78 
Mr. Robertson on the Precession 
w a xS C 
ax T 
r-, and M = But, by article 1 1 , the dis- 
turbing force of the sun on a particle at G (Fig. 7. ) is equal 
t° — ; and at the distance a from DF the disturbing force 
is - The foregoing value of M being substituted for it 
in this expression, we have = d , the sun’s disturbing 
force at the distance a from DF. 
This value of d being put for it in the expression at the 
end of the last article, it follows that the angular velocity of 
libration, at its commencement at the equinox, is to the uni- 
form angular diurnal velocity as x mn x to w, or as 
3 P a^—e 1 
—~r x mn X — -r- 
to 1 . But, according to the preceding nota- 
tion, t : i : : 360° : — ^ = the uniform angular diurnal velocity, 
and therefore 1 : -p— x mn x a -~- : : — • : 360 x ^ x 
mn x 
a e 
the angular velocity of libration, at its commencement 
at the equinox. But as the product mn is the only variable 
quantity which enters into the value of the librating force, ob- 
tained in article 16, it is evident that 360 x x mn x ~r~ 
expresses the momentary angular velocity of libration at any 
time. We are now to consider this effect of the librating 
force in the direction in which the force is exerted, viz. in a 
meridian analogous to PEAQ in Figure 7. 
22, Let FLGA (Fig. 11.) represent the ecliptic on the 
sphere, S the sun’s place in it, L the first point of Libra and 
A that of Aries ; LBA the position of the equator when the 
sun is at S, and SB the sun’s declination. Let FBG be 
the position into which the equator is pressed in the time 
f, by a combination of the librating force and the diurnal 
