241 



u 

 where a =: [^{(y, r' (/r. If a is neglected these are the terms of the 







first order in the development of (6 A) in powers of A = ^j IV, 



11. Consider again the equations (10), (11), (12). Tf these were 

 exact, they would be dependent on each other. The}' are, however, 

 not exact, and consequently they are contradictory. If we make 

 the combination : 



2 . im^ -I- 2 [m' - /'I . (12) - [m' + n'\ . (11) - m' . (10), 

 dr 



we find ') 



[)—na^Q. . . (18) 



Consequently the equations are dependent on each other, i.e. a 

 stationary equilibrium, all matter being at rest without internal forces, 

 is only possible, when either <5 = or n' = 0, i.e. g^^ = constant. 

 In the system A q is never zero, since outside the sun q = q,,. A 

 stationary equilibrium is then only possible if g^^ is constant, i.e. 

 if no "ordinary" matter exists, for all ordinary matter will, by the 

 mechanism of the equation (10) or (13) produce a term y in g^^ 

 which is not constant. If ordinary or gravitating matter does exist 

 then not only in those portions of space which are occupied by it, 

 but throughout the whole of the world-matter 7V. will differ from 

 T,jJ. We can e.g. consider the world-matter as an adiabatic incom- 

 pressible fluid. If this is supposed to be at rest, we have 



Tii = — gu p , T^^ r= t/^^ 9o, 

 where /; is the pressure in the world-matter. I then find 



1 



and, to the first order, and for the coordinates r, lf^ »>: 



/ cos 2 X 1 

 \K sm X J^ 



For our sun a/R is of the order of lO-^^. 



For X = è ^ ^ve have y = 0, and for x = ^ we should find 



1) It is easily verified that (18) becomes identical with (17) if all terms of 

 higher orders than the first are neglected. 



