32 
MR. T. Y. BAKER AND PROF. L. N. G. FILON: LONGITUDINAL 
The advantage of the double even suffix notation in this case is that we have a symbol, 
M. (0 , for the magnification when light passes backwards through the system, the order 
of the suffixes being material. Where odd suffixes are used, we have to use l/M ls 
l/M 13 , &c., for the reversed magnifications. 
Ray magnifications will be denoted by M. These are the limit of the sine-ratio for 
small inclinations, thus M 4 = M o2 - L sin a 0 /sin a 2 . M = M when the initial and final 
“o"A"0 
media are the same. 
With regard to inclinations, they will be treated as positive when the rays converge 
to the axis, as in fig. 1. The inclinations of the rays calculated by Gauss’ process 
will be denoted by /3. Thus /% = a 0 , tan /3 2 = tan a 0 /M 02 , tan /3 S = tan a 4 /M u4 , &c. 
We may also use angles y, calculated from a constant sine ratio, viz., y 0 = a 0 , 
sin y 2 = sin a 0 /M 02 , sin y 4 = sin a 0 /M 04 , &c. 
Throughout much of the work we shall use the same trigonometrical function 
(tangent or sine) of the angles a. If the tangent is used, we shall employ the following 
abbreviations :— 
q 2n = tan a. in t 2n = tan fi 2n . 
If the sine is used, the meaning of q. t will be as follows:— 
? 2 n sm CL 2n t 2n — Sill y 2n . 
It will be found that many formulae remain unaltered, whichever of the two inter¬ 
pretations for q and t is used. 
