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  1. For the following energy, pressure, and mass relations see H. E. Ives, J. Opt. Soc. Am. 32, 32 (1942).
  2. The formula for any interval between two velocities ν1 and ν2, derived by the same reasoning as above is ƒ(ν1, ν2) = [c2(g2-g1)]/(ν2g21g1). If we put ƒ(ν1ν2) =ν1+[(ν21)/2], and put ν12/2, we have for g1, in term of ν2, g1=1/[1-(ν22/8C2)]. Putting this in the above expression and solving for g2, we get g2=1/[1-½(ν22/c2)-3/32(ν24/c4)]. Repeating this process for successive equal increments we get values for the coefficient of ν4/c4, of 1/9, 15/128, 3/25, etc., which asymptotically approach the value ⅛; and values for the coefficient of ν6/c6 which similarly approach 1/16
  3. See F. K. Richtmyer, Introduction to Modern Physics (McGraw-Hill, New York, 1934), second edition, D. 723.
  4. If we assume, contrary to our result, the M is invariant with velocity we would have for the conservation of momentum [Equation] where m′ is a new (variable) coefficient of mass equivalence of radiation. The conservation of mass would then be expressed by [Equation] giving [Equation] so that [Equation] The kinetic energy of the particle corresponding to momentum Mν is ½Mν2, giving [Equation] which obviously is not equal to [Equation]; so that conservation of energy and momentum would not hold, in the impact process here studied, for an invariant M.
  5. A. S. Eddington, Mathematical Theory of Relativity (Cambridge University Press, London, 1937), second edition, p. 31.
  6. F . K. Richtmyer, reference 3, p. 719.
  7. Of interest in this general connection is an article by P. S. Epstein [Am. J. Phys. 10, 1 (1942)] in which it is pointed out that, given the variation of mass with velocity here deduced, the variation of clock rate may be derived. It thus appears probable that all the behaviors characteristic of the restricted theory of relativity may be obtained from earlier principles.

Eddington, A. S.

A. S. Eddington, Mathematical Theory of Relativity (Cambridge University Press, London, 1937), second edition, p. 31.

Ives, H. E.

For the following energy, pressure, and mass relations see H. E. Ives, J. Opt. Soc. Am. 32, 32 (1942).

Richtmyer, F . K.

F . K. Richtmyer, reference 3, p. 719.

Richtmyer, F. K.

See F. K. Richtmyer, Introduction to Modern Physics (McGraw-Hill, New York, 1934), second edition, D. 723.

Other

For the following energy, pressure, and mass relations see H. E. Ives, J. Opt. Soc. Am. 32, 32 (1942).

The formula for any interval between two velocities ν1 and ν2, derived by the same reasoning as above is ƒ(ν1, ν2) = [c2(g2-g1)]/(ν2g21g1). If we put ƒ(ν1ν2) =ν1+[(ν21)/2], and put ν12/2, we have for g1, in term of ν2, g1=1/[1-(ν22/8C2)]. Putting this in the above expression and solving for g2, we get g2=1/[1-½(ν22/c2)-3/32(ν24/c4)]. Repeating this process for successive equal increments we get values for the coefficient of ν4/c4, of 1/9, 15/128, 3/25, etc., which asymptotically approach the value ⅛; and values for the coefficient of ν6/c6 which similarly approach 1/16

See F. K. Richtmyer, Introduction to Modern Physics (McGraw-Hill, New York, 1934), second edition, D. 723.

If we assume, contrary to our result, the M is invariant with velocity we would have for the conservation of momentum [Equation] where m′ is a new (variable) coefficient of mass equivalence of radiation. The conservation of mass would then be expressed by [Equation] giving [Equation] so that [Equation] The kinetic energy of the particle corresponding to momentum Mν is ½Mν2, giving [Equation] which obviously is not equal to [Equation]; so that conservation of energy and momentum would not hold, in the impact process here studied, for an invariant M.

A. S. Eddington, Mathematical Theory of Relativity (Cambridge University Press, London, 1937), second edition, p. 31.

F . K. Richtmyer, reference 3, p. 719.

Of interest in this general connection is an article by P. S. Epstein [Am. J. Phys. 10, 1 (1942)] in which it is pointed out that, given the variation of mass with velocity here deduced, the variation of clock rate may be derived. It thus appears probable that all the behaviors characteristic of the restricted theory of relativity may be obtained from earlier principles.

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