]>i; R. A. SAMPSON ON A 



id mirror. It will be seen from the expressions (14) that it is desirable that the 

 corrector should lie as far as practicable from the principal focus if its aberrations are 

 to be as small as possible, that is to say, if its curves are to be as shallow as possible. 

 It cannot be too far forward or it will cut off some of the rays coming from the great 

 mirror to the revereer. It appears that a convenient distance is O'OOOO from the 

 revereer, or 07000 from the principal focus. That is to say, in the formula; (19) of 

 p. 40, 



*=-'5000, '=+-8750, w=-'6667, v=+l'6000, 



so that, with e' = 1 , for a spherical reverser, 



3.jg = + '3383, S.& = -3-0301. 

 Now we have to make 



S 3 G = Q, $,G+4H = 0, 

 and we have 



<J,G-4H = H^ = +4'8000 x -'3750 = -1'8000. 



Hence the changes A,, A 3 , which the corrector must introduce, are respectively, 



A 2 =-'3383, A s =+2-1301. 



These are the quantities so denoted in (14) p. 38. In the same equation, the 

 values of k, I to be used come from the scheme resulting from the combination of the 

 two mirrors, viz., 



g= , h =+4-800, =-'2083, I = +2'1667, 

 and v giving the position of the corrector with respect to the principal 'focus, 



v = -7000. 

 Hence 



A-'A, = + 1 -6238, ko A 3 = + -3 1 06, 

 H*-+-S160, (!-,)- = 1-4620, (-2 + Mv)/(l-Uv) 

 (-3 + 4klv)/(l-klvY = -37107, 



Ay= -1-6238- '4541 = -2'0779, 

 A* = -17472-1-1525 = -2'8997. 



** for thin 



] = +2-0779 



