Abstract

No abstract available.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. W. Wood, Physical Optics (Macmillan, second edition, 1911), p 690.
  2. F. E. Hackett, Phil. Mag. 44, 740 (1922).
    [Crossref]
  3. A. S. Eddington, Mathematical Theory of Relativity (Cambridge University Press, 1923), p. 112.
  4. Both stationary and moving rotating disks are subject also to the dishing effect already discussed.

1922 (1)

F. E. Hackett, Phil. Mag. 44, 740 (1922).
[Crossref]

Eddington, A. S.

A. S. Eddington, Mathematical Theory of Relativity (Cambridge University Press, 1923), p. 112.

Hackett, F. E.

F. E. Hackett, Phil. Mag. 44, 740 (1922).
[Crossref]

Wood, R. W.

R. W. Wood, Physical Optics (Macmillan, second edition, 1911), p 690.

Phil. Mag. (1)

F. E. Hackett, Phil. Mag. 44, 740 (1922).
[Crossref]

Other (3)

A. S. Eddington, Mathematical Theory of Relativity (Cambridge University Press, 1923), p. 112.

Both stationary and moving rotating disks are subject also to the dishing effect already discussed.

R. W. Wood, Physical Optics (Macmillan, second edition, 1911), p 690.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Plan view of double Fizeau toothed wheel.

Fig. 2
Fig. 2

Fitzgerald contraction of rectangle.

Fig. 3
Fig. 3

Construction for determining Fitzgerald contraction of rectangle with base constrained to definite orientation.

Fig. 4
Fig. 4

“Dishing” of a rotating disk subject to Fitzgerald contraction.

Fig. 5
Fig. 5

Fitzgerald contraction of rotating disk moving in its own plane.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

B = B cos ( θ + δ ) cos θ
and             tan ( θ + δ ) tan θ = t t = 1 ( 1 - R 2 / c 2 ) 1 2 .
B = B ( 1 - R 2 / c 2 ) 1 2 cos θ ( 1 - ( R 2 / c 2 ) + tan 2 θ ) 1 2 .
H = H ( tan 2 θ + ( 1 - R 2 / c 2 ) 2 tan 2 θ + ( 1 - R 2 / c 2 ) ) 1 2 ,
H = H ( tan 2 θ + ( 1 - R 2 / c 2 ) 2 tan 2 θ + ( 1 - R 2 / c 2 ) ) 1 2 · tan 2 θ + ( 1 - R 2 / c 2 ) ( [ tan 2 θ + ( 1 - R 2 / c 2 ) ] 2 + R 4 / c 4 tan 2 θ ) 1 2 ,
T = H ( tan 2 θ + ( 1 - R 2 / c 2 ) 2 tan 2 θ + ( 1 - R 2 / c 2 ) ) 1 2 · ( R 2 / c 2 ) tan 2 θ ( [ tan 2 θ + ( 1 - R 2 / c 2 ) ] 2 + R 4 / c 4 tan 2 θ ) 1 2 .
B = B ( 1 - V 2 c 2 ( 1 - v 2 / c 2 ) ) 1 2 ,
H = H ( 1 - v 2 c 2 + V 2 v 2 c 4 ( 1 - v 2 / c 2 ) ) 1 2 ,
H = H ( 1 - v 2 / c 2 ) 1 2 ,
T = H V v c 2 ( 1 - v 2 / c 2 ) 1 2 .
V s / c = d / H ,
d = H r ω / c .
H + v t = c t ,
d = V m t - T ,
d = V H / ( c - v ) - T .
d = H V m c ( 1 - v 2 / c 2 ) 1 2 .
d = H V s / c = H r ω / c ,
d = d .
or             r ψ = r ψ ( 1 - r 2 ω 2 c 2 ) 1 2 [ ( 1 - r 2 ω 2 / c 2 ) 1 2 ( 1 - r 2 ω 2 / c 2 ) 1 2 ] r = r ( 1 - r 2 ω 2 / c 2 ) 1 2 ,
r = r ( 1 + r 2 ω 2 / c 2 ) 1 2 .
r = x ( 1 - x 2 α 2 ) 1 2 , d r = d x ( 1 - α 2 x 2 ) 3 2 , ( 1 + ( d y d x ) 2 ) 1 2 = d r d x = 1 ( 1 - α 2 x 2 ) 3 2 , ( d y d x ) 2 = 1 ( 1 - α 2 x 2 ) 3 - 1 , d y = α x ( 3 - 3 α 2 x 2 + α 4 x 4 ) 1 2 ( 1 - α 2 x 2 ) 3 2 d x ,
y = 3 2 - ( ( 3 + α x 2 ) ( 1 - α x ) ) 1 2 2 + 2 [ tan - 1 ( 1 - α x 2 3 + α x 2 ) 1 2 - tan - 1 1 3 ] .
d y / d x 3 α x , y 3 2 α x 2 = 3 r 2 ω c ,