## Abstract

A ray of light is propagated in the <i>XY</i> plane and its angle with the <i>X</i>-axis is determined by two observers, <i>S</i> and <i>S</i>′, who are in relative motion to each other along the <i>X</i>-axis at a velocity <i>q</i> (expressed as a fraction of the velocity of light). If the angles measured by them are δ and δ′, then it is proved that tan½δ/tan½δ′=cos(45°′½α)/cos(45°-½α), where Sin α=<i>q</i>. This relationship is interpreted geometrically by means of a cone in oblique coordinates. The axes of coordinates are <i>X, Y</i>, and time <i>T</i>. The <i>T</i> and <i>X</i> axes are different for the two observers, and the four axes <i>T, X, T</i>′, <i>X</i>′, 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 <i>q</i>, 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.

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