1072 
may be calculated by means of formula (5), if we so to say neglect 
the field of gravitation, which is directly due to the earth, or, more 
exactly, if we replace the g,,’s of the original stationary field of 
gravitation by the quantities g,, + 4',,, where the A',,’s represent 
the small terms proportional to M4, which are discussed on p. 1066. 
We shall now prove, that the just mentioned factor & is equal to 
; ze : a 
zero, at any rate with neglect of small quantities of the order 4 
This may most easily be proved by using the results of classical 
mechanics, which — with neglect of small quantities of the relative 
at 
order of magnitude — — will coincide with the results of Ernsruin’s 
4 
theory of gravitation. In fact, it is well known, that according to 
classical mechanics, the precession of the axis of rotation of the earth 
will entirely be due to the inhomogeinity of the Newtonian field of 
gravitation due to the sun at the place of the earth. In the mathematical 
expression for this precession there will therefore, whether we take the 
mass of the earth into account or not, not occur terms independent of 
the constitution of the earth and of the kind discussed on p. 1070, 
terms, which only appear, when the modifications in the phenomena 
of gravitation required by EiNsreiN’s theory are taken into account. 
Hence we have the result, mentioned above that, with neglect of 
a 
small quantities of the order —, that is of the same order as the 
square of the velocity of the earth, the mentioned factor & will 
be zero. 
Consequently we find, that the influence of the earth’s own field 
of gravitation on the non-Newtonian contribution to the precession 
of the rotation-axis of the earth, considered in the present §, will 
LE a 
A Mz 
thermore clear that, if the mass of the earth is not neglected, also 
the contribution to the value of the precession, which is due to 
the inhomogeinity of the sun’s field of gravitation at the place of 
the earth will be altered by small quantities, which relative to the 
at most be a small quantity of the order w > is fur- 
M, 
main term are of the order non and that this alteration will be 
IVEY 
the same as that calculated by means of Newtonian mechanics. 
In connection with this result it might be of interest to draw 
attention to the fact that we have made use of the circumstance, 
that for the system under consideration, which consisted of bodies 
moving under mutual gravitational influence, the results obtained 
