Abstract
A ray of light is propagated in the XY plane and its angle with the X-axis is determined by two observers, S and S′, who are in relative motion to each other along the X-axis at a velocity q (expressed as a fraction of the velocity of light). If the angles measured by them are δ and δ′, then it is proved that , where Sin α=q. This relationship is interpreted geometrically by means of a cone in oblique coordinates. The axes of coordinates are X, Y, and time T. The T and X axes are different for the two observers, and the four axes T, X, T′, X′, form a Lorentzian Plane to which Y is perpendicular. The properties of the cone are considered in detail and a mechanical model of the cone, built of wood and iron, is described. At a desired velocity q, one can compare directly the angles δ and δ′. It is also shown that the relationship between the angles δ, δ′, and α can be represented on a pyramid. References are made to other articles by the same writer, in which oblique axes are also used for the solution of problems in the theory of relativity.
© 1924 Optical Society of America
Full Article | PDF ArticleMore Like This
Vladimir Karapetoff
J. Opt. Soc. Am. 13(2) 155-182 (1926)
Irwin G. Priest
J. Opt. Soc. Am. 8(1) 173-200 (1924)
Walter P. White
J. Opt. Soc. Am. 8(6) 767-782 (1924)