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

sfurface, tlhe velocity is increased ill proportion of radilus to tlhe
sine of obliquity.'lithus the shadows of evening heave a far
more rapid motion than those of noonday.
L.et Ius endeavor to form a just conception of thle manner in
w\hicll these three bodies- — the sull, the earth, and tlhe moon — t are
situated withl respect to each otlher at the l time of a solar
cclisce. First, suppose tllc conjunction to take place at the
node.'l'cltn tlhe straight line which connects the centers of
the sun and the earthl, also passes tlhrouglt the center of thle
moon, and coincides Nwithl the axis of its shadow; and, since
the earth is bisected by tihe plane of the ecliptic, the slhadow
would travcirse the earlth in tlhe direction of the terrestrial
ecliptic, from w\est to east, passing over tlhe middle regionls of
the earth. Itcre the diurnal motion of the eartl being inl the
samle dircctionl witht tie shadow, but with a less velocity, ttle
shadow wvill appealr to move with], a speed equal only to tlhe
difilerence between the two. Sceonldly, suppose thle mloolt is
onl tile north side of tlhe ecliptic at the time of conjunction, tltnd
110moving toward h]er descending inode, and that tlhe conjunction
taklcs p)lace just within thell solar ecliptic limit) say 160 from
the node. The shadow\ will now not fall in tle plalne of thte
ccliptic, buti a little noltltward of it, so as just to gra'Xze tie
carth near the pole of the ecliptic. The nearer thle conjunctioll comes to the node, tlhe further tlhe slhadow will fall fr1om
tile pole of the ecliptic towarl the equatorial regionis. In cer'tain cases, the shadow strikes beyond t.he polo of thle earth;
and thlcen its easterly motion beingl opposite to the diurlnal imotion of the places w\licli it traverses, consequently its velocity
is greatly increased, being equal to the sum of both.
264-. After tflcse general considerations, we will now examine more )particularly the method of investigating the clements
of a solar colipse..'The lcength of the moon's shtadow is the first object of inquir-y.'The loon, as well as t.he earth, is at different distances friom tile s\un at difleclrt timlles, and hence the length of
her shadow varies, beinll always glreatest wltln she is furtltcst
froln thle sull. Also, sincoe helr distance firom the earth varies,
the section of thle mloon's stladow made by thle earth, is greater
in propo'tion as thie moon is nearer tflc eartl. The greatest