201 
from the point, where the radius intersects sphere r— a, if r >a 
and supposing that (7) remains valid up to 7a. In future we will 
always make these two supposilions; as we shall see, that a moving 
particle outside sphere 7 —« can never pass that sphere, we may, 
in studying its motion. disregard the space 7 < a. Should (7) cease 
to be valid as soon as 7 becomes < hè, we need only exclude the 
space r< R from the conclusions which will still be made, to make 
them valid again. 
If r be very large with respect to a, the proportion d:7 ap- 
proaches to 1. | 
~The circumference of a circle 7 == const. is 2ar by (7); this shows 
how r can be measured. Circle « has the circumference 224. 
One might in (7) perform a substitution t—= f(r‚t). Then a term 
containing drdr would arise and the velocity c of light, travelling 
along r, would have to be calculated from an equation of the form 
se (7,7) an FH, (7,7) Cae FP, (7,t) a) 
and would have two values, one for light coming from the centre, 
the other for light moving towards it. Moreover these values would 
depend on f. In consequence of the last fact we should not name 
the field stationary and the first fact does not agree with the way 
in which time is compared ‘in two different places. So, if we want 
to retain both advantages, such a substitution is not allowed, though 
it may, of course, always be done, if we are willing to give up these 
advantages. 
We will point out that, as (7) is known now, G can be found 
as a function of 7. The result is G == 0, as it must always be found 
where matter is absent. 
4. We now proceed to the calculation of the equations of motion 
of a particle in the field. 
The equations of motion express the fact that the first variation 
of the integral 
ty 
fe dt 
h 
will be zero, if the varied positions for ¢=¢, and =‘, are the 
same as the actual ones. 1 represents the quantity 
ds : a r? . : 
L=—= he ot — F9 — 7? sin? 9 yp’, … . (9) 
dt a 
jk 
j ee 
r 
