,; i M;. I; A. SAMPSON ON A 



Inclination of Kxtreme Kay to Axis. 

 For b =+-200. 0---01. = -00. /i=+-OI. 



I: Inn- siuC.r,. () -0'6 0'0 +0'6, 



i <) and O a -6'3 -57 -5'1, 



O, O' 2 -4'6 -4'4 -4'1, 



O', O", -T9 -TO 0'0, 



O", O 4 -3'6 -2-4 -n, 



o, O' 4 -2'5 -T2 -0% 



<>', O, -4-1 -01 +3'9, 



<> O' -27 0'0 + 2'6, 



<>' F' 7 -3'6 -2-3 -0'9. . (41) 



The inclinations of the ray to the normals of the surface (.,) are given by 

 . + ' l *B;h,. /^'a. + hj.Bj, which may be calculated at once from the normal schemes; 

 but note that as these include reversals for the case of a mirror we must then take 

 in place of the latter ft f . Jn b^E^ : 



Inclination of Extreme Ray to Normal to Surface. 

 For6=+-200. ft = - -01. ft = -00. /3 = + -01. 



r-3'4 

 |_3'4 



-2'9 - 2'3 



-2'9 - 2'3 



r-4'8 -3'9 - 3'01 



1-8-2 -2'6 - 1'9 J 



(V f-3'3 -27 - 2-n 



1-3-3 -27 - 2-1 J 



O", f-3'3 -2'8 - 2'31 



1 _5'0 -4"2 - 3'3 J 



O f-3'4 -3-5 - 3-6-1 



-2'3 - 2'4J 



' 4 /- 3 ' 1 +2'1 + 7-3-1 



ll-Oj 



-47 +3'2 -Hll- 



- 4 ' 1 -O'l 



-27 -0-1 



O rt - -O'l + 3-81 



+ 2-5J 



O'. l'-17 -4'2 - 6-81 



L-2'6 -6'4 -10-2J . . (42) 



Thus the greatest angle of incidence is ll'O degrees upon the second surface of the 



the corrector. This is much below what is permitted in the construction 



t glass of a refractor; we find, for example, in STEINHEIL and VOIT'S 



J an aperture ratio of 1 : 12, the angle of incidence of extreme rays, 



Jly parallel to the axes, upon the first surface if the flint-lens exceeds 1 5 degrees 



