CASSEGRAIX KKFLKCTOlt WITH CORRECTED FIELD. 55 



curvatures of (28), that is to say, the material to repeat the approximation, if 

 required, and finally to pro\.- that no further change is necessary. 



The numerical calculation of all aberration! follows the model given in the Memoir, 

 pp. 172 ct ?</. , and it will l>e unnecessary as a rule to give details of the working 

 here, though I may mention thai I have found a noteworthy abbreviation of it. 



The great mirror and reverser together, the former treated as parabolic, contribute 



atF, 



J,G = ... + '057176, S y G = +' 354860, SjGr = -3'297523. 



\Vc must also introduce the deviation of the mirror from a paraboloid, viz., we 

 have at the surface of the mirror the additional term S t k = ...+2e B 8 = '0312500e (l , 

 and all the others unaffected. To find the effect of this in the final set S t G. ... , by 

 (17) of the Memoir we must take h'i t k in <J,G merely, where h' belongs to the scheme 

 <>....F' 7 and is simply equal to the final focal length, which comes out +5*087942; 

 hence we must supplement the numerical values above by the unknown term 



J,G = ... -'i58998e , ,G = *, <J 3 G = *. 



Next we find that the other two lenses contribute together at F; 



J,G = ... -'0301G7, 3 3 G = ...- '342260, ^G = ... + 2'494419. 

 Further, for the three sections 



$ = - '417950+ '937763-'885449 = -'365636, 

 H = +5*087942, ^H = -'930167, 



and the three equations to satisfy being 



<5,G = 0, * 2 G = 0, <J,G = -'930167, 

 we find the actual numbers leave residuals in the left-hand memliera of the values 



+ '027009, +'012600, +'127057 ....... (29) 



These are to be brought to zero when supplemented by the proper expressions in 

 * ?4 <? an d o is dealt with above. 



Now referring to the expressions for a thin lens and writing q = qjk so that for the 

 system just computed q 4 = +2'3734, q fl = +4'8325, and confining attention to the 

 forms in which q is introduced at the surfaces of the lenses, these are respectively : 



First lens 



S l7 <= ... -'671321q 4 , 



<V 4 = +'959031il,+ > JC.5793q/, S^ = ... +'671321q, 

 <J,A 4 = ... +'67i:i21q 4 , 

 and the rest zero ; 



