compound lenses and object-glasses, 
229 
and after refraction let it proceed in the direction M q. Draw 
PM perpendicular to QA q, the axis, and put as follows : 
■i= f m 'p n f ldenc - out of the medium QAM into oAM or = the 
relative refractive index of the medium on which the ray is 
incident. 
y=PM, the semi-aperture 
D=-q^ the reciprocal distance of the radiant point from 
the surface * 
r=-Ar, the reciprocal radius, or curvature of the surface 
Put also, for brevity, -^^==~==£ ; -^-==Sin. ACM=s, and 
1st. QM 2 == QC 2 + CM 1 — 2QC . CM. cos. ACM. 
2d. Sin. Incid. = Sin.QMC=r . s. 
Sin. CM(^ = Sin. Refrac. = m . . s. 
3d. Angle G7M = ACM — CM^. 
Sin.CgM==Sin. ACM . cos. CM</— cos. ACM . Sin.CM^. 
C ? =CM . ; A ? =AC+C g . 
If we put these expressions into algebraic language, and 
developing them in powers of s , neglect all beyond the 
cube of that quantity, we find 
Q M = 
Sin. CMg=m(i-f e) js — e(i -J- e ) . -j-j 
Sin. C^rM = 5 (1 — m — me)- i-{-e-j-e 2 — m — me^s*. 
* In conformity to the language already explained respecting powers and cur- 
vatures, may we not call this the proximity of the radiant point ? 
we shall have 
1 
