1 
Bee a hy) Os Bet A ree OD 
Exactly the same equations are found from the generalised principle 
of HAMILTON, as enounced by Lorentz’). The equations as here given 
are only exact to the required order of accuracy. In a recent com- 
munication *) Mr. Droste has derived the complete equations from 
the same principle, and by an elegant analysis has succeeded in 
rigorously integrating them. In the present paper no rigorous solution 
will be attempted, but only an approximation to the order which is 
required for practical applications. 
It is easily found that 
1 d ee 5 / Sahl i 
Ei riet 3. (9), 
Consequently the equations (4) and (5) are not independent of 
each other. To determine «, 8, y completely we must, as has already 
been pointed out above, add an arbitrary condition. 
EINSTEIN *) advises ~— g—1, which, to the required order of 
accuracy, is equivalent to 
Bikathy=0 
This equation, together with (3) and (5) determines a, B and y. 
EinsreiN finds 
yee A ae ieee I) c= —y. 
" 
Droste in the paper already quoted introduces a condition, which 
is equivalent to B= 0. He finds | 
Br B= ] sige sera BE 
This result is entirely rigorous, while EINsTEIN’s was only approxi- 
mate. Within the limits of the approximation given by Einstein the 
two are identical. Both Eisrrin and Drostr consider only the field 
outside the sun. 
I will take as arbitrary condition 
1) These Proceedings, Feb. 1916 (Not yet translated into English). 
*) These Proceedings, Vol. XIX, page 197 (May 1916). 
3) Erkldrung der Perikelbewegung des Merkur aus der allgemeinen kelatiri- 
tdtstheorie, Sitzungsber. Berlin, Nov. 1915, page 833. It would be better to say 
that Einstein's condition is that '—g shall be independent of gravitation, For 
rectangular coordinates Erysrem has indeed g = — }, for polar coordinates this 
becomes g = — r' cos? p. 
24 
Proceedings Royal Acad. Amsterdam. Vol. XIX. 
