ARE THERE ANY FIXED STARS ? 
365 
grave, than the natural tone of the fork.'^ And a little con- 
sideration will show, that if, instead of the fork being moved, 
the ear were brought rapidly towards or from the vibrating 
fork, similar effects would follow — a rapid approach rendering 
the sound more acute, a rapid retreat rendering the sound 
more grave. 
It is absolutely necessary, here, that the velocity either of the 
fork or of the ear should bear an appreciable proportion to the 
velocity of sound. In other words, aa' or aa" must bear an 
appreciable ratio to ah. This is obvious, since what is wanted 
is, that ef or kl should differ appreciably from ah. 
Now, if we only suppose the vibrating end a of the fork to 
be a particle whose vibrations are generating light of a par- 
ticular wave-length — that is, of a particular colour^ we see that 
the reasoning we have applied to sound-waves must be equally 
true of these light- waves. If the source of light be approaching 
us, through its own motion, or ours, or both, the waves will seem- 
ingly be shortened ; and if the source of light be receding, the 
waves will be lengthened. In other words, there will be in 
either case a change of colour — the change being towards the 
blue end of the chromatic scale in the former case, and towards 
the red end in the latter. 
But here, as in the case of sound, the condition has to be ful- 
filled, that the velocity of approach or recess shall bear an 
appreciable proportion to the velocity with which the waves 
travel ; that is, to the velocity of light. Now, light travels at 
the rate of about 185,000 miles per second; and it seems 
hardly conceivable that any material movements in the universe 
should bear an appreciable relation to so enormous a velocity as 
this. 
We could not hope, then, that any luminous object in the 
universe should indicate by a change of colour a change in the 
direction of its motion. 
But this is not the only nor the principal difficulty in the 
application of such a mode of estimating motion. Doppler, 
who was, I believe^ the first to suggest that the colours of the 
stars may serve to indicate whether these bodies are approach- 
ing us or receding from us, omitted to notice a circumstance 
which rendered his whole argument nugatory : — 
In the case illustrated by figs. 2, 3, and 4, we dealt with the 
affections of only a single wave-length. If all stars sent us 
^ light-rays having a definite wave-length, then what we have 
* Professor Tyndall has remarked that when a train rushes rapidly past 
a station a change in the tone of the whistle may he noticed by a person on 
the platform, the sound being more acute as the train approaches than after 
it has passed the station. 
