60 On the UNEQUAL 



Thus, if the fine of the angle of incidence of any ray, in 

 patting 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 fpherical fegment of glafs, furrounded with oil of tur- 

 pentine, will be found to be above eighteen femi-diameters of 

 the fphere from the apex of the lens, when light paffes from 

 oil of turpentine into glafs, and feventeen femi-diameters of the 

 fphere diftant from the fpherical fegment, when light paffes 

 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 fphere 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 objcct-glafTes, or object-fpeculums, are as the focal diflances 

 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. 



The 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 reflectors. 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 



