30 
NATURE 
[May 13, 1886 
As not a trace of Delambre’s investigation remains in 
print, and probably not in manuscript, it is impossible to 
subject it to any discussion.! 
The discovery of aberration by Bradley afforded an 
independent and yet more accurate method of determining 
the hght equation. We call to mind that the latter con- 
stant, and that of aberration, are not to be regarded as 
independent of each other, but only as two entirely 
distinct expressions of the same result. The constant of 
aberration gives a relation between the velocity of light 
and the velocity of the earth in its orbit from which, by a 
very simple calculation, the time required for light to pass 
from the sun to the earth may be deduced. 
It is remarkable that the early determinations of the 
constant of aberration agreed with Delambre’s determi- 
nation of the light equation, although we now know they 
were both in error by an amount far exceeding what was 
at the time, supposed p:obable. Struve’s value, 20"'445, 
determined in 1845 from observations with the prime 
vertical transit of Pulkowa, has been the standard up to 
the present time. The recent determinations by Nyrén 
being founded on a much longer series of observations 
than those made by Struve, and including determinations 
with several instruments, must be regarded as a standard 
at present. His result is :—? 
Definitive > value of the constant of aberration = 
“006, 
At the time Struve’s result was published there was 
an apparent difference of 1 per cent. between its value 
and that of the light equation determined by Delambre. 
The question then naturally arose whether the light 
equation, deduced on the hypothesis that the tangent of 
the angle of the constant of aberration was the ratio of 
the velocity of the earth in its orbit to the velocity of 
light, might not need correction or modification. This 
question cannot yet be considered as definitely settled, 
since the modifications or corrections might arise from a 
variety of causes. One of these causes is connected with 
a very delicate question in the theory of the luminiferous 
medium; a question which can be most clearly under- 
stood when placed in the following form :—It is a result 
of optical principles that a ray falling perpendicularly 
upon the bounding surface of a refracting medium retains 
its direction unaltered. Now, if this surface is carried 
along by the motion of the earth, and the light comes 
from a star, and it is desired that this surface shall be 
so directed that there shall be no refraction, must it be 
placed perpendicular to the /vwe direction of the star as 
freed from aberration, or to its afparent direction as 
affected by aberration? ‘The difference of the two direc- 
tions may exceed 20”, and since the index of refraction of 
glass exceeds 1°5, there will be a difference of more than 
10” in the direction of the refracted ray, according as we 
adopt one or the other hypothesis. Assuming that the 
standard direction would be perpendicular to the true or 
absolute direction of the star, it is easily shown that the 
constant of aberration determined in the usual way would 
be too large by a quantity depending on the ratio of the 
thickness of the objective to the focal length of the tele- 
scope. In an ordinary telescope the difference would be 
nearly one-hundredth of the total value of the aberration, 
and would, therefore, closely correspond to the discre- 
pancy between Delambre’s result from the satellites of 
Jupiter and the modern determinations of the constant 
of aberration. The question of this particular cause was 
set at rest by Airy’s experiments with a telescope filled 
with water, which showed that the result was independent 
of the thickness of the objective, and, therefore, that the 
apparent direction of the star was that on which refraction 
depended. 
If, in accordance with the undulatory theory of light, 
* The author could find no remains of this investigation among Delambre’s 
papers at the Paris Obser\atory. 
* Mémoires del Académie Impériale des Sciences de St. Pétersbour, “gy Vil. 
série, tome xxxi. No. 9. 
20'°492 
EO 
| used to determine the second. 
we suppose the hypothetical entity called “the lumi- 
niferous medium” to be a substance, each part of which 
has its own definite and fixed location in space, then we 
must conceive that another unknown quantity may enter 
into the problem, namely, the motion of the heavenly 
bodies through this medium. We have relative motions 
in the solar system, exceeding 50 kilometres per second, 
and possibly greater relative motions among the stars. 
Now it is clear that the heavenly bodies cannot all be at 
rest relative to the medium, but must move through it 
with velocities at least of the order of 50 kilometres per 
second, and possibly greater without limit, since it is con- 
ceivable that the whole visible universe might be moving 
in a common direction relative to the medium. 
It is easily seen that if we suppose the velocity of the 
earth, through the medium, to have a small ratio, a, to the 
velocity of light, then the observed constant of aberra- 
tion may be altered by an amount found by multiplying 
its value by a quantity of the order of magnitude of a. 
This alteration would be entirely insensible if the earth 
does not move through the medium with any greater 
velocity than it does around the sun, since the value would 
then be only yodo9- It is remarkable that so far as yet 
investigated every optical effect arising from such a motion, 
which could be measured on the surface of the earth, is 
of the order of magnitude of the square of a. Thus, no 
phenomenon has yet been discovered which can be traced 
to the motion in question. 
Assuming that there is no general motion of the solar 
system through the ether of a higher order of magnitude 
than that of the relative motions of the fixed stars to each 
other, and that the ordinary theory of aberration is correct, 
there will be three constants between which a relation 
exists, such that when any two are found the third can be 
determined. These constants are :— 
The distance of the sun in_ terrestrial 
measure ; 
2. The velocity of light in units of the same measure ; 
and 
3. The constant of aberration, or, which is supposed to 
be equivalent, the light equation. 
Until our own time the first and third constants were 
From the fact that light 
required about 500 seconds to traverse the distance from 
the sun to the earth, and that the distance of the sun was, 
as supposed, 95,000,000 of miles, it was concluded that 
light moved 190,000 miles per second. The hopelessness 
of measuring such a velocity by any means at the com- 
mand of physicists was such that we find no serious 
attempt in this direction between the date of the futile 
effort of the Florentine Academy, and that of the 
researches of Wheatstone, Arago, Fizeau, and Foucault 
nearly two centuries later. One of the most curious 
features presented by the history of the subject is that 
two entirely distinct methods, resting on different princi- 
ples, were investigated and put into operation almost 
simultaneously. The revolving mirror of Wheatstone, 
and its application to determine the duration of the 
electric spark and the velocity of electricity, come first in 
the order of time. But, before this ingenious instrument 
had been applied to the actual measurement of the velocity 
of light, Fizeau had invented his toothed wheel, by which 
the same object was attained 
Fizeau’s paper on the subject was presented to the 
Academy of Sciences on July 23, 1849.1 We have already | 
shown that his method and that of Galileo rest funda- 
mentally upon the same principle. _The arrangement of 
his apparatus was substantially as follows :— 
A telescope was fixed upon a house at Surésne pointing 
to the hill Montmartre. On this hill was a second fixed 
telescope looking directly into the first, the distance 
between them being about 8633 metres. In the focus of 
this second telescope was fixed a smal] reflector, so that 
* Comptes rendus, Vol. Xxix. 1849, Pp. 90- 
units of 
