4 58 Mr. Ivory on the astronomical refractions. 
/being nearly equal to In this hypothesis it has been 
shown that the same pressures, densities, and temperatures, 
would take place at the same altitudes as in the real atmos- 
phere, as far at least as observation enables us to determine. 
We may therefore presume, that it is not far from that mean 
state which would prevail, if the regular disposition of the 
strata of air were not continually deranged by disturbing 
causes. It remains now to find the refractions in this hypo- 
thesis, and to compare them with the quantities observed by 
astronomers. 
22. We have hitherto supposed that «, i, x — 4 -, are quan- 
tities varying with the pressure and temperature of the air ; 
but it will now be necessary to restrict those symbols to the 
particular values that take place at the mean temperature of 
50 0 of Fahrenheit, and the mean pressure of 30 English 
inches. We shall use the expressions a (1 +— ), i ( 1+ i ), 
A + lx, to denote the like quantities as altered by the changes 
in the atmosphere. What was before signified by 
2 is — 2 a u, or 2 z (s — Xu), 
will now be thus written, viz. 
21 0 + t) • j/~“ ; 
and, by substituting the assumed value of s, and rejecting 
quantities of the second order with regard to the variations, 
the same expression will become, 
** • (0 -/)* + */■ C~“] 
+ • T ' \ 0 — /) » + 2/<T“ } 
— 2 i . lx . ( 1 — c~ u ) ; 
or, more simply, 
