456 Mr. Ivory on the astronomical refractions. 
but, 
fu =/(i— ~ u ) +4( i — 
consequently, 
+/(i— — 4 (i— c “T* 
We have therefore 
_ T + t' 
i + 0 ■ — 
and because 5 = ■ f we sret as before 
x = / x log. -f x { i + £ • I 4 JL } • 
The very exact coincidence in the properties of all the at- 
mospheres comprehended in the assumed formula, with the 
phenomena actually observed at the surface of the earth, ac- 
counts in a satisfactory manner for the near approach of the 
refractions in every case to the quantities determined by as- 
tronomers. It appears that, although the refractions near 
the zenith are affected in a degree hardly perceptible by the 
peculiar constitution of the atmosphere, yet, near the horizon, 
they depend entirely on the same arrangement of the strata 
of air indicated by terrestrial experiments. The causes of 
the irregularities observable in these last, likewise disturb the 
celestial phenomenon in a more remarkable manner. In 
measuring the height of a column of air, the accidental dis- 
turbances to which the atmosphere is continually subject, are 
in some measure corrected by means of the temperatures 
observed at both extremities of the column ; but, in com- 
puting the refractions, the astronomer has no guide but the 
thermometer placed at his Observatory. In the remote parts 
of the atmosphere, there may occur innumerable changes de- 
flecting the light of a star from its proper course, of which 
