THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 21 
The equation y, = ¢.q; gives 
log. y. = log. g + log. q 
Putting 
looag = loon f= y, 
we have for q, 
log. g, = log. 7 — y. 
Writing s for the number of seconds in the radius, and 2) for the modulus of 
the common system of logarithms, we find 
Q=F+2 
log. g =log. f + y (24) 
log. q: = log. i —y 
in which 
ga eee + Z,,) sin 27+ s (2 — 1.) sin 4F a 
p= Np i iy a dn) cos 277—A, Cue = +) cos 47 
And for C' we haye from the first of (15) 
C=y7 +y72-sin >Q. (26) 
By means of the last three equations we are enabled to find the values of 
Q, 9; Gi, C, with the greatest accuracy. The equations (17), where not sufficiently 
approximate, will, nevertheless, furnish a good check on the values of these quantities. 
All the quantities in the expression for (e) are thus known; and substituting their 
values corresponding to the various values of g, we have the values of ie =) for the 
different pomts of the circumference. 
