41 8 Mr. Ivory on the astronomical refractions. 
media has no effect in altering the velocity, we may consider 
the more simple case, when light passes out of a vacuum into 
a medium possessed of the density It is to be observed 
that the forces, with which matter acts on the rays of light, 
extend to distances that are imperceptible to our senses, and 
incapable of being measured ; and, on this account, what has 
been said is modified in no respect by the thinness of the shell 
of air. However small $ x, the thickness of the shell is 
supposed to be, it may still be considered as infinitely great 
in comparison of the range of the corpuscular force with 
which the light is refracted by the air. If we now put v for 
the velocity with which the light enters the shell of air, and 
express by an equation the physical principle already men- 
tioned, namely, that the refractive power of air is propor- 
tional to its density, we shall get, 
(u + J'u ) 2 — u 2 = K ^ p,* 
K expressing a constant coefficient to be determined by ex- 
periment. And, because u and ^ are functions of the same vari- 
able quantity x, the foregoing equation may be translated into 
the language of the differential calculus, in which case it will 
become, 
d -v 2 = K'x.d(>: 
and, by integrating, 
u 2 = i-fK ? , 
v = V 1 + Kf ; 
unit representing the primitive velocity of the light in vacuo. 
Let us next consider the trajectory described by the light 
in its passage through the atmosphere. Conceive two per- 
pendiculars to be let fall upon the tangents drawn to the 
* Newton’s Optics, Book z, Part 3, Prop. X. 
