An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

3centers'of the and earth (see Fig. i not i the plane
cenlterls of tfie sunlt and earthl (see Iig. 4.q), is niot ill tle plane
of the rmoon's orbit (sillnc this is inclined to the ecliptic about
W5), except when the sun itself is in that plane, or w-hml tlhe
line of the nodes being produced passes tlrough tile sun. In
all otlher cases it is oblique to the plane of tlie orbit, antd may
be resolved into two forces, one of wlich is at righlt angles to
that plane, and is dirccted toward thle ccliltic. h'lis force of
courset dravws the moon continually toward tlle ecliptic, or0 1leduces a contiual deflection of thc!m~oon from the plane of her
own orblit toward that. of the earth. Hience the mloon meets
the plane of the ecliptic sooner thlan it would lhave dolle if that
force had not acted. At every, l alf revolution, tlherefore thle
point in whichl tle mloonll meets the ecliptic sllifts ill a lirlection
contrary to that of the moon's motion, or contrary to the older
of tire signs. I f tlhe earth and still weret at rest, the efkfect
of the detilctting force just described would be to prodnce a
retrograde motion of th}e lile of thle nodes till tltat line wtas
b)rought to pass through t}le saun, alld, of consequence, the p)latr
of the moon's orbit to do tlle same, after whiclt tlhey weo'
both remain in their position, there beintg no longer at> ny fot
tending to produce chanrge il eitlher. Butt the Iotion of the
earttll calices tile line of thle nodes out Of thlis position, alld po1'duces, by that Imeanls, its continual retrogradation. The santo
force produ(ces a small varication in thie inclination of the hmlnoon's
orbit, giving it anll alternate increase and decrease witinl very
na'rrow limits.x Thlese point s will be easily inderstood by thla
aidl of a (diagramn. lterefore, let MNr (Fig. 50) be the ecliptic,
ANB3 the orbit of thie moon, time moon1 beingl in LJ, and iN its
descending node. Let the disturblhinl f'orce of tile sun which
tends to bring it down to the ecliptica be represented by,b, anld
its velocity in its orbit by:Lat. Ulnder the action of t.lese two
forces, the o11100on oill dcselrib the dingolal Le of thle p1)arallelogram ha, and its orbit will ble changed friom AN to — N'; trte
no10e iN passes to`N'; and tlc exterior anlle at N' of the triantgle',NN" being greater' tlhan the interior and opp)osite angll
nt,:N, tite inclination of the orblit is increased at the node.
After tflhe oon has passed tle cecliptic to the south siide to 1,
the disturbing force id produces a new change of the orbit iN'le, Playfair.