C J 5S> ] 
VII. A finite and exact expression for the Refraction of an 
Atmosphere nearly resembling that of the Earth. By Thomas 
Young, M. D. For. Sec. R. S. 
Read February 5, 1824. 
It has lately been demonstrated, in the Journal of the Royal 
Institution, that if the pressure of the atmosphere ,y, be re- 
presented either by the square or by the cube of the square 
root of the density ,2, the astronomical refraction ,r, may be 
obtained in a finite equation. Mr. Ivory, in a very ingenious 
and elaborate paper lately presented to the Royal Society, 
has computed the refraction, by means of several refined 
transformations, and with the assistance of converging series, 
from an equation which expresses the pressure in terms of 
the density and of its square : I have now to observe, that if 
we substitute, for the simple density, the cube of its square 
root, and make y = \ 2* — is 3 , we shall represent the con- 
stitution of the most important part of the atmosphere with 
equal accuracy, although this expression supposes the total 
height somewhat smaller than the truth, and belongs to one 
of those hypotheses, which Mr. Ivory has considered as 
inadmissible : it has the advantage, however, of affording a 
direct equation for the refraction, which agrees very nearly 
with Mr. Ivory’s table, and still more accurately with the 
French table, and with that which has been published for 
some years in the Nautical Almanac. 
Since d x = m being the number of times that the 
m z 0 
modulus of the atmospherical elasticity is contained in the 
