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 fixed to opposite walls of the room, sending the light round a large oblong instead of a square, and letting two sides of this oblong pass through the channel between the disks. (The arrangement of this experiment is shown in fig. 8.) Meanwhile, we dismantled the machine and sent the disks back to &  to be fitted with a third one for electrification. (26th Oct. 1893.)

If there were good reason to push the experiment still further (and for the present I see no such good reason), I should be disposed to attempt placing the disks in an air-tight chamber, kept exhausted by a mechanical oil pump, so as to do away with the greatest part of the troublesome air phenomena.

A possible reason for the concertina effect, and for the slight residual irreversible shift sometimes observed, suggests itself in the gradation of density in the air between the disks, due to centrifugal force. To estimate its magnitude under any circumstances, we may consider the equilibrium of an element $$dm$$ of air at radius $$r$$ and write :—

$r\omega^{2}dm=\frac{dp}{dr}dr\cdot rd\theta$

or

$pr\omega^{2}dr=dp=kd\rho,$

whence the density at any radius is

$\rho=\rho_{0}e^{-\frac{\omega^{2}}{2k}\left(a^{2}-\tau^{2}\right)}.$|undefined

Hence, for disks a yard in diameter making 3000 revolutions a minute, the density at centre is about $8⁄9$ths of that at circumference; and the change of density per centimetre breadth of beam, at a radius of 1 foot, is

$\frac{dp}{dr}=.425\times10^{-5}$

which, if $$\mu-1$$ be taken as proportional to $$\rho$$, gives $$d\mu$$ about equal to .23$$d\rho$$; or say 10-6 as the difference of refractive index, on either side of a beam of light 1 centimetre broad, in the region of the mean light path. This is equivalent to the effect of a difference of temperature, in the air on either side of the beam, of a $1⁄5$th of a degree centigrade.

The gradation of density could therefore cause a distinct effect if the beam of light had an odd number of paths between the disks; but since there are in our case an odd number of reflexions, and therefore an even number of paths, with the beam laterally inverted at each reflexion, the effects must very nearly compensate each other.

If by reason of some want of symmetry there was on the whole a centimetre length of path uncompensated by a laterally inverted portion elsewhere, the corresponding retardation due to gradation of density would be a millionth of a centimetre, causing an irreversible shift of $1⁄50$th of a band. This cause may therefore account for part