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May 13, 1886] 
NATURE 
31 
a beam of light from the first would be reflected directly 
back to it. By means of a transparent glass, fixed in the 
eye-piece at an angle of 45°,a beam of light was sent 
from the first telescope to the second, and, on its return 
through a total distance of 17 kilometres, could be 
seen as a star by an eye looking through the fist. 
Alongside the eye-piece of the latter a revolving wheel, 
with 720 teeth cut upon its circumference, was fixed in 
such a way that the beam of light both in going and 
coming had to pass between the teeth. When the wheel 
was set so that the tooth was in the focus, the beam would 
be entirely cut off in its passage through the telescope. 
Changing the position of the wheel through half the 
space between the middles of two consecutive teeth, the 
light would go and come freely between the teeth. When 
the wheel was set in revolution a succession of flashes 
would be sent out. If, on the return of each flash, a tooth 
was interposed, it would be ‘invisible to the eye looking 
through the telescope. Fizeau found that with a velocity of 
12°6 turns per second each flash which went out was on its 
return cut off by the advancing tooth. With a velocity 
twice as great as this it was seen on its return through 
the opening next following that through which it went. 
With three times this velocity it was caught on the second 
tooth following, and so on.! 
This experiment of Fizeau was soon followed by the 
application of the revolving mirror of Sir Charles Wheat- 
stone. Shortly after measuring the duration of the 
electric spark this investigator called attention to the 
fact that the same system could be applied to determine 
the velocity of light, and especially to compare the velocities 
through air and through water. In 1838 the subject was 
taken up by Arago, who took pains to demonstrate that 
it was possible, by the use of the revolving mirror, to 
decide between the theory of emission and that of undula- 
tions by determining the relative velocities inair and in a 
refracting medium.” 
The difficulties in the way of securing the necessary 
velocities of the mirror and of arranging the apparatus 
were such that Arago never personally succeeded in 
carrying out his experiments. This seems to have been 
done almost simultaneously by Foucault and Fizeau 
about the beginning of 1850. Both experimenters seem 
to have proceeded substantially on the same principle and 
to have reached the same result, namely, that the motion 
of light through water was slower than through air in the 
inverse proportion of the indices of refraction of the two 
media.* 
An important and most necessary modification of 
Arago’s plan was made by these experimenters. As 
originally proposed, the plan was to send an instan- 
taneous flash of light through water and through the air, 
and to receive it on the revolving mirror and determine 
the relative deviations in the positions of the images 
produced by the two rays. This system would, however, 
be inapplicable to the measurement of the actual time of 
transmission, owing to the impossibility of making any 
comparison between the time at which the flash was 
transmitted, and that at which it was received on the 
mirror. This circumstance would, indeed, have rendered 
the actual realisation of Arago’s project nearly impossible 
for the reason that the flashes of light, seen through the 
water, would have reached the mirror at every point of 
its revolution ; and only an exceedingly small fraction of 
them could have been reflected to the eye of the observer. 
This difficulty was speedily overcome by Foucault and 
2 It is curious that the author's account of this remarkable experiment, 
which forms an epoch in the history of physical sc.ence, is contained within 
_ the limits of two pages, and terminates without any definite discussion of the 
results. It is merely stated that the result is 70,948 leagues of 25 to the 
degree, but the velocity, in kilometres, which must have been that first 
obtained, is not given, nor is it stated what length the degree was supposed 
to have in the computation. 
* Comptes rendus, 1838, vol. vii. p. 954; Geuvres de Frangois Arago, 
vol. vii. p. 569. 
3 Comptes rendus, xxx. 1850, pp. 551 and 771. 
Fizeau by a most ingenious arrangement, of equal import- 
ance with the revolving mirror itself. Instead of sending 
independent flashes of light to be reflected from the 
mirror, a continuous beam was first reflected from the 
revolving mirror itself to a fixed mirror, and returned 
from the fixed mirror back on its own path to the revolving 
one. A succession of flashes was thus emitted as it were 
from the fixed mirror, but their correspondence with a 
definite position of the revolving mirror was rendered 
perfect. Moreover, by this means, the image was rendered 
optically continuous, since a flash was sent through and 
back with every revolution of the mirror, and after the 
velocity of the latter exceeded 30 turns per second, the 
successive flashes presented themselves to the eye asa 
perfectly continuous image. 
It was not until 1862 that this system was put into 
operation by Foucault for the actual measurement of the 
velocity of light through the atmosphere. A new interest 
had in the meantime been added to the problem by the 
discovery that the long-accepted value of the solar parallax 
was too small, and that the measurement of the velocity 
of light afforded a method of fixing the value of that 
constant. The central idea of the method adopted by 
Foucault was that already applied in comparing velocities 
through different media. The element sought is made to 
depend upon the amount by which the revolving mirror 
rotates while a flash of light is passing from its surface to 
the distant reflector, and coming back again. As the 
details of Foucault’s method will be best apprehended by 
a comparison of them with those adopted in the present 
investigation, a complete description of his apparatus will 
here be passed over. It may, however, be remarked, that 
what he sought to observe was not the simple deviation 
of a slit, but the deviation of the image of a reticule. The 
deviation actually measured was 0°7 millimetre, and the 
system adopted was to determine at what distance, witha 
definite velocity, this amount of deviation could be 
obtained. His result for the velocity of light was 298,000 
kilometres per second. 
The next measures of the element in question were 
those of Cornu. The method which he adopted was not 
that of the revolving mirror, but Fizeau’s invention of the 
toothed wheel. His earlier measures, made in 1870, and 
communicated to the French Academy in 1871, led to a 
result nearly the same as that of Foucault! This result 
was, however, not so satisfactory that the author could 
record it as definitive. He, therefore, in 1874, repeated 
the determination on a much larger scale and with 
more perfect apparatus. The distance between the two 
stations was nearly 23 kilometres, and therefore much 
greater than any before employed. He was thus enabled 
to follow the successive appearances and extinctions of 
the reflected image to the thirtieth order; that is, to 
make fifteen teeth of his wheel pass before a flash returned 
from the distant reflector, and to have it stopped by the 
sixteenth tooth. 
This method has a defect, the result of which is evident 
by an examination of Cornu’s numbers. It is that the 
extinctions and reappearances of the light as the wheel 
changes its speed are not sudden phenomena, occurring 
at definite moments, but are so gradual that it is difficult 
to fix the precise moment at which they occur. Of this 
defect the able experimenter was fully conscious, and his 
discussion of the disturbing causes which come into play, 
and of the amount of error due both to the apparatus, 
the observer, and to the method of eliminating them, 
form altogether one of the most exhaustive discussions of 
a physical problem.? But the uncertainties are not of 
a kind which admit of complete investigation, and it now 
appears that although his result was far superior in point 
of accuracy to that of Foucault, it was nevertheless in 
error by about ooo15 of its whole amount. It was, in 
i Comptes rendus, vol. \xxiii. 1871, p. 857. Fos 
2 Annales de |’Observatoire de Paris, Mémoires, tome xiul. 
