Sjjherieal and Chromatic Aherration. Bij Dr.Royston-PigoU. 129 



Professor Littrow concludes bis paper by saying, 



" Tbe preceding calculations are tberefore equally simple and 

 exact, as tbey leave tbe beaten patb of finding tbe spberical aberra- 

 tion by an approximate expression, and determine tbis aberration 

 for any angle bowever large witb perfect accuracy . . . ." 



It would be of no interest to tbe Fellows to quote tbe wbole 

 formula used by Littrow as an improvement on Sir J. F. Herscbel's 

 metbod, but 1 may be excused for quoting anotber example, as it 

 bears very strongly on tbe principal feature of tbese papers. He 

 says, 



" In order to find how far the chromatic aherration has been 

 destroyed, we have (if B ' he focal length and n, n' indices of 

 refraction) 



B \r s I \r s I 11 /■•= 



wben tbe radii of tbe lenses are r and s and r and s, and d tbe 

 tbickness of tbe first lens : and tbis equation is absolutely tbe 

 expression for finding tbe aberration of two lenses for eacb kind 

 of coloured liglit tested. 



Tbe same formula is employed over and over again to test tbe 

 amount of spberical and cbromatic aberration introduced by tbe 

 lenses: and bence in tbis respect tbe cbaracters of tbe two are 

 absolutely identical. 



In standard works on optics, cbromatic aberration and spberical 

 are treated for convenience as distinct tbings. It may be noticed, 

 bowever, tbat Professor Potter bas discarded tbe term cbromatic 

 aberration and employs tbe term longitudinal disi^ersion, also used 

 by Coddington in 1831. 



Tbus, in Art. 84, p. 113, pt. i., 3rd edition, Professor Potter's 

 proposition is tbus worded : 



" To find the longitudinal dispersion and least circle of chro- 

 matic dispersion in a given lens.'' 



He tben finds tbe longitudinal dispersion for rays wbose 

 indices are different (sucb as red and violet), wbicb is simply tbe 

 cbromatic aberration along tbe axis of tbe coloured rays. 



Furtber on be says tbe condition of acbromatism is tbat v, 

 i. e. tbe distance of tbe focal point from tbe last lens sball remain 

 tbe same for all colours. 



Inasmucb tberefore as tbe longitudinal dispersion or cbromatic 

 aberration is obtained from tbe spberical equations, in otber words, 

 as tbe particular coloured ligbt entering a given lens is tben sub- 

 jected to tbe spberical laws of refraction in precisely tbe same way 

 as bomogeneous ligbt would be — so far tbeir cbromatic and spberical 

 aberration are identical in cbaracter, 



Tbe question turns entirely upon tbe definition of tbe terms 



