: 519 
ivin 
ig B=-13; C=+4+,5.- (42) 
Thus, if we neglect eccentricities and inclinations, and con- 
fine ourselves to the first power of the disturbing force, or to 
the second power of m, the perturbation of the moon’s vector, 
produced by the sun’s attraction, is composed of the three fol- 
lowing terms : 
2 2 2 
38 = — p— ypy+ By BB. (43) 
The first of these three terms expresses that the sun’s abla- 
titious force, by partially counteracting the earth’s attractive 
force on the moon, allows our satellite to revolve in a some- 
what smaller orbit than would otherwise be consistent with 
the observed periodic time: the ratio of the diminished to the 
| undiminished radius of the orbit being that of 1— =! to 1. 
The second term expresses a displacement of the moon, through 
perturbation, from its diminished circular orbit, of which dis- 
placement the constant magnitude or length bears to the radius 
19m? 
16 
the direction of this displacement is always from that fictitious 
moon, ¢o which it has been seen that one of the two principal 
components of the sun’s disturbing force is directed : an oppo- 
sition of sign which may at first surprise, but which is exactly 
analogous to the contraction of the orbit produced by the ab- 
 latitious force (when the periodic time is given), and is to Ve 
explained upon similar principles. Finally, the third term of 
the formula (43) for 66, expresses that with the two foregoing 
_ displacements a third is to be combined, which is, like them, of 
constant amount, being equal to =5,ths of the second displace- 
ment, or bearing to the radius of the moon’s orbit the ratio of 
3m? ; j ‘ 
Fe tO unity; but being always directed to what, by an exten- 
sion of a recently employed phraseology, might be called the. 
of the undiminished orbit the ratio of 
to unity ; while 
