u 
Dr. Young's Lecture on 
Since the velocity was denoted by x r , on the supposition of a 
projectile, it will be as x ~ on the contrary supposition, (Phil. 
Trans, for 1801, p. 27. Schol. 2. Prop. I.) and the fluxion of the 
1 
distance described being 77==, that of the time will be %====:• 
o v 1 —yy v 1 — yy 
or-^-. — of which the fluent is — — . — . \/i~ yy. 
1 — r yy.s/i-yy i-r y 
1 
Therefore, with the radius x lm ~r 9 describe a circle concentric 
with the surfaces of the inflecting atmosphere, then the angle 
described by the ray during its passage through the atmosphere, 
will always be to the angle subtended by the line cut off by 
this circle from the incident ray produced, in the ratio of r to 
r — 1; and the time spent in this passage, will be in the same 
ratio to the time that would have been spent in describing this 
intercepted portion with the initial velocity. For y, being equal 
t 6 sxT~\ is the sine of the inclination of the incident ray to the 
radius, where it meets this circle ; therefore, by the proposition 
quoted, the angle described is in a given ratio to the angle at 
the centre, which is the difference of the inclinations. Making 
— — or ~ radius, the sine, instead ofy, becomes s, and the co~ 
y 
sine S ~L — ss, or A \/i — yy, and, when y = ss, %/ 1 — ss ; 
y y y 
therefore the line intercepted is to the difference of the fluents 
as r to r — 1. (See also Young’s Syllabus, Art. 372.) 
PROPOSITION IX. 
Radiant Light consists in Undulations of the luminiferous Ether. 
This proposition is the general conclusion from all the pre- 
ceding ; and it is conceived that they conspire to prove it in as 
satisfactory a manner as can possibly be expected from the 
