294? Sir W. R. Hamilton on a Lens of Uniaxal Crystal. 



i) (i - ol 



2r 



(29.) 



a formula for the focal lengths and aberrations of a lens of 

 uniaxal crystal bounded by any two infinitely near surfaces, 

 which have the optical axis of the crystal for their common 

 axis of revolution : all cases of cusps of other singular curva- 

 tures at the common vertex being here set aside. 



8. We shall content ourselves at present with drawing two 

 conclusions from this formula. First, that because the extra- 

 ordinary index v disappears from the part unaffected with the 

 small factor £®, the central focus of the extraordinary rays, 

 after emerging from the thin crystalline lens, coincides with 

 the central focus of the ordinary rays which emerge from the 

 same lens, wherever in the axis the focus of the incident rays 

 may be : whereas Mai us # , misled by an error of sign in a ra- 

 dical which he employed for expressing the law of extraordi- 

 nary refraction in the case of an uniaxal crystal, thought that 

 these foci, ordinary and extraordinary, might differ widely 

 from each other. And second, that on account of the pre- 

 sence of v in the term 



e-^g (30.) 



the ordinary and extraordinary aberrations cannot be exactly 

 the same (the power (/a — 1) (r — r') of the lens being sup- 

 posed to be different from 0), unless the M in the denominator 

 of this term become infinite ; that is, unless, wherever the 

 focus of incident rays may be, the lens is so placed as to allow 

 the rays within the crystal to be exactly parallel to the axis. 

 If then a lens of this sort be used for the object-glass of a te- 

 lescope, it seems to be desirable that its anterior surface, or 

 that on which the parallel rays fall, should be plane, and that 

 the correction of the aberration of figure should be effected 

 entirely by another lens, composed of an uncrystallized mate- 

 rial. W. R. H. 



Observatory of Trinity College, Dublin, 

 September 14, 1841. 



* Perhaps it may not be improper to mention here, as I am not aware 

 that the correction of Malus's result, respecting the extraordinary focal 

 length of a lens of uniaxal crystal, has been hitherto published by any other 

 person, that this correction occurred to me many years ago, in treating the 

 question by my own methods, which made it scarcely possible to fall into 

 the same error. The discrepance between my conclusion and his was, how- 

 ever, so great, that I was at first perplexed to account for it, until I traced 

 that error of sign in his calculations, to which allusion has been made above. 



