239 



If however the mass of the sun is not neglected, then a stationary 

 state of equilibrium, with all matter at rest, cannot exist without 

 internal forces within this matter. The 7',, are then different from 

 T,J. If the world-matter is considered as a continuous "fluid", then 

 this fluid can only be at rest if there is in it a pressure or stress. 

 If it is considered as consisting of separated material points then 

 these cannot be at rest. The difference 7',v — T.J vanishes with q, 

 for if ()=0, both 7),,, and T,J are zero. This difference, therefore, is 

 of the form b.q, e being of the order of the gi-avitation produced by 

 the sun. The right-hand-members of the equations (1), and thei-efore 

 also of (lO), (11), (J 2) require corrections of the order x.^.q. If 

 these are neglected, the equations are no longer exact. 



10. The mass of the sun being small, the values of a, b,f will 

 not differ much from those of the inei'tial tield. We can then, in 

 the system A, and for the coordinates r, tf', {>, put 



and in a first approximation we can neglect the squares and products 

 of «; ii, y. The equations then became: 



y +^y co«/=:ax^p ....... (13) 



cot y , , 2« 



^"+ -^(2^'-«'-r') + ^==-a;c9, - . . (U) 



cot y 

 /? cosec-^ X - « '-ot' X + (/i' -f y') —^ = 0. . . (15) 



From (13) we find, lemembering that the accents denote differen- 

 tiations with respect to /' = /^ . / : 



( = j a xo^ sin* 



y' sm* / = I « >«o^ sin* / dr 







Outside the sun we have pi^O. Thus if we put 



R 



a = A'^ I ay.Q^ sin^ x f^'' 







then outside the sun 



from which 



E' sin* X 



.r= — ^co<7 -— y ...,,• (16) 



