350 Mr. J. Bridge on the Oblique Aberration of Lenses. 

 small, direct, centrical pencil. Then 

 MN y 



or 



■»c AM . v . o b 2 , n , .m— 1 



21 ' y y v? 2mn 



*>=2fuA S+ m)- 

 For the secondary focus, 



AM A „ v . „ g 6 2 .. ?w — 1 



# 2 = A£= A£=t> 2 ^ (m + 1 ) -= — 



z z z u l 2mn 



~2/"V" V + m/' 



2/ 

 (See Coddington, p. 119.) 



Primary and secondary foci of a small eoccentrical pencil which 

 crosses the axis (z = 0). 



For the primary, 



At? Ay d-n , 



— - =—2- x, = — v -p- nearly, 

 a.'j v ay 



c m — \( n (~~ n -r,bi/ b 2 b q \ 



= +v*.- (3.A7y 2 + 2B^ + TO -2+-^) 



Zmn \ u vr mv 



\ tr ra / 



\ m -g / 



2/ w* \ m / 



since it is found that 



Aw 2 + 2B^ + m^- 

 u u~ 



b* 

 m-s- 



ir 



is equal to what in Coddington is called V*. (See Coddington, 

 pp. 137 and 138, or the resume in pp. 196, &c.) 



* This is a much more convenient form than Coddington's V, since it 

 enables us to distinguish immediately the effects due to aperture and ob- 

 liquity. 



