1224 
orbital plane is not disturbed. In case A there are no secular terms 
depending on 6. 
In B the terms produced by oare of a lower order, in consequence 
of the fact that all g,, depend explicitly on the time. The motion 
of the perihelion is 
30a* 
2 
“0 
and also the other elements have terms with c?/ 
parameter of the elliptic orbit is 
Jo = 
nt—206 c7t’, 
*; thus e.g. the 
P= pees 
where A,? = xm/82, m being the sun’s mass, and e= 2.718 ... 
These “perturbations” *) being insensible according to our experience, 
we can here also assign an upper limit to o. 
I shall not attempt to determine this upper limit with any 
accuracy. For both cases we will be safe in taking e.g. o < 10-24 
in astronomical units, or 26 << 10~-°° in centimeters *). We can. 
however, do no more than assign an upper limit to o. To make 
possible a determination of the value of this constant, it would be 
necessary that it had a measurable effect on some physical or astro- 
nomical phenomenon. Now it cannot, of course, be excluded a priori 
that at some future time observations will be made, or phenomena 
will be discovered which can be explained with the aid of the 
constant 6, but so far no such phenomena are known, and there 
are no indications of anything in that direction. The constant 6 only 
serves to satisfy a philosophical need felt by many, but it has no 
real physical meaning, though it can be mathematically inter- 
preted as a curvature of space. 
Finally we can also reject both systems A and B, and stick to 
the original tield-equations (8) and the values (1) of the g,,, which 
1) The terms of the lowest order in the ‘perturbing forces” are for the two 
cases: 
2655 ; ae tee Sten ee 
In A: S= —30 + — 2(r?—7*3’) , T= —rrd, W=—), 
Ys Aen 
20 20 = eee 5 
nB: S=—r— —cdr , T=— —ard, W—0. 
a,” Aen U : 
(For the notation see e.g. DE SITTER, On Ernstetn’s theory of gravitation, M.N. 
Vol. LXXI, pages 724 sqq.). 
The terms with c/? in the case B arise through the fact that the units both 
of time and space (in coordinate-measure) depend on the time. 
2) The density of the world matter in the system A then becomes g <3.10—!7 
(astronomical units), or » < 2.10—-% (C. G. S. units). This corresponds to one star 
(of the same mass as the sun) in a sphere of one parsec radius, 
