20 



OPTICAL INSTRUMENTS. 



the red and violet light, caused by the 

 refraction of the two mediums, is equal, 

 the divergency of the red and green 

 light is always greater in the crown than 

 in the flint, and the divergency of the 

 violet is always less in the crown glass*. 

 Hence it must be observed, that in 

 order to have a complete correction of 

 all the colours, more than two media 

 must be used, and, therefore, the best 

 telescopes have their object -lens com- 

 posed of three kinds of glass. When 

 the dispersive ratio is known, and the 

 refractive focus of the compound lens 

 is given, the refractive focus of each 

 must be calculated, and to obtain the 

 radius of the tools for working the lenses, 

 their refractive foci must be converted 

 into the geometrical shown as at (11), 

 when the object-glass would be com- 

 pleted, and the task would not be dif- 

 ficult to perform; but the spherical aber- 

 ration, although much less in quantity, 

 is more troublesome to correct, and in 

 making this correction, the proportion of 

 the radii of the two surfaces of the con- 

 vex lens must be assumed. When a suit- 

 able selection is made, the aperture of the 

 lens being given, the spherical aberra- 

 tion must be calculated, when its thick- 

 ness is ascertained^. And lastly, the 

 curvatures and thickness of a concave 

 flint glass must be found that will ex- 

 actly balance the spherical aberrations 

 produced by the convex glass ; always 

 keeping the foci of the two lenses in the 

 ratio of their dispersive powers. 



(33.) The radii of curvature of the 

 different surfaces of the lenses necessary 

 to form a double achromatic object- 

 glass, when the sine of incidence is to 

 the sine of refraction in the crown glass 

 as 1.528 to 1, and in the flint as 1.5735 

 to 1, the ratio of their dispersive powers 

 being as 1 to 1.524, and assuming the 

 curvatures of the concave as 1 to 2, are 

 shown in the following TABLE. The first 

 column F is the compound focus of the 

 object-glass in inches ; r the radius of 

 the anterior surface of the crown ; R 

 its posterior side ; r' the radius of the 

 anterior side of the concave lens of 

 flint glass ; and R' its posterior surface. 



* Dr. Blair. 



t The longitudinal aberration of a lens of glass 

 may be found by the following general theorem, 

 where r is the radius of the first surface, R the se- 

 cond surface, and T the thickness of the lens. 

 / 2? f* + 6 r R + 7 R 2 N 

 \ 6 + r x~R3 + 



F r R r' R' 



12 3. 4.652 4.171 8.342 



21 6. 9.304 8.342 16.684 



30 7.5 11.63 10.428 20856 



36 9. 13.956 12.552 25.027 



43 12. 18.603 16.684 33.869 



60 15. 23.260 20.856 41.712 



120 30. 46.520 41.712 83.42 1 



In these computations it may be re- 

 marked that the radius of the anterior 

 surface of the concave being less than 

 the posterior side of the convex, admits 

 of its approach without touching in the 

 centre, which should always be a neces- 

 sary practical condition. 



CHAPTER VIII. Aplanatic Telescopes 

 of Clairaulfs Construction Mr. J. 

 F. HerscheWs Object- Glass Triple 

 Object- Glasses Fraunhofer 's and 

 Tulley's Telescopes Galilean Tele- 

 scope and Opera Glass Achromatic 

 Opera- Glass Dr. Brewstcfs Fluid 

 Opera- Glass. 



(34.) The problem for the choice of 

 the proportional curvature of the as- 

 sumed convex lens is of the kind called 

 indeterminate, /or admitting of an infi- 

 nite variety of solutions. In conse- 

 quence of this, it allows an endless 

 number of combinations of lenses, and 

 each may be free from spherical aber- 

 ration. It becomes therefore a matter of 

 considerable delicacy to fix our choice 

 among them, and numerous construc- 

 tions have been calculated by different 

 authors. Thus Clairault, a French 

 mathematician, has given a construc- 

 tion in which the two internal surfaces 

 are worked of equal radii, the one con- 

 vex and the other concave, so as to ad- 

 mit of being cemented together, and thus 

 avoiding the loss of light by reflections 

 at the two surfaces. But having em- 

 ployed indices of dispersion in his com- 

 putations, higher than what are usually 

 met with in practice, and when those 

 most likely to be obtained are used, the 

 radii change so rapidly as to render this 

 construction difficult to interpolate, 

 where the artist is no algebraist ; and 

 hence it must lose much of its value to 

 the practical optician. 



(35.) Another construction has lately 

 been proposed by Mr. J. F. Herschel, 

 in which he states, that the destruction 

 of the spherical aberration is ensured, 

 not only for parallel rays from celestial 

 objects, but also for those that diverge 

 from objects situated at a moderate 



