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  1. H. E. Ives and G. R. Stilwell, J. Opt. Soc. Am. 32, 25 (1942).
    [Crossref]
  2. “On the Dynamics of Radiation,” Int. Congress of Mathematics (Cambridge, 1912), p. 208, and references to earlier articles.
  3. J. H. Poynting, “Radiation in the Solar System,” Phil. Trans. A202, 525–552 (1940).
  4. A. H. Bucherer, Ann. d. Physik 11, 274–276 (1903).
  5. H. A. Lorentz, Proc. Amst. Akad. 4, 678 (1940).
  6. M. Abraham, Theorie der Electricität (Teubner, Leipzig, 1905), Vol. II, p. 384.
  7. Larmor, in an appendix to Poynting’s paper“On the momentum of radiation,” as reproduced in the latter’s Collected Works, points out (p. 433) that Poynting’s expression for the pressure of a wave-train against a traveling obstacle is in agreement with his own expression for the pressure on a moving mirror, sinceEi(1+υc)+Er(1−υc)=2Ei(c+υc−υ)=P.This does not however prove Poynting’s value correct since alsoEi(c+υc−υ)+Er(c−υc+υ)=2Ei(c+υc−υ),the value of Er= Ei(c+υ)2/(c− υ)2being used in both cases. Poynting’s expression calls for the incident and reflected radiations to contribute different pressures to the mirror, the expression (7) makes the contributions alike.
  8. The reduction of the distance r to r′=r(1−υ2/c2)12 by the Fitzgerald contraction is offset by the Larmor-Lorentz change of frequency and consequent reduction of amplitude, so that this relation holds equally for r and r′.
  9. In the similar electrodynamic case, for a Hertzian oscillator, as solved by the use of retarded potentials ( Bucherer, Ann. d. Physik 11, 276 (1903))the energy density isE=K¯a2n48πr2c3(1+υ/c)2.Taking into account the length and frequency contractions we put, n=ns(1−υ2/c2)12 and r=rs(1−υ2/c2)12, and getE=K¯a2ns4(1−υ/c)8πrs2c3(1+υ/c)=Es(1−υ/c1+υ/c),in agreement with our solution (12) derived from consideration of mechanical wave motion.

1942 (1)

1940 (2)

J. H. Poynting, “Radiation in the Solar System,” Phil. Trans. A202, 525–552 (1940).

H. A. Lorentz, Proc. Amst. Akad. 4, 678 (1940).

1903 (2)

In the similar electrodynamic case, for a Hertzian oscillator, as solved by the use of retarded potentials ( Bucherer, Ann. d. Physik 11, 276 (1903))the energy density isE=K¯a2n48πr2c3(1+υ/c)2.Taking into account the length and frequency contractions we put, n=ns(1−υ2/c2)12 and r=rs(1−υ2/c2)12, and getE=K¯a2ns4(1−υ/c)8πrs2c3(1+υ/c)=Es(1−υ/c1+υ/c),in agreement with our solution (12) derived from consideration of mechanical wave motion.

A. H. Bucherer, Ann. d. Physik 11, 274–276 (1903).

Abraham, M.

M. Abraham, Theorie der Electricität (Teubner, Leipzig, 1905), Vol. II, p. 384.

Bucherer,

In the similar electrodynamic case, for a Hertzian oscillator, as solved by the use of retarded potentials ( Bucherer, Ann. d. Physik 11, 276 (1903))the energy density isE=K¯a2n48πr2c3(1+υ/c)2.Taking into account the length and frequency contractions we put, n=ns(1−υ2/c2)12 and r=rs(1−υ2/c2)12, and getE=K¯a2ns4(1−υ/c)8πrs2c3(1+υ/c)=Es(1−υ/c1+υ/c),in agreement with our solution (12) derived from consideration of mechanical wave motion.

Bucherer, A. H.

A. H. Bucherer, Ann. d. Physik 11, 274–276 (1903).

Ives, H. E.

Lorentz, H. A.

H. A. Lorentz, Proc. Amst. Akad. 4, 678 (1940).

Poynting, J. H.

J. H. Poynting, “Radiation in the Solar System,” Phil. Trans. A202, 525–552 (1940).

Stilwell, G. R.

Ann. d. Physik (2)

A. H. Bucherer, Ann. d. Physik 11, 274–276 (1903).

In the similar electrodynamic case, for a Hertzian oscillator, as solved by the use of retarded potentials ( Bucherer, Ann. d. Physik 11, 276 (1903))the energy density isE=K¯a2n48πr2c3(1+υ/c)2.Taking into account the length and frequency contractions we put, n=ns(1−υ2/c2)12 and r=rs(1−υ2/c2)12, and getE=K¯a2ns4(1−υ/c)8πrs2c3(1+υ/c)=Es(1−υ/c1+υ/c),in agreement with our solution (12) derived from consideration of mechanical wave motion.

J. Opt. Soc. Am. (1)

Phil. Trans. (1)

J. H. Poynting, “Radiation in the Solar System,” Phil. Trans. A202, 525–552 (1940).

Proc. Amst. Akad. (1)

H. A. Lorentz, Proc. Amst. Akad. 4, 678 (1940).

Other (4)

M. Abraham, Theorie der Electricität (Teubner, Leipzig, 1905), Vol. II, p. 384.

Larmor, in an appendix to Poynting’s paper“On the momentum of radiation,” as reproduced in the latter’s Collected Works, points out (p. 433) that Poynting’s expression for the pressure of a wave-train against a traveling obstacle is in agreement with his own expression for the pressure on a moving mirror, sinceEi(1+υc)+Er(1−υc)=2Ei(c+υc−υ)=P.This does not however prove Poynting’s value correct since alsoEi(c+υc−υ)+Er(c−υc+υ)=2Ei(c+υc−υ),the value of Er= Ei(c+υ)2/(c− υ)2being used in both cases. Poynting’s expression calls for the incident and reflected radiations to contribute different pressures to the mirror, the expression (7) makes the contributions alike.

The reduction of the distance r to r′=r(1−υ2/c2)12 by the Fitzgerald contraction is offset by the Larmor-Lorentz change of frequency and consequent reduction of amplitude, so that this relation holds equally for r and r′.

“On the Dynamics of Radiation,” Int. Congress of Mathematics (Cambridge, 1912), p. 208, and references to earlier articles.

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Equations (26)

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E r = E i ( c + υ c υ ) 2 .
E r ( c υ ) E i ( c + υ ) = P υ .
E i ( c + υ ) 2 ( c υ ) 2 ( c υ ) E i ( c + υ ) = P υ
P = 2 E i ( c + υ ) / ( c υ ) .
m E i c Δ t
m E i c · Δ t · c = m E i c 2 Δ t .
m E i c 2 ( 1 + c + υ c υ ) Δ t
m E i c 2 ( 2 c c υ ) Δ t = P c Δ t c + υ = [ 2 E i ( c + υ c υ ) Δ t / ( c + υ ) ] ,
m = 1 / c 2 ,
E / c 2 .
E i c Δ t c 2 · c + ( E A t ) c 2 · υ = P t ,
E i ( c + υ ) + P υ = E A ,
E i c Δ t c 2 · c + ( E i ( c + υ ) + P υ c 2 ) ( υ c Δ t c + υ ) = P c Δ t c + υ ,
P = E i ( c + υ ) / ( c υ )
P s = E s ,
R s = E s c ,
R M = E M ( c + υ ) + P M υ ,
P M = E M ( c + υ ) / ( c υ ) .
E M = E s ( 1 + υ / c ) 2 .
E M = E s ( 1 υ 2 / c 2 ) ( 1 + υ / c ) 2 = E s ( c υ c + υ ) ,
P M = E S ( c + υ c υ ) ( c υ c + υ ) = E s = P s
R M = E s ( c υ ) + P s υ = E s ( c υ ) + E s υ = E s c = R 3 .
Ei(1+υc)+Er(1υc)=2Ei(c+υcυ)=P.
Ei(c+υcυ)+Er(cυc+υ)=2Ei(c+υcυ),
E=K¯a2n48πr2c3(1+υ/c)2.
E=K¯a2ns4(1υ/c)8πrs2c3(1+υ/c)=Es(1υ/c1+υ/c),