432 Mr. Ivory on the astronomical refractions. 
show that similar inequalities are perceptible much nearer 
the zenith.* Now these inequalities do not arise from any 
thing imperfect in the manner of observing ; they are un- 
doubtedly produced by alterations in the remote parts of the 
atmosphere, which do not affect the barometer or the ther- 
mometer placed at the Observatory. It appears, therefore, 
that the peculiar constitution of the atmosphere has a per- 
ceptible influence on the refraction at 75 0 from the zenith ; 
and when Laplace’s formula is made to extend to 74 0 , it is 
carried to its utmost limit. 
However mutable we may suppose the condition of the 
atmosphere to be, there must be a mean state equally removed 
from the opposite extremes. Now, a table of refractions that 
should have this mean state of the atmosphere for its basis, 
would be the most advantageous of any. For although, with 
respect to single observations, the errors of such a table 
might be as great as in some other hypotheses, yet, in a 
numerous set of observations made at different times, so as 
to embrace all the usual changes, the inequalities of an op- 
posite kind would counterbalance one another. But, to a 
certain distance from the zenith, Laplace’s formula is suffi- 
ciently exact for practical purposes ; and it has the advantage 
of taking away the necessity of having recourse to precarious 
suppositions respecting the constitution of the atmosphere. 
As the formula we are considering contains nothing except 
what is common to every atmosphere, it must be deducible 
from the hypothesis of Cassini ; and it may be worth while 
to establish this point by a strict investigation. Cassini sup- 
posed that the earth is surrounded by a pellucid spherical 
* Dr. Beinkley’s Paper, Philosophical Transactions, 1821, p. 342. 
