the excentricity of the earth, g is then a constant. The equations 
ae _ {pg Pq 
of motion are (17), in which the brackets ) ; { and 4 must be 
t 
derived: by means of the usual formulae from the gj, which are 
determined by (1). The right-hand members of (1), i. e. the 
quantities 7, are zero except in those parts of the four-dimensional 
time-space, where the sun and the earth are. Since these two bodies 
never co-incide, we have always only one 7, either (7), or (Tij. 
We can suppose the sun to be at rest. Then (Tij), has the same 
‘ralue as above. For the earth, which moves, we can put 
(Lis), = (ij) + I (Tis 
the first term on the right being the value which we should find 
if the earth were at rest. 
I will restrict the determination of the g;; to an approximation 
which is sufficient to give all secw/ar terms of the order of mag- 
nitude of observable quantities. 
We can conceive the-g;; to be made up of several parts, thus 
gij = (Gis)o + (gij), + Gis: 
The first two terms taken separately need not correspond to a 
real problem, they are only mathematically defined as follows: 
(gij), is what we. find if in (1) we take account of (77;), only, 
and similarly (g;;), arises from (7;;),. If now the equations (1) were 
linear in the g;; and their differential coefficients, then (9:;), + 
(gij), would be the complete solution. It follows that gij is of the 
second order, and need therefore only be computed for 7 — j= 4. 
Let us first consider the others, of which (g;;), is the same as 
before. We can take (g;;), = (gij):° + d(gi;),, where the two parts 
arise from the two parts of (7’;,;),. The term d(77;;), is at least of 
the order 4, ie. of the order of the velocities, and need only be 
taken into account in the determination of gis. It there produces a 
term of the order 22, § which contains odd functions of the angle 
Moon—Earth—Sun, and therefore only gives rise to periodic terms 
of the order &.7, which we neglect. It will appear that even the 
secular terms of this order are entirely negligible. 
By a similar reasoning we find that the term d(y,,); will be of 
the order 4,??, and the secular terms which may perhaps result 
from this term will be far beyond the limit of observability. 
There remains the termg,,. This will be of the order 2°7,°, and 
will also contain the angle already mentioned. It can consequently 
also be neglected. 
