‘for computing the Astronomic Refraction. 29 
values of g and 4, as found from the observations, we may ob- 
tain that of m for all heights of the mercury in the thermo- 
meter. 
With respect to the value of p, Mr. Delambre found it to 
be 60499872” at 45 degrees of apparent altitude, when the 
barometer stood at 29°92152 English inches, and Fahrenheit’s 
thermometer at 32°. Mr. Groombridge found it 58°132967” 
at the same altitude, when the barometer was 29:60 English 
inches, and the thermometer at 45°. 
To compare these two values of p together, it is necessary to 
reduce one of them to the tenor of the other. Thus Mr. De- 
lambre’s determination, when brought to the same state of the 
atmosphere as that of Mr. Groombridge, will be 
j 29-60 1 
69:499872" x = (srascanoeos) = 58.9331”, 
and Mr. Groombridge makes his 58-1382967”; the difference 
0-200143” is small, and confirms the accuracy of the observations 
of both; yet small as it appears, it will very materially affect the 
refractions from 87° downwards to the horizon. 
It is much to be doubted, whether this theorem or any other 
can be brought to agree with the utmost exactness in all cases 
with the refraction observed at very low altitudes, and for the 
following reasons : 
The ray P S in its progress through the atmosphere from the 
star S to the observer P, has probably to encounter layers of air 
of various temperatures and densities, which differ considerably 
from that indicated by the barometer and thermometer fixed 
up for use at P, the station ofthe observer; therefore, to be 
enabled to form any just conjecture of the deviations which the 
ray may have undergone, we ought to know the state of the at- 
mosphere all the way from P to; or at least we ought to be 
acquainted with the heat and density indicated by these two in- 
struments along the surface of the earth, from the station of 
the observer at P to Q, the point immediately beneath the ob- 
ject observed, 
It 
