236 



tances are smaller, also have a much smaller systematic displacement 

 towards the red, which can very well be explained by the gravita- 

 tional Meld of the stars themselves. 



Lately some radial velocities of nebulae ') have been observed, 

 which are very large ; of the order of 1000 Km/sec. If we take 

 600 Km/sec, and explain this as a displacement towards the red 

 produced by the inertial field, we should, with the above value 

 of R, find for the distance of these nebulae r = 4 • 10' = 2000 

 parsecs. It is probable that the real distance is much larger. ^) 



About a systematic displacement towards the red of the spectral 

 lines of nebulae we can, however, as yet say nothing with certainty. 

 If in the future it should be proved that very distant objects have 

 systematically positive apparent radial velocities, this would be an 

 indication that the system B, and not A, would correspond to the 

 truth. If such a systematic displacement of spectral Imes should be 

 shown not to exist, this might be interpreted either as pointing to 

 the system A in preference to B, or as indicating a still larger 

 value of R in the system B. 



8. In the paper which has already repeatedly been quoted, 

 ScHWARZscHiLD determined the value of R for elliptical space by the 

 condition that space should be large enough to contain the whole 

 of our galactic system, the star-density being taken constant and 

 equal to the value near the sun. This reasoning cannot be applied 

 to the system Ax, since the field-equations give a relation between 

 M and q, which contradicts Schwakzschild's condition. 



We have 



2 



The volume of the elliptical space is n^ /?'. The total mass is 

 therefore n^ R^ q^, or 



1) NG.C. 4594 ^ Pease +1180 km/sec. 



i Slipher +1190 

 N.G.G. 1068 (Slipher +1100 

 Pkase + 765 

 Moore + 910 



The nebula in Andromeda however appears to have a considerable negative 

 velocity, viz. : 



/ Wright — 304 km/sec. 

 < Pease — 329 

 ( Slipher — 300 „ 



2) Eddington (Monthly Notices, Vol. 77, p. 375) estimates r> 100000 parsecs. 

 This, combined with an apparent velocity of +600 km/sec, would give i? > 3.10". 



