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ecliptic. This involyes a complication in comparing the relative 
positions of the two sets of spatial axes of reference. In the case 
of a planet moving in a cireular orbit this difficulty is readily 
overcome. 
If then we compare the falling axes, before and after a year’s 
revolution, with axes fixed to the sun and directed to fixed points 
in the heavens, we find a precession to the amount stated above. 
As pointed out by De Sitter the difficulty in testing the predicted 
precession by a comparison with observation lies not so much in 
the limits of accuracy of observation as in the fact that owing to 
our ignorance of the true values of the earth’s principal moments 
of inertia we do not know with the precision required how much of 
the observed precession is accounted for by the actions of sun and 
moon according to Newton's law. 
We now proceed to the analytical treatment of the problem. 
The geodeste falling coordinates. 
Consider some point-instant in an arbitrary field of ee 
where the potentials are denoted by gas, (a,6=0, 1, 2, 3), x, being 
the time and zb, x, «@) space-coordinates. In the usual Say we 
write the symbols of CHRISTOFFEL : 
ab ab Odam Òg sn Ògao 
=> J gm Sgr. bi 5 ss : 
9 ES 7 E 2 dze | 
where ger are the algebraical complements of the gen. 
A vector Ve is displaced parallel to itself over an inter val dar, 
if its components decrease during the displacement according to the 
formula 
b 
ave is TED ge 
a 
In the point-instant considered: 2°, (a= 0,1, 2, 3), choose a vector 
of unit length having time-character A°,: 
= Jab Ae. Ao, = J 
and three other vectors of unit length, all perpendicular to the 
former and to one another: At, A*,, A*,, such that 
= Jap A*, A, = — 1; and 2 9,,A%A%=0 if 147. 
As in our argument the component of time and the components 
of space will be treated in a different way, we shall establish the 
rule that whenever a suffix is indicated by a Greek character, it 
will not be liable to take the value 0. 
We change variables by introducing the coordinates z' according 
to the following formulae: 
