422 
Mr. Ivory on the astronomical refractions . 
p i + & w , . 
y*r+Tr*P : 
but we have put p for the density when the pressure is p and 
the temperature r ; wherefore, 
p I + 0T , 
which is equivalent to the foregoing formula. 
From what has just been proved we get, 
(i+0t')p' — (i+0t) p » 
which shows that the quotient of the pressure divided by the 
density reduced to the fixed temperature zero, has always 
the same value. Therefore if l denote this constant value, 
we shall have. 
= /x (i +£t) x p; 
and l is a quantity to be determined by experiment. 
Suppose now that a tube or cylinder of air extends from 
the surface of the earth to the top of the atmosphere ; then 
the barometric column^), will be equal to the pressure of all 
the air in the cylinder above the height x. Let the barometer 
be lowered down through the small space dx ; the mercury 
will rise a small height dp ; and we shall have 
dp == — - dx x p, 
an equation which merely expresses that the small column 
of mercury dp is equivalent to the weight of the column of 
air having its length equal to dx, and its density to p. Divide 
the left side of the equation by p', and the right side by the 
equivalent quantity / x ( i + jGr' ) x p r ; then, 
dp __ dx f 
J lx (I +0r') x 7 ’ 
and by integrating, 
P __ f* — dx p 
