38S ACHROMATIC EYE-PIECES. 



always oppose the accelerating effects of the wheel in the short 

 vibrations, and so cause the whole of them to be performed 

 nearly in the same time. 



I am, Sir, 

 Your most obedient humble servant, 



WILLIAM HARDY. 



IV. 



JRemarks on Achromatic Eye-pieces. By David Brewster, 

 A. M, 



I 



To Mr. NICHOLSON. 

 SIR, 



Introductory J. OBSERVE, in the last number of your Journal, a query 

 respecting a rule for achromatic eye-pieces, contained in my 

 appendix to Fergusons Lectures. Your correspondent seems 

 to question the accuracy of that rule, and to imagine that 

 no combination of lenses whatever can form an eye-piece 

 capable of removing the chromatic aberration. Were this prin- 

 ' ciple to be admitted, the rules which I have given for achro- 



matic eye-pieces, composed of three or four lenses, would 

 likewise be inaccurate ; and the ingenious eye pieces by which 

 Dolland and Ramsden have rendered their telescopes supe- 

 rior to those of every other artist, would be liable to the 

 same imputation, I could easily demonstrate, were it ne- 

 cessary, that an eye-piece consisting of two lenses, whose 

 focal lengths, reckoning from that next the object, "are as the 

 numbers 3 and 1, and whose distance is equal to the difference 

 of their focal lengths, will almost wholly remove the aberration 

 of colour. But I imagine it will be a sufficient answer to the 

 query of your correspondent, and a sufficient vindication of the 

 rule to which he alludes, if I can explain to him the reason 

 why the error, arising' from the different refrangibility of the 

 coloured rays, may be corrected by a judicious combination of 

 lenses ^f the same refractive and dispersive power. 

 Explanation of Let A B, Fig. 1. PI. XL, be an achromatic object-glass, and 

 Jye^pk?^^''' D, E two lenses of the same kind of glass. Let C D- E be the 



