Page:The principle of relativity (1920).djvu/248

 maximum value of u, the velocity of light emitted being u_{0} = c + ku, k = 0 Lorentz-Einstein k = 1 Ritz. Prof. de Sitter admits the validity of the criticisms. But he remarks that an upper value of k may be calculated from the observations of the double sar β-Aurigae. For this star. The parallax π = ·014´´, e = ·005, u_{0} = 110 km/sec T = 3·96, Δ > 65 light-years, k is < ·002. For an experimental proof, see a paper by C. Majorana. Phil. Mag., Vol. 35, p. 163. [M. N. S.]  Note 10. Rest-density of Electricity.

If ρ is the volume density in a moving system then ρ[sqrt](1 - u^2) is the corresponding quantity in the corresponding volume in the fixed system, that is, in the system at rest, and hence it is termed the rest-density of electricity. [P. C. M.]  Note 11 (page 17). Space-time vectors of the first and the second kind.

As we had already occasion to mention, Sommerfeld has, in two papers on four dimensional geometry (vide, Annalen der Physik, Bd. 32, p. 749; and Bd. 33, p. 649), translated the ideas of Minkowski into the language of four dimensional geometry. Instead of Minkowski's space-time vector of the first kind, he uses the more expressive term 'four-vector,' thereby making it quite clear that it represents a directed quantity like a straight line, a force or a momentum, and has got 4 components, three in the direction of space-axes, and one in the direction of the time-axis.