5{) |i|!. R. A. SAMPSON ON A 



The initial **lUptlM, *, does not enter the calculations, Imt is carried through 

 at ite wl..ptl vain.-, which is recorded here for reference. 

 It follows that 



K, = +'875000, (K,) = - '010297, 

 0,H, = -0",H", = + '013200, 



K 4 = +1-428571, 4 H 4 = +-006116, O' 4 H' 4 = -'002089, 



K= -1'359456, 0^,,= + -008211, 0',^.= -'000012, 



and that 



0,,H 2 = +1-333333, H" 2 F", = +1'600000, (26) 



and the power of the combination of great mirror and reverser is the same as in the 

 preliminary solution. The achromatism of the system proved also satisfactory, but 

 the numbers had to be recast because of the following defect. As will be seen on 

 p. 63, the semi-aperture of the lenses of the corrector is about a = +'0615. Hence 

 the separations of the vertices of the surfaces which are next to one another must be 

 at least ^*(B' 4 B g ) = +'00387. Hence enough separation has not been allowed, 

 since we have taken d & = + "00250. I therefore increased d b to the value of + '005000. 

 At the same time I decided to increase the thickness t 6 also to 6 = +'015000. To 

 change rf & , / means upsetting the balance of achromatism between the lens of the 

 revereer and the lenses of the corrector. All the quantities then will require adjust- 

 ment. The first step is to re-establish the achromatism. In doing so I keep the 

 first lens of the corrector unchanged, and two trials at least will be requisite to get 

 material for a proper adjustment of the other two as explained on p. 48. I found 

 by inspection and by previous trials that an alteration of the second lens of the 

 corrector produces its effect almost solely upon the coefficient K of the final scheme, 

 ami hardly at all upon G ; hence- 1 first adjust the lens of the 1 reverser so as to make 

 A< I = for variation of refractive index, and then the second lens of the corrector so 

 as to make AK = also. .Since the system 0" 2 ...0 6 from the last face of the 

 ivvereer to the first face of the second lens is unaltered throughout I take it in one 



o 



pier.-, taking the lens (4) with the data of p. 49, and 



da = +'906760, d & = + '005000, 

 and taking in succession 



fi = n-' = 1 "520000, n = "657895 

 and 



' = 1"()1 xrr 1 = 1"535200. n + Sn = '651381, 



