12 



the index of refraction being taken at TSO = ju for plate- 

 glass : 



Focal length . . ^0*^1 iQch = -05" 

 Aperture . . . xoo'l^s „ = '02" 



The diameters of the aberrating penumbra of a point — 



Diameter of least aberration. 



Plano-convex . "0009" = ^^\^ t,h of an inch nearly. 



Equiconvex . -00033" = aoVot^i 



Convexo-plane . -00023" = ^^^th • 



Crossed lens . -000214" = -^'-i-^th. 



If an equiconvex lens be used where the diameter of circle of 

 least aberration = '835 x ,-^',S5linSi:' *^^^ aberration will be 

 a minimum when the object and image are equidistant 

 from the lens, and each at twice its focal length from it, or 

 V = 2f and u = 2f. 



Now, by a combination of many glasses, objectives may be 

 corrected to show scarcely any penumbral aberration, but, 

 imfortunately, nearly all opticians using the Podura markings 

 as an unequalled standard, all the best glasses are corrected 

 to show what is absolutely false and delusive, and the result is 

 a misplaced belief. Till the explosion of this creed, every one, 

 being taught to look upon the Podura spectral markings as 

 the ne plus ultra of objective accuracy, is satisfied Avith that 

 ignorance which is bliss. The glasses are constructed on 

 purpose to show this supposed standard appearance; but 

 ojDticians will be obliged, at some future day, to elect a new 

 standard. The same glasses which show this admirable 

 note (! ! !) fail in the higher tests, such as will now be 

 descriljcd. 



I have found in the best objectives a residuary aberration, 

 and some of it, when the glasses arc pressed with too high 

 an amplification by deep Dl) eye-pieces, will in some degree 

 always remain to put a stop to further research, except 

 with deeper objectives still; and these objectives, rising 

 already to the 50th of an inch, will probably soon reach 

 their limit owing to manipulative defects in their manuficture. 

 The precious stones, such as the topaz and sapphire, and 

 lenses formed by accident or fortunate working, may perhaps 

 assist a further development of power or detection of 

 error. 



For forming beautiful images of bright discs, to imitate 

 close double stars, I recommend the use of two minxite crossed 

 lenses, set with their deepest convexities in contact ; but a 

 fine objective analyser may be formed of two lenses in contact. 



