the Aberration of the fixed Stars , &c. 67 
media beyond the objeff-glafs if bounded by tranfparent planes 
to which the axis produced is perpendicular, yet if the veloci- 
ties and refractions fo correfpond, ftill the ray in queftion will 
pafs relatively along the axis till it meet the relt at the focus : 
for here the refraCted ray in the firft medium becomes the inci- 
dent ray in relation to its path in the fecond, and this in its 
turn becomes an incident ray in relation to its path in the third 
medium, &c. and therefore by the prop. A. can never deviate 
from the moving axis whatever be the ref raft ive denfity of the 
media, or however thefe are diipofed in the order of fucceftion. 
And lince, by Sir Isaac newton’s theorem, the ratio of the 
fine of incidence to the line of refraction in the paflage of a 
ray out of one medium into another, is compounded of the 
ratio which the former has to the latter in the paftage of that 
ray out of the firft medium into any third, and of the ratio of 
the former to the latter in the pafliige of the fame ray out of 
the third medium into the fecond, &c. it follows, that if the 
velocities be related to the degree of refraction as before men- 
tioned, the ray in the la ft denfe medium will, notwithftanding 
any number of previous refractions by glafles, &c. have the 
fame final velocity that would have been acquired on its palling 
immediately out of air into that medium. This being the cafe, 
it appears, that though the intervention of an objeCt-glafs may 
lhorten the focal diftance of fuch a telefcope, yet it will not 
difplace the image nor alter the rule of interring the final velo- 
city of the ravs in the denfe medium from the aberration given ; 
at leaft when this is fuppofed to be the fame with Dr. Bradley’s. 
Fig. 3. But further, if the aberration of fuch a telefcope 
fhould differ from the Bradleyan one, and give, for example, 
the angle OMB, ftill the ray PO, which falls on O the vertex, 
muft be confidered as an incident ray, which, after refra&ion, 
K 2 pafies 
