Ahhot and Fowle^ Jr. — Aberration of Prisms. 255 



Art. XXXI Y. — The Longitudinal Aberration of Prisms ; 

 bj Chaeles G. Abbot and Fredeeick E. Fowle, Je. 



Having had occasion recently to consider the propriety of 

 dispensing with collimation in the spectro-bolometric train at 

 the Smithsonian Astrophysical Observatory, we hav.e consulted 

 with profit the equation given by Lord Rayleigh"^ for the longi- 

 tudinal aberration of a prism in the case of a cone of rays 

 incident with the central ray in minimum deviation. We have 

 had occasion in doing so to develop formulae slightly differing 

 from those of Lord Rayleigh, and have thought it not without 

 interest to present the results of a somewhat closer approxima- 

 tion. In the following demonstration we have employed, so 

 far as possible, the same notation as Lord Rayleigh to facilitate 

 comparison. 



Let QA be the central ray of the pencil incident at the 

 angle for minimum deviation. Let the angles of incidence 

 and refraction of QA be (^ and (^' respectively. Let QC be a 

 second ray incident at the angle ((^-{-Sc^) and let the foci of the 

 prism be Q' and Q". The angles AQ'C and BQ^^D are h(i>' and 

 h(^" respectively. And let AE, AF, BG and BH be perpen- 

 dicular to QC, Q'C, Q'G and Q''H respectively. Let QA = w, 

 Q'A = u\ q"B = 'y, AB = I. Powers of S<^ higher than the 

 first will be neglected. 



AC 



AE = uh<^ 

 AE 



COS. (<^ + 8<^) 

 AF = ACcos (<^' + 8<^') 

 , AF 



BG = AF-f-/8<^' 



* Pnilosophical Magazine, V, ix, p. 44, 1880. 



0) 



(2) 

 (3) 



(5) 



