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It is well known that among the possible motions of a relativistically rigid body (as defined by Born and Herglotz) there is uniform rotation, such as is familiar to us from the kinematics of ordinary classical rigid bodies.

If the endpoints (any two points) of a light path be in such a plane, the whole light path is contained in that plane.

For whom the rotation of S is clockwise.

G. Sagnac, "L'ether lumineux démontré par l'effet du vent relatif d'ether dans un intérferomètre en rotation uniforme." C. R. Paris, 157 (1913), p. 708. Ibidem, p. 1410, "Sur la preuve de la réalité de l'ether lumineux par l'experience de l'interférographe tournant." The titles seemed interesting enough to be quoted in full. But Sagnac's experiments (even apart from the question of the reliability of his measurements) by no means decide for the aether as against relativity.

Such a terrestrial experiment was already hinted at by Oliver Lodge, in 1897, Phil. Trans. Roy. Soc. A, vol. 189, p. 151, where also the experiment carried out by Sagnac twentyfive years later is suggested, only with "telescope and observer" instead of a photo camera mounted on a rotating "turntable."

As we already know, the same light path cannot be described in the opposite sense.

Prof. Michelson's paper of 1904, (l.c.) has by a manifest slip the factor 2 instead of our 4.

In Sagnac's case k=1, since such small masses as was his table certainly do not drag the aether, as follows from the widely known older experiments of Sir Oliver Lodge.

Of any point of S relatively to S* say.

M. v. Laue, Relativitätstheorie, vol. 1, 3rd ed. Braunschweig, 1919, p. 125–127. Laue seems, by the way, to be under the misapprehension that the light rays relative to the rotating table are straight lines, which they are not. As we saw before, their departure from straight lines is a first order effect and does, therefore, by no means disappear though "the Lorentz contraction" be neglected. The influence of the curvature of the rays on (12) or (12r) remains, of course, negligible.

H. Thirring, Ueber die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Phys. Zeitschrift, Vol. 19, 1918, p. 33–39.

Not only that Thirring's "centrifugal force" had also a component along the axis of rotation, but the coefficients of the centrifugal and the Coriolis force, apart from being very unsatisfactory in their structure, bore a wrong numerical ratio to one another.

H. Weyl, ZeitRaumMaterie, 3rd ed., Berlin, J. Springer, 1920.

The only effect of terrestrial gravitation on the opticalcircuit experiment would according to relativistic gravitation theory, be represented by the term [Equation] to be subtracted from the factor 2 of the second term in (16), φ being the geographic latitude, M the mass and R the radius of the Earth. But since M/c^{2}= 0.45 cm., the correction term due to gravitation amounts, even at the equator, only to 1.2×10^{9} which is entirely negligible in presence of 2.

E. v. Oppolzer, Erdbewegung and Aether, Sitzber. Akad. Wien, vol. CXI, IIa, Febr. 1902, pp. 244–254.

H. A. Lorentz, Abhandlungen, Vol. I.
Laue, M. v.
M. v. Laue, Relativitätstheorie, vol. 1, 3rd ed. Braunschweig, 1919, p. 125–127. Laue seems, by the way, to be under the misapprehension that the light rays relative to the rotating table are straight lines, which they are not. As we saw before, their departure from straight lines is a first order effect and does, therefore, by no means disappear though "the Lorentz contraction" be neglected. The influence of the curvature of the rays on (12) or (12r) remains, of course, negligible.
Lorentz, H. A.
H. A. Lorentz, Abhandlungen, Vol. I.
Oppolzer, E. v.
E. v. Oppolzer, Erdbewegung and Aether, Sitzber. Akad. Wien, vol. CXI, IIa, Febr. 1902, pp. 244–254.
Sagnac, G.
G. Sagnac, "L'ether lumineux démontré par l'effet du vent relatif d'ether dans un intérferomètre en rotation uniforme." C. R. Paris, 157 (1913), p. 708. Ibidem, p. 1410, "Sur la preuve de la réalité de l'ether lumineux par l'experience de l'interférographe tournant." The titles seemed interesting enough to be quoted in full. But Sagnac's experiments (even apart from the question of the reliability of his measurements) by no means decide for the aether as against relativity.
Thirring, H.
H. Thirring, Ueber die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Phys. Zeitschrift, Vol. 19, 1918, p. 33–39.
Weyl, H.
H. Weyl, ZeitRaumMaterie, 3rd ed., Berlin, J. Springer, 1920.
Other (16)
It is well known that among the possible motions of a relativistically rigid body (as defined by Born and Herglotz) there is uniform rotation, such as is familiar to us from the kinematics of ordinary classical rigid bodies.
If the endpoints (any two points) of a light path be in such a plane, the whole light path is contained in that plane.
For whom the rotation of S is clockwise.
G. Sagnac, "L'ether lumineux démontré par l'effet du vent relatif d'ether dans un intérferomètre en rotation uniforme." C. R. Paris, 157 (1913), p. 708. Ibidem, p. 1410, "Sur la preuve de la réalité de l'ether lumineux par l'experience de l'interférographe tournant." The titles seemed interesting enough to be quoted in full. But Sagnac's experiments (even apart from the question of the reliability of his measurements) by no means decide for the aether as against relativity.
Such a terrestrial experiment was already hinted at by Oliver Lodge, in 1897, Phil. Trans. Roy. Soc. A, vol. 189, p. 151, where also the experiment carried out by Sagnac twentyfive years later is suggested, only with "telescope and observer" instead of a photo camera mounted on a rotating "turntable."
As we already know, the same light path cannot be described in the opposite sense.
Prof. Michelson's paper of 1904, (l.c.) has by a manifest slip the factor 2 instead of our 4.
In Sagnac's case k=1, since such small masses as was his table certainly do not drag the aether, as follows from the widely known older experiments of Sir Oliver Lodge.
Of any point of S relatively to S* say.
M. v. Laue, Relativitätstheorie, vol. 1, 3rd ed. Braunschweig, 1919, p. 125–127. Laue seems, by the way, to be under the misapprehension that the light rays relative to the rotating table are straight lines, which they are not. As we saw before, their departure from straight lines is a first order effect and does, therefore, by no means disappear though "the Lorentz contraction" be neglected. The influence of the curvature of the rays on (12) or (12r) remains, of course, negligible.
H. Thirring, Ueber die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Phys. Zeitschrift, Vol. 19, 1918, p. 33–39.
Not only that Thirring's "centrifugal force" had also a component along the axis of rotation, but the coefficients of the centrifugal and the Coriolis force, apart from being very unsatisfactory in their structure, bore a wrong numerical ratio to one another.
H. Weyl, ZeitRaumMaterie, 3rd ed., Berlin, J. Springer, 1920.
The only effect of terrestrial gravitation on the opticalcircuit experiment would according to relativistic gravitation theory, be represented by the term [Equation] to be subtracted from the factor 2 of the second term in (16), φ being the geographic latitude, M the mass and R the radius of the Earth. But since M/c^{2}= 0.45 cm., the correction term due to gravitation amounts, even at the equator, only to 1.2×10^{9} which is entirely negligible in presence of 2.
E. v. Oppolzer, Erdbewegung and Aether, Sitzber. Akad. Wien, vol. CXI, IIa, Febr. 1902, pp. 244–254.
H. A. Lorentz, Abhandlungen, Vol. I.
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