OPTICAL INSTRUMENTS. 



21 



finite distance ; and on these conditions 

 he has rendered the problem deter- 

 minate, \vhile the radii resulting from 

 the construction are such as will satisfy 

 the following more important condi- 

 tions : 1st. The curvatures assigned to 

 each surface are more moderate than 

 in any other theoretical combination. 

 2nd. The exterior surfaces of the com- 

 pound lens vary within narrow limits by 

 any variation in either the refractive 

 or dispersive powers that generally occur 

 in practice. 3rd. That the two interior 

 surfaces approach in all cases so near 

 to coincidence, that no sensible error 

 can arise from neglecting their dif- 

 ference ; finally, he states as a theorem, 

 which will be found sufficiently exact in 

 practice, that a double object-glass 

 will be free from aberration, provided 

 the radius of the exterior surface 

 of the crown lens be 6.720, and of 

 the flint 14.20, the focal length of the 

 combination being 10.00, and the radii 

 of the interior surfaces being computed 

 from these data so as to make the focal 

 lengths of the two glasses in the direct 

 ratio of their dispersive powers. Fig. 

 25, is a section of this object-glass, the 



anterior glass A, or that which receives 

 the incident ray, is an unequally convex 



Fig. 25. 



lens of crown glass, the flatter side being 

 placed outermost; the posterior glass 

 B is a meniscus of flint glass. 



The rule here stated is given only as an 

 approximation, and will no doubt be suf- 

 ficiently exact for ordinary practical pur- 

 poses ; but when object-glasses of great 

 aperture and value are to be constructed, 

 their radii must be computed more 

 strictly, and for this purpose we shall 

 subjoin; Mr. HerschelTs TABLE, calcu- 

 lated upon the rigorous formulae as 

 given in the Philosophical Transactions 

 for 1821 : 



Dimensions of an Aplanatic Double Object- Glass. 



Refractive index of the Crown Lens 



Ditto ditto of the Flint Lens. . , 



1.524 



1.585 



> Compound Focal Length, 10,000. 



