DR. OLIVER LODGE ON ABERRATION PROBLEMS. 
799 
A separate figure may save confusion ; and though the general case is easily drawn 
(like fig. 17) a special case serves better for illustration, and I depict the case of drift 
d" and e" are the angles between refracted ray and the drift direction and wave- 
normal respectively ; the angle of refraction, defined as usual, may be called j ; so 
that 
^ -J, 
* // cc , 
sin € = - sin ^ , 
H- 
vlfjr Yjfx V/yU. cos e" + vj/x^ cos 6" ’ 
AF _ sin (j — e") 
AC cos e" 
These are the equations to be used in conjunction with the previous set, and so it 
follows that 
sin_/ — cosy tan e" AF 1 cos e" + ujfx cos 6" 1 cos e — « cos (i — (/>) 
sin i -}- cos i tan e BC fx cos e + x cos 6 fx cos e" — xj/x cos (J — 0 ) 
Wherefore 
Or 
sm t cos e 
sin i cos e — a sin (f) — a tan e cos ^ cos (^ — (f)) 
p. jsiny cos e” — -sin ^ -f- - tan e" cosy cos (j — 
— p siny cos e" = I cos ^ sin 2 (f — - cosy sin 2 {j — 
I H' 
Which shows that the difference between sin i and p sin^, or the error of refraction, 
is likewise of the second order of aberration magnitude, i.e., ordinarily speaking, nil; 
