424 Mr. Ivory on the astronomical refractions. 
two foregoing values of p , we shall obtain 
I + 0r f — ds ( I — a) 
7+1?“ * 
and by taking the fluxions, 
i + 
I — (!) 
d . 
dx 
(L±lL) 
\ I + 0t ' ’ dui f—ds{ l — u) 
ds 1 I" dSj (i— u) z 
-jr ; therefore, observing that r decreases when 
but ds — . , , . 
l (I + 0r) 
x increases, 
(i — ’ 
now, at the surface of the earth, P= f — ds (l — u) = l ; 
wherefore, 
S (wheni = o) = l -/3/ x t 
Suppose that [x represents the height through which the 
thermometer must be carried at the surface of the earth, in 
order to depress the mercury one degree ; it is obvious, that 
— is the numerical value of d f - : wherefore, 
h- dx ’ 
7s (making i = o) = i— (B) 
The quantity ^ is derived from the function of the height 
that represents the decrease of density. It appears that the 
value of it at the surface of the earth depends upon p ; and 
\ 
terrestrial observations show that this quantity is subject to 
great irregularities, which are not well understood. It is 
found that the refractions near the horizon are liable to vari- 
ations equally irregular and unknown. There can be little 
doubt that both these effects are produced by the same causes, 
which disturb the gradation of heat, and the arrangement of 
the strata of air near the earth's surface. 
It will now be necessary to resume the former value of dr , 
