38 



|iK. K. A. SAMPSON <>\ A 



<J,K = <5,L = -iiG and the rest are zero. These are the values at the surface of the 

 corrector. \V- notir.- that all are zero when qjk + q'jV = 0, that is, when the 

 curvatures of the two surfaces in contact are the same. 



In onli-r t<> illustrate the manner of using these, for example, let it be proposed to 

 timl the curvatures of a corrector, which when interposed at a given point of an 

 aherrant beam shall produce assigned changes in it. Let this place be at a distance 

 v befon> the beam comes to its focus. After passing through the corrector it will 

 still come to a focus at the same place, so that applying the formulae of the Memoir, 

 p. 164, (22), we have for the distances from the first conjugate focus to the 

 corrector d = r, which is negative, and from the corrector to the second conjugate 

 fo<-us d' = r, and transferring from the surface of the corrector to these conjugate 

 foci, we have 



where <J,y, J,* are written for the values of ^G, <5,K given in (13). 



We must now apply the formulae (4) of p. 32. For the corrector g' = 1. Let the 

 assigned changes be, say, 



A,, = 4G-4gr, A, = 8 9 G-S#, 

 so that the equations (4) of p. 32 give 



therefore 



J .A 3 . . (14) 



From these equations the values of the curvatures of the two lenses may be found 

 with the help of equations (13). An example of their use will be found below, on 

 p. 44. 



In connection with the question of assigning a system which will produce definite 



may I* remarked that it is not difficult to solve the equations (17) of 



. Menu,,,- so aa to give explicitly either S>g, ... or *J, ... so that we have 



>-s.r,d either the antecedent set or the consequent set which combine to 



.ilrat,on coefficients J.G, ... . The former are obviously obtained by 



J ' Mi '^ L ' -^ G+ ^ K ' -WH-AL, which give respec 

 ^.UUn'V For the latter coefficients V,.- we form 



