738 
Now, if we calculate the geodesic increment along ds of the 
vector components: 
ETE, he Ab; Am, de, 
we find 
dAa, = 0, 
dA, = 0, 
but 
dAt, = — Va/2R*. At, ds, or = — w At, ds, 
and 
dA+, = +Va/2R*. At, ds, or = + w AY, ds. 
From this we infer that the falling axes of ZW, Z@), after the 
lapse of interval ds, as compared with the local axes reached after 
the interval, show a retrograde rotation of amount wds in the plane 
of these axes. Meantime the planet’s anomaly has increased by wdt. 
Thus, the two angular velocities are the same if the one is measured 
in ds and the other in dt. The ratio is 
ds — V(1—3a/2R). dt. 
In the circular planetary motion this will continue uniformly, and 
it follows that when the planet has completed a revolution, the 
falling axes will not yet have completed theirs if compared with 
the local axes passed by during their motion. At the instant the falling 
axes will have completed a revolution, the radius vector will make 
an angle of 
2R 
an Wm 
with the radius from which they started. Relative to this new radius 
everything will be in exactly the same position as it was in the 
beginning of the revolution, 
Neglecting higher powers of a/R we conclude that there is a 
precession which, per annum, amounts to the excess of the angle 
between the two radii ovef 2x, i.e. 
per annum. 
For the earth, it is 0.019 of a second of arc per annum. 
