790 
DR. OLIVER LODGE ON ABERRATION PROBLEMS. 
Hence. 
^ T, ^ 
SS 3 T„ 7-2 ’ 
wheiefore SM, bisects the angle SjMSo, or the angles of incidence and reflexion are 
jn'ecisely equal, and the required mirror is normal to SM, but is not tangential to the 
wave-front. 
Fig. 15. 
Details of normal reflexion with moving source or moving medium. 
Let Qj, Q, Q 3 be the images in this mirror of S, S 3 , and with centre construct a 
circle of radius QM cutting the wave-front in N ; MN is the mirror able to throw a 
light ray back on the moving source. 
A stationary observing telescope will observe the source along QoM; one moving 
with the source will observe it along QM, that is, in its true direction at moment of 
vision. The colour will change by the amount log rjr, as already said; and, as for 
any possible interference effect, the fringes will shift by an amount depending on 
Tj -I- To _ r^ + r„ _ cose -^{1 — a? siin 6) 
Ji Iv 1 — a" 1 — a'' 
which gives very approximately 
+ T 3 - 2 T aH (1 + cos2 0). 
There is, therefore, always a lag of phase caused by the motion, which cannot be 
made negative, or even zero, but which is a minimum when the motion is across the 
line of light, and a maximum when along it; being, indeed, twice as great for motion 
along as it is for motion across. Supplementary angles give the same effect. 
One may express the fact by saying that the virtual distance the light has to go 
is Sj^Qo, or SoQi, instead of SQ. 
