417 
Mr. Ivory on the astronomical refractions. 
2. The first investigation that presents itself in the problem 
of the refractions, is to find the velocity of light at any given 
height in the atmosphere. The only physical principle wanted 
for this purpose, is the refractive power of air according to 
its density. Hauksbee first determined by experiment, that 
air refracts light in proportion to its density ; and this result 
has been confirmed by succeeding philosophers. There is 
even good reason to think that the conclusion of Hauksbee is 
not materially affected by the variable quantities of aqueous 
vapour contained in the atmosphere at different times. Ad- 
mitting, then, the principle we have mentioned, we must 
conceive that the light coming from the sun, or from a star, 
moves in vacuo with a uniform velocity till it reaches the 
atmosphere. It is there deflected from its course by the 
spherical and concentric shells of air it meets with, each of 
which acts upon it with a force perpendicular to its surface, 
and directed to the centre of the earth. Now, as all the light 
enters the atmosphere with the same velocity ; and as the 
deflecting forces are of the same intensity at the same dis- 
tance from the common centre to which they tend ; it follows, 
that the new velocities acquired by the action of the forces, 
will be independent of the direction of the light's motion, and 
will be the same at the same distance above the earth's sur- 
face. Let a denote the radius of the earth ; x , any height in 
the atmosphere ; and p, the density of the air at that height : 
conceive also a shell of air having the thickness S x, and the 
increased density ^ -J- Sp ; then we shall have to consider the 
relation between the velocities of light when it passes out of 
a medium having the density into another medium having 
the density ^ ; or, since the density common to both 
mdcccxxiii. 3 H 
