DR. OLIVER LODGE ON ABER,RATION PROBLEMS. 
783 
least) by travelling towards the source, when the observed rise of pitch must be caused 
by increased frequency of arrival, the wave-lengtli remaining unaltered. 
But when we consider the effect observed in a spectroscope, there might possibly be 
a difference according as its essential part was a grating or a prism. 
For it may be argued that a grating, consisting as it does of a set of apertures of 
fixed width, must deviate and disperse in pro]iortion to wave-length ; and hence that 
if a grating be supplied with crowded waves, either by holding it to an approaching 
source, or by immersing it in a denser medium, or in a medium flowing from it 
towards source, it must act as if coarser relatively to the waves, and so deviate and 
disperse them less. 
But although this is a simple and plausible statement it is only half the truth. 
We had better examine the problem particularly (§ 56), for it is a curious mixture of 
Doppler effect and aberration, but at present it will suffice to say : 
If 6 is the deviation caused by a given grating for a given fixed source of frequency 
1 /T, so that 
|sin6» = VT, 
N 
then if the source be approaching at the rate v, the time-interval between successive 
like phases is diminished in the proportion (V — v)iy ; and accordingly 
s sin 6' = \ (T - ^) = (V - y) T. 
If it be the grating that is advancing towards a fixed source, the time interval 
between the arrival of like phases is likewise diminished, but in the ratio V/(V + v) ; 
so that 
s sin 0" = ^ ~ T. 
V -I- -y 
It is noteworthy that between 6' and 0" there is a minute difference of the second 
order of aberration magnitude ; 
0” _ 0' ^ tan 0. 
Y2 
If the grating be plunged into a different medium, the velocity of advance is 
changed, and 
s sin 0"' = ^ T. 
Lastly, if both source and grating are stationary, but the medium flowing from one 
to the other, or (what is the same thing) if source and grating are moving at the same 
pace, chasing each other through a stationary medium, the velocity and the wave¬ 
length are affected together, and 
ssin 0"" = {Y v)T = (V v) T = s sin 0. 
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