60 On th UNEQUAL 
Tuus, if the fine of the angle of incidence of any ray, in 
paffing out of glafs into air, be to the fine of its angle of re- 
fraction as twenty to thirty-one, and the fine of the angle of 
incidence of the fame ray, in pafling from air into oil of tur- 
pentine, be to the fine of its angle of refraction as twenty-five 
to feventeen, the proportion of the fine of the angle of inci- 
dence of that ray, ,to the fine of its angle of refraction, in paf- 
fing out of glafs into oil of turpentine, will be as five hundred 
to five hundred and twenty-feven. 
Hence the point to which light is converged by the refrac- 
tion of a f{pherical fegment of glafs, furrounded with oil of tur- 
pentine, will be found to be above eighteen femi-diameters of 
the {phere from the apex of the lens, when light paffes from 
oil of turpentine into glafs, and feventeen femi-diameters of the 
{phere diftant from the fpherical fegment, when light .pafles 
from glafs into oil of turpentine ; whereas in glafs furrounded 
by air, the focal diftance in thefe two cafes is only two femi- 
diameters, and three femi-diameters; and when light is con- 
verged to a point by a concave reflecting fpeculum, the focal 
diftance is only half a femi-diameter of the {phere to which the 
fpeculum is ground concave.. Now, in all thefe cafes, the er- 
rors of the rays arifing from imperfections in the workmanfhip 
of object-glafles, or objeét-{peculums, are as the focal diftances 
to the radii of convexity; fo that what Sir Isaac NewTon 
mentions, of his having nearly defpaired of reflecting telefcopes 
from this confideration, need not be wondered at. 
Tue great pains, however, which he took with his own 
hands, and the ingenious methods which he fuggefted, and 
which have been fo ably profecuted fince his time, have 
gone farther than could be expected towards obviating this_ 
fundamental. fault of refletors. Whatever can be perform- 
ed by reflection, may be expected from the long experience and 
indefatigable exertions of Dr HERSCHEL, aided by the counte- 
nance 
