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

IUNAR IRIEXGoULA XflTIICS. 139
between the gravitation at the peri'gee and at the apogee, and
conselquentfly increase tile eccentricity of the orbit. Agail,
tlany cause which at the perigee shlould have the effect to lessen
thle oonle's gravitation toward the earth, alndl at thle pocoee
to intcrease it, would( lessen thoe diflrenee between thle two, and
consequenltly diminish tie eccentricity of t1he orbit, or 11bri)g it
nearerl to a circle. Let us sce if the disturbilngt force of the sull
prodluces these cffects.'T.le sulln's disturbing force, as we hlave
see in article 228, admits of two resolutions, one in the dilection of the radius vector (OA,, Fig. 48), tle other (ON) inl the
direcction of a tangent to the orblit. First, lct AB3 be the line
of the apsides in syzygy, A beilng the place of the perigee. The
sun's disturbing force OAt is greatest in the direction of the
line of thle syzygrics yet dependingll as it does on the utneqial
action of thile sun upon the earth, and tie moon, lanld being
greater as their distance fiom eachl otlher is greater, it is at a
minimu whlenl acting at the perigee, atld at a intaxtzsitmunl whenl
acting at the apogee. ltence its effect is to draw away the
moon from tlhe carth less than usttual at the perigee, and of
course to make hler gravitation toward the cart]h greater than
Iusufal; while fat the apogee its effect is to diminish the tmendlecy
of the moon to the earth more than usual, l>and thusll to increalse
tile disproportion bIetween thlie two distances of the mooln firom
the focus at these two poilts, atnd of course to increiase the
eccentricity of thte orbit. Thc moon, thcrefore, if mrtoving
toward the perigee, is brouglht to the line of the apsides in a
point between its menan place and the earth; or if movingl toward the apogee, shle reaches the line of the apsides in a point
more remote firom the earth than its mean place.
Secondly, let C1) be the line of apsidcs inl quadraturte. The
effect of tihe sunl's action is to incset te llooll's tenldellcy
to the earth, whten in quadrature. If, how\ever, the moon is
then att perigree, such inrease vwill be less than uslual, because
the sun's action is less oblique; and if at apogee, it will be
momre than usual, because more oblique. 11t1ence its effect -will
be to lessen the disproportion between the two distances of tthe
tmoon fiom trhe focus at these two points; and of course to diminishl tihe eccentricity of the orbit. Thl e mlooln, therefore, if
moving towar(l the perigee, meets t.he line of the apsides in a
point more remote fi'omn the earth than the mean place of the