l>l;. |;. \. SAMPSON ON A 



\\ . LOW return t.. tin- .-ilHMT.-iti.mH ; we have replaced the numbers of p. 49 by the 

 following: 



B, = - -250000, 



,/, = +1-320133, 



B, = -B", = +'472584, B' 3 = +'4 5 1898, t, => +'020000, 



,l t = +'906760, 



B = -'697845, B' 4 = +2'043309, t t = +'012500, 



(i, = +'005000, 



B,= +'003667, B',= -2'584570, ^=+'015000, ...'.. (28) 



;unl in these changes the aberrations calculated for the lenses of p. 49 will be changed ; 

 \\ now require to find new values for q t , q t , which will restore the disturbed correction. 

 It may be remarked that the chromatic correction depends very little upon the 

 distribution <>f the curvatures between the two faces which is indicated in the value of 

 q, and it might have been reflected that as the surface (6) is nearly plane, and the 

 U-.-im meets it nearly at right angles, while the surface (6') produces almost the whole 

 deviation of the beam for which the second lens is answerable, it would have been 

 better to keep B' 6 unmodified while the second lens was adjusted for achromatism, but 

 this was not noticed until the solution which follows had been made, and was found to 

 reproduce almost exactly the value of B' 8 of p. 49. 



The aberration coefficients for a thin lens at its surface are given by (6), p. 33. I 

 have not so far succeeded in supplementing these by any algebraic expression containing 

 ivt'crence to thicknesses or separations of lenses, which are simple enough to be useful. 

 IliMice the procedure for finding q t , q e , e must be by approximation, and the following 

 is the method adopted. Calculate at the principal focus of the complete combination 

 tjivt'n by (28) the numerical values of the aberration coefficients, or at least the 

 essential ones <5,G, S a G, <5 g G, in three parts, namely, first, the great mirror and reverser 

 together in which e,, is easily included as an unknown ; second, the first lens of the 

 corrector ; and third, the second lens of the corrector. The conditions for a corrected 

 system are then 



these are not satisfied we must bring in corrected values of g 4 , q, e to satisfy 

 I asKiim.- lor the purpose of approximate correction that the quantities q, q' J 

 .Iculated aberrations with the same coefficients as if the lenses were thin ; 

 this Hup,Miti..i. I calculate the algebraic values of the aberrations, carrying them 

 the surfaces of the lenses forwards to F' 7 and backwards to O by a double 

 tl..- formula. (17) of p. 160 of the Memoir. Assuming that these 

 W* , tl,.. adjustable parameters ,, q tt q t account for the discrepancies 

 10118 to determine e , q t , q t> and in consequence amended values of the 



