the two results lie on opposite sides 
of the true quantity : from which it follows, that a value of 
m greater than 4 may be found, that will accord exactly 
with the observation of Gay Lussac. No confidence, how- 
ever, could be placed in a calculation founded on a single 
instance, where an enormous difference in the results would 
be produced by a small error in the quantities determined by 
experiment. But at any rate, what has just been remarked, 
agrees very well with all the arguments that have been ad- 
vanced to prove the finite extent of the atmosphere sur- 
rounding the earth. 
For farther illustration, some other observed heights have 
been selected from the same work of Ramond, the calcula- 
tions being made in the same manner. The results are 
contained in the following table. 
Places. 
By Observation. 
By Theory. 
Heights. 
Logarithms P. 
T* 
T 
Density. 
Dei 
sity. 
Fathoms. 
Puy de Dome, in 7 
Auvergne, } 
—I.94529 
O 
18.6 
0 
11 7 
0.9035 
m zz 4 
0.9041 
m — 00 
0.9035 
00 
!-/> 
Mont Perdu, in 7 
the Pyrenees, j 
• — 1.88944 
20 
7 5 
O.8106 
0.8157 
0.8132 
1185 
PicduMidi,High 7 
Pyrenees. j 
1 
bo 
ON 
00 
25.4 
10.4 
0.7768 
07833 
0.7798 
1429 
Etna - - - - 
— 1.82811 
23.I 
4.4 
0.7196 
0.7286 
0.7232 
1825 
Chimborazo, in 7 
the Andes, j 
Gay Lussac’s ? 
— 1.69582 
— 1.63611 
z 5*3 
30.8 
— 1.6 
0.5468 
0.5710 
0.5580 
3215 
3816 
ascent, ) 
— 9.5 
0.5004 
0 - 5 1 15 
0.4951 
