534 
ME. W. HUGGINS ON THE SPECTEA 
the retardation which a ray experiences on account of having to traverse a dense medium 
instead of a vacuum. Let us calculate this retardation. 
Let there be a transparent medium whose thickness is a, and let it be supposed fixed. 
Let the luminiferous ether be supposed to move with velocity v in air, and with velocity 
v' within the medium. Let light be propagated through the ether with velocity V in air 
and with velocity V' within the medium. Then the absolute velocity of the light will 
be w-f-V in air and «/+V' within the medium, and the retardation, or difference of time 
in traversing a thickness a of the medium, and an equal thickness of air, will be 
a (v'+y' v+Y ) ; 
and the retardation in distance reckoned as at the velocity, Y will be 
[V v' /V 2 v\ v'*/Y 3 v*\ . "} 
a [V' — 1 “V ^V ,2 ~ v' ) + V2^V ,3 “?;' 2 ) ~ &C - J 
Y 
Now, according to every form of the theory, y,=^, the index of refraction, and 
according to Fresnel’s form of the theory, in which the density of the medium varies 
as yj 2 , the equation of continuity requires that ^=^ 2 . In this case the second term dis- 
appears and the retardation is terms in which may be neglected, as V is 
more than 10000 times v. 
Hence, on Fresnel’s theory, the retardation due to the prism is not sensibly affected 
by the motion of the earth. The same would be true on the hypothesis that the lumi- 
niferous ether near the earth’s surface moves along with the earth, whatever the form of 
the theory of the medium. 
Since the deviation of light by the prism depends entirely on the retardation of the 
rays within the glass, no effect of the earth’s motion on the refrangibility of light is to 
be expected. Professor Stokes (Phil. Mag. 1846, p. 63) has also given a direct proof of 
this statement, and the experiment of Arago confirms it to a certain degree of exactness. 
In order to test the equality of the index of refraction for light moving in opposite 
directions through a prism, I employed in 1864 the following arrangement. 
I made use of a spectroscope constructed by Mr. Becker, and provided with a tube at 
right angles to the axis of the observing-telescope, carrying a transparent plate of parallel 
glass placed between the object-glass and its focus, so as to reflect the light which enters 
the tube along the axis of the telescope towards the object-glass. In this tube is placed 
a screen with a vertical slit, in the middle of which is a vertical spider-line so arranged 
that its virtual image formed by the first surface of the glass plate coincides with the 
crossing of the spider-lines of the telescope at the principal focus of the object-glass. 
This coincidence is tested by observing the cross lines through the other telescope, with 
the two telescopes facing each other. The eyepiece of the second telescope is then 
removed, and a plane mirror is placed at the focus of the object-glass, perpendicular to 
the axis, and the telescopes are so adjusted that light entering by the side tube is 
