235 



by the world-matter. It is about Ybo ^^ ^1^® absorption which King ^) 

 used in liis calculation of the density of matter in interstellar space. 

 The density of the world-matter would thus be about ^j^^ of the 

 density found by King, or (>, z=f -lO-i^ in astronomical units. 

 The corresponding value of R (see art. 8) is /? = 2 • 10'". The total 

 absorption in the distance ^R would then be only 3.6 magnitudes. 

 To get the required absorption of 40 magnitudes we must increase 

 (»o, and consequently diminish R. We then find ^^ =: 2 • 10~ ^2, 

 R = 2 iO^ This value of course has practically no weight, as it 

 is very doubtful whether the considerations by which King derived 

 the density from the coefficient of absorption are applicable to the 

 world-matter. 



The whole argument is inapplicable to the system B, since in 

 this system the light requires an infinite time for the "voyage round 

 the world", One half of this time is 



T=JU, 







and, since v = c cos x, we find 7^=^ go. 



7. In the system A g^^ is constant, in B g^^ diminishes with 

 increasing r. Consequently in B the lines is the spectra of very 

 distant objects must appear displaced towards the red. This dis- 

 placement by the inertial field is superposed on the displacement 

 produced by the gravitational field of the stars themselves. It is 

 well known that the Helium-stars show a systematic displacement 

 corresponding to a radial velocity of -f 4.3 Km/sec. If we assume 

 that about 7, of this is due to the gravitational field of the stars 

 themselves'), then there remains for the displacement by the inertial 

 field about 3 Km/sec. We should thus have, at the average distance 

 of the Helium stars 



f =1 — 2. 10-5 = cos'-. 



-^ R 



If for this average distance we take r = 3 • 10^ (corresponding 

 to a parallax of 0"007 by the formula p = a/r), this gives R = f. 10'". 

 Also for the i¥-stars, whose average distance is probably the largest 

 after^hat of the Helium-stars, Campbell ') finds a systematic dis- 

 placement of the same order. The other stars, whose average dis- 



1) Nature, Vol. 95, p. 701 (Aug. 26, 1915). 



2) Gf. DE Sitter, On Einstein's theory/ of gravitation and its astronomical 

 consequences., Monthly notices. Vol. 76, p. 719. 



s) Lick Bulletin, Vol. 6, p. 127. 



16* 



