t>8 Mr. Robertson on the Precession 
particles in DF may be considered as equal to the sun’s dis- 
turbing force, on the principle of action and reaction being 
equal as to magnitude, but directly contrary as to direction. 
But on the side of DF nearest to S the disturbing force is 
greater than the inertia of any particle G, and it therefore 
urges the particle from DF towards S, by a pressure whose 
direction and power is as HG. On the side of DF opposite to 
S the disturbing force is less than the inertia of any particle 
K, and therefore the inertia of K opposes the disturbing force 
of the sun by a pressure whose direction is from N towards 
K, and whose power is as NK. 
22. As, by the nature of the spheroid, PELQ is an ellipse, 
let GK be the diameter conjugate to DF, and let VI, parallel 
to DF, meet it in T, and AB in R ; and then VI is bisected in 
T. Let RI be bisected in v, and let w, q be two points in RI, 
equally distant from R and I respectively. Let a = EC, and 
d — the disturbing force of the sun at the distance of EC 
from DF. Then by the preceding article, a : RC : : d : x RC 
= the force at R, or at any point in VI, as any two points in 
VI are equally distant from DF. Now it is evident that the 
disturbing force on a particle at R, or on any particle in AC, 
has no power to turn the ellipse about C ; but the force on a 
particle at w tends to turn the ellipse about the centre, for it 
is applied at the end of the lever Rw. Consequently, by what 
has been already proved in this article, and by the property 
ct 
of the lever, the force on w to turn the ellipse is — x RC x Rie. 
For the same reasons, the force on q to turn the ellipse is 
~ x RC x R q, and therefore the force on w and q combined, 
to turn the ellipse, is — - x RC x RI, for Rw -f- IF/ = RL 
