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References

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  1. “Graphical Exposition of the Michelson-Morley Experiment,” J. Op. Soc. Am. 27, 177 (1937).
  2. See Born, Einstein’s Theory of Relativity, p. 109, except for the factor cos φ.
  3. “Light Signals on Moving Bodies as Measured by Transported Rods and Clocks,” J. Op. Soc. Am. 27, 263 (1937).
    [Crossref]
  4. The crucial character of such experiments for deciding between the several possibilities for explaining the Michelson-Morley experiment (entrained ether, ballistic character of light emission, contractions of matter in traversing the universal pattern of radiant energy) was pointed out by Einstein and by Ritz thirty years ago.

1937 (2)

“Graphical Exposition of the Michelson-Morley Experiment,” J. Op. Soc. Am. 27, 177 (1937).

“Light Signals on Moving Bodies as Measured by Transported Rods and Clocks,” J. Op. Soc. Am. 27, 263 (1937).
[Crossref]

Born,

See Born, Einstein’s Theory of Relativity, p. 109, except for the factor cos φ.

J. Op. Soc. Am. (2)

“Graphical Exposition of the Michelson-Morley Experiment,” J. Op. Soc. Am. 27, 177 (1937).

“Light Signals on Moving Bodies as Measured by Transported Rods and Clocks,” J. Op. Soc. Am. 27, 263 (1937).
[Crossref]

Other (2)

The crucial character of such experiments for deciding between the several possibilities for explaining the Michelson-Morley experiment (entrained ether, ballistic character of light emission, contractions of matter in traversing the universal pattern of radiant energy) was pointed out by Einstein and by Ritz thirty years ago.

See Born, Einstein’s Theory of Relativity, p. 109, except for the factor cos φ.

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Figures (4)

F. 1
F. 1

Representation of parallel moving source (s) and observer (o) for obtaining formula for Doppler effect.

F. 2
F. 2

Frequency of displaced canal-ray line as function of angle of observation and direction of rays, for the case of n = 1.

F. 3
F. 3

Wave-length of displaced canal-ray line as function of angle of observation and direction of rays, for the case of n = 1.

F. 4
F. 4

Frequency of displaced canal-ray line as function of angle of observation and direction of rays for the case of n = 0

Equations (18)

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[ ( 1 υ 2 / c 2 ) 1 2 ] n + 1 : 1
[ ( 1 υ 2 / c 2 ) 1 2 ] n : 1
[ ( 1 υ 2 / c 2 ) 1 2 ] 1 n : 1 .
ν = ν 1 ( υ 0 / c ) cos φ 1 ( υ s / c ) cos φ ,
ν s = ν 0 [ ( 1 υ s 2 / c 2 ) 1 2 ] 1 n ,
1 / [ ( 1 υ 0 2 / c 2 ) 1 2 ] 1 n ,
ν = ν 0 [ ( 1 υ s 2 / c 2 ) 1 2 ( 1 υ 0 2 / c 2 ) 1 2 ] 1 n 1 ( υ 0 / c ) cos φ 1 ( υ s / c ) cos φ .
ν = ν 0 1 ( υ 0 / c ) 1 ( υ s / c ) = ν 0 ( 1 υ 0 c ) ( 1 + υ s c + υ s 2 c 2 + ) = ν 0 [ 1 + ( υ s υ 0 ) c + υ s c ( υ s υ 0 ) c + ] .
υ s υ 0 = υ c υ s = υ c + υ 0 ,
ν = ν 0 [ 1 + υ c c + ( υ c + υ 0 ) c + υ c c + ] = ν 0 [ 1 + υ c c + ( υ c + υ 0 ) c · υ c c + ] = ν 0 [ 1 + υ c c + υ c 2 c + υ 0 υ c c 2 + ]
ν = ν 0 [ 1 υ c c + υ c 2 c + υ 0 υ c c 2 ] .
ν = ν 0 [ 1 ( υ 0 2 / c 2 ) 1 ( υ s υ 0 / c 2 ) ] = ν 0 [ 1 υ 0 2 c 2 + υ s υ 0 c 2 ] = ν 0 [ 1 + υ 0 c ( υ s υ 0 c ) ] = ν 0 [ 1 + υ 0 υ c c ] .
ν = ν 0 ( 1 ( υ s 2 / c 2 ) ) 1 2 ( 1 ( υ 0 2 / c 2 ) ) 1 2 · 1 ( υ 0 / c ) cos φ 1 ( υ s / c ) cos φ .
ν = ν 0 [ ( 1 υ s c ) ( 1 + υ s c ) ( 1 υ 0 c ) ( 1 υ 0 c ) ] 1 2 [ ( 1 υ 0 c ) ( 1 + υ 0 c ) ( 1 υ s c ) ( 1 υ s c ) ] 1 2 = ν 0 [ 1 + ( υ s υ 0 ) c ( 1 ( υ 0 υ s / c 2 ) ) ] 1 2 [ 1 + ( υ 0 υ s ) ( 1 ( υ 0 υ s ) / c 2 ) ) ] 1 2 = ν 0 1 + ( υ s υ 0 ) c ( 1 ( υ 0 υ s / c 2 ) ) [ 1 ( υ 0 υ 2 ) 2 c 2 ( 1 ( υ 0 υ s / c 2 ) ) 2 ] 1 2 .
υ s υ 0 ( 1 ( υ 0 υ s / c 2 ) ) .
ν = ν 0 1 + ( υ c / c ) [ 1 ( υ c 2 / c 2 ) ] 1 2 .
ν = ν 0 1 ( υ c / c ) [ 1 ( υ c 2 / c 2 ) ] 1 2 .
ν = ν 0 ( 1 ( υ s 2 / c 2 ) ) 1 2 ( 1 ( υ 0 2 / c 2 ) ) 1 2 · 1 ( υ 0 2 / c 2 ) 1 ( υ 0 υ s / c 2 ) = ν 0 ( 1 ( υ s υ 0 ) 2 c 2 ( 1 ( υ 0 υ s / c 2 ) 2 ) 1 2 = ν 0 ( 1 υ c 2 c 2 ) 1 2 .