532 
ME. W. HUGGINS ON THE SPECTEA 
He appears to consider that, to produce a certain alteration of refrangibility, half the 
velocity would be required in the case of the approach of a star to that which would be 
necessary if the star were receding. This is not the case, for equal velocities of separa- 
tion or approach give equal changes of wave-length. It is true that a difference of an 
octave is produced by a relative velocity of separation equal to that of light, and by a 
velocity of approach equal to half that of light ; but the difference in length of a wave 
and its octave below (which is twice as long) is in the same proportion greater than the 
difference between it and the octave above (which is half as long). 
The experiments of M. Fizeau in connexion with this subject are referred to by 
Mr. Maxwell in the following statement of his views and experiments, which was received 
by me on June 12, 1867. 
On the Influence of the Motions of the Heavenly Bodies on the Index of Refraction of 
Light. 
Let a source of light be such that it produces n disturbances or vibrations per second, 
and let it be at such a distance from the earth that the light requires a time T to reach 
the earth. Let the distance of the source of light from the earth be altered, either by 
the motion of the source of light, or by that of the earth, so that the light which ema- 
nates from the source t seconds afterwards reaches the earth in a time T'. 
During the t seconds nt vibrations of the source of light took place, and these reached 
the earth between the time T and the time #-j-T', that is, during tffi-T' — T seconds. 
The number of vibrations which reached the earth per second was therefore no longer n, 
but n t+T ,_ T - 
If v is the velocity of separation of the source of light from the earth, and V the velo- 
city of light between the bodies relative to the earth, then ^=Y(T'— T), and the 
number of vibrations per second at the earth will be n *r— • 
L V +v 
If V 0 is the velocity of propagation of light in the luminiferous medium, and if v 0 is 
the velocity of the earth, v— v 
V — V 0 v 0 , 
and the wave-length will be increased by a fraction of itself equal to 
V 
v o-^o 
Since v 0 only introduces a correction which is small compared even with the alteration 
of wave-length, it cannot be determined by spectroscopic observations with our present 
instruments, and it need not be considered in the discussion of our observations. 
If, therefore, the light of the star is due to the combustion of sodium, or any other 
element which gives rise to vibrations of definite period, or if the light of the star is 
absorbed by sodium vapour, so as to be deficient in vibrations of a definite period, then 
the light, when it reaches the earth, will have an excess or defect of rays whose period 
of vibration is to that of the sodium period as Y-f-w is to Y. 
