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

1[.:[~[ Til,; MOO~N.
s:hadow at everyl full moon. lFor similar reasons, tile moon
vwould occasion ain eclipse of the stun, partial or total, ill some
portions of tilc earth at every new moon. hBut tile lunlar orbit
is inlclined to tile ecliptic about 5, so that; the center of the
mt1ootn, w\hell shil is furtlhest from 1'her nlode, is 5~ friom the Taxis
of thle earth's shladow (which is always ill the ecliptic); and, ias
we shall show presently, tile greatest distance to whlicel the
shadow extendls oil eaelh sidle of the ecliptic, that is, the g(reatest
selmi-dlilllnter of thle slhadow, w\'l1er the n 100l psses tlrought
it, is ontl., about -} of a degree, while thle semi-dialmeter of thle
moll)s; diss only ablout' of a delree; lence tl t\two scmidianleters, namely, thlat of tile moon 1anl the earthl's shadow,
cannot overlap one another, unless, at the time ot nlew or fill
moo0, tile stunl is at or very near tLhe moon',s niode. -In tlhe
course of t]he sun's apparent revolutiol around thce earth once
a year, he is successively ill ever y part of tle ecliptic; consequently, the conjunctions alld oppositions of the sitil and moonl
may occur at, any )art of tile Celiptic, eithler whe\ tlC silunl is
at the mooll's node (or when lie is passing' that poinlt of tlhe
celestial vtault onl which the moon's nllode is projected as seen
frotm tile earth), or tlley may occur wihn tle sunll is 900 fiolm
the moonl's node, where t}et liunar and solar orbits iare at tile
greatest distance fiom each other; or, finally, tlhey may occur
at any interinediate pointC. JNow the sun, in his ai-tnnal rtvo-!lutionl, passes each of tile mooii's nodes on o)losite sides of tilhe
ecliptic, and of coursel at opposite seasons of tlhe year; so that,
for any given year, the eclipses cotmmonly hlll)cel in t\o opl)1)osite lmonths, as January and J1uly, I'ebruar land Aul.glst,
i\ay and Niovember. Thlese are called iW/odae iOt/hs, and
become earlier each year, because the nIodes retrograde.
24-6. If the sun were of the same size with the earth, thle
shadowr of tthe earth woutld b1e cylindrical and inflMite in length,
since tlhe tangents drawn froml the sull to tile Carth (whlich
form thle boundaries of the slhadow\) mwould be parallel to each
other; but as tile sui is a va tly larger body than tle earthll,
thel tangents converge and meet iln a point at somne distance
behind the eartlh, fiormintr a cone, of whtichl thle earthl is tlhe
base, andt wlhose vertex (and of course its axis) lies ill the ecliptic. A little rellection will also.show us tihatt thle form and