12 On the UNEQUAL 
fraction of the mean refrangible ray, which obtains in that me- 
dium, I took a direct method, fimilar in principle to that em- 
ployed by Sir Isaac Newron, and defcribed by him in the 
feventh propofition of the firft book of his Optics, and likewife 
in his Optical Lectures, p. 54. ; but which I may venture to fay 
will be found much eafier, and perfectly accurate. 
InsTEAD of caufing the rays to pafs through the. fights of a 
large and accurate quadrant, at the diftance of ten or twelve 
feet, as directed by Sir Isaac Newton, I employed a Hap- 
LEy’s quadrant, in the following manner: 
Fic. 1.—I reprefents the index-glafs and H the horizon- 
glafs of a Hapiey’s quadrant. SI reprefents a folar ray, in- 
cident on the index-glafs, thence reflected to the horizon-glafs. 
H, and from it to the eye at E. The line sg reprefents another 
folar ray, incident on thegprifm P, and through it refracted to 
the eye at E. When the prifm is turned flowly round its axis, 
till the fpectrum G appears at its greateft height, this is its pro~ 
per pofition. The angle formed by the dire and refracted 
ray is then the leaft poffible, and the angles of incidence and 
emergence are equal. Let the prifm be fecured in this pofition. 
A flight infpection of the figure will thew, that when the re- 
flected and refracted images of the fun are made to coincide, 
the angle marked by the index of the quadrant, is the fame 
which the incident ray sg forms with the refracted ray PE 
produced. For SZH is the angular diftance of the fun and 
his doubly reflected image, marked by the index; and the an- 
‘gle sgG, which the ray incident on the prifm forms with the 
refracted ray produced, is equal to it; sg and S,I being paral- 
lel, and PZ and HZ being coincident. 
Tue manner in which the ratio of the fines of the angles of 
incidence and refraction may be computed from the above an- 
gle, and the refracting angle of the prifm being given, is fully 
explained in the celebrated works which have juft been quoted. 
Ir 
