Page:VaricakRel1912.djvu/5

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and the representative length U is by the way about 3mm greater than 100km. The velocity of 100000 km/sec corresponds to a length of 103700 km, which is quite a difference. We additionally consider two velocities of β-rays that were calculated in the famous experiments of Kaufmann, and to which the velocity relations 0,7202 and 0,9326 are connected. They amount ca. 216060 and 279780 km/sec and they were represented by the lengths of 272400 and 503400 km.

For v = c we have $\operatorname {th} \,u=1$ , thus U = ∞.

In graphical illustration these relations can be easily summarized. If we take u as abscissa and ${\tfrac {v}{c}}$ as ordinate, then (2) will be represented by curve K. The straight line P or the first term in the infinite row (3), corresponds to the ordinary definition $u={\tfrac {v}{c}}$ . The straight line is the inflexion tangent of K in O; so it fits well to the curve in the very far surrounding of the coordinate origin.

It seems convenient to introduce a name for length U. In my cited Serbian paper I have called it pseudo velocity. The easiest way would be, if we simply denote U and u as (physical) velocity and denote v as reduced velocity. As long as they are small, they practically cannot be distinguished. The pseudo velocity of light is infinitely great. By this definition it seems natural to us, that the velocity of light constitutes the upper limit for velocities.^[1]

2. Einstein's addition law of velocities.

Also in relativity theory the vector addition of velocities

↑ Norman Campbell, The Common Sense of Relativity, Phil. Mag., 1911, I, 508, says: "it is the fact that the second part of the Second Postulate proposes to represent the physically infinite velocity by a mathematically finite number which causes surprises. ... physical and mathematical infinity could by easily brought into agreement by a change of definition. This line of thought will be developed in a latter paper." Whether Campbell executed his plan, is not known to me. In Physik. Zeitschrift, XIII, 1912, 128, at the end of his respond to Wiechert, Campbell says, however, that such a ‚definition‘ would be very complicated.

[1] Norman Campbell, The Common Sense of Relativity, Phil. Mag., 1911, I, 508, says: "it is the fact that the second part of the Second Postulate proposes to represent the physically infinite velocity by a mathematically finite number which causes surprises. ... physical and mathematical infinity could by easily brought into agreement by a change of definition. This line of thought will be developed in a latter paper." Whether Campbell executed his plan, is not known to me. In Physik. Zeitschrift, XIII, 1912, 128, at the end of his respond to Wiechert, Campbell says, however, that such a ‚definition‘ would be very complicated.

[1]