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

lE:rwsl:s8. 149
mlospllere, wlich acts as a convex lens, and converges the light
into the shadow.'.hle lower, rays, if they coulid escape, would
be bent twice 34' (Art. 89), and reachl the axis tllousands of
miles this side of the moon. As it is, only a little light emerfges,
whichl is sfisflciently bent to fall onl tihe mloon whenll centrally
cclipscd. An observer at the moon, in witnessing a.solar eclipse,
would see thle sun expanded into a dim narrovw ring, lhavilng
ni'early four times its usual diametcr.
257. In calculatting an eeb' se of t1e moon, wAe first learn
filom the tables in what month the sun, at the time of full
miioo1n in that mlolnth, is near the mooon's node, or within the
lunar ecliptic limit. This it must evidently be easy to determine, since the tables enable us to find both the longitudes of
the nlodes, 1and thle longitudes of the sun11 and moon, for every
day of thle year. Consequently, we canl filld when tlce sun has
nearly tile same longitude as one of the nodes, and also the
pr'cisc moment when the longitude of the mIoon is 1800 from
that of the slln, for tlhis is the time of opposition, fiom wvlich
mlay be derived the time of the middle of the eclipse. Iaving
thle time of the middle of the cclipse, and the breadth of the
sltadlow (Art. 249), and knowing, fiom the tables, the rate at
whllich thll moon moves per htour faster than tile shlttlow, we
ca1n find hlow Iong it Nwill take herlc to tiaverse half thle breadth
of tle shadow; and this time subtracted from the time of tho
middle of the eclipse, will grive the becginning, and addel to thlo
time of the middle will give the end of the colipsce. Or if illnsteadl of the breadthl of the shladow, we emtploy the breadth of
thi l)Cnmnl)nbra (Art. 253), we may fin(d, in the same mannerl
tlc tllhe moon entelrs and when she leaves telt ) pe numbrla.
Vre see, therefore, ]ow, hoby havingn a few tllings known by observation, such as thle sun and loon's siemi-dialmeters alnd tllheir
horizontal parallaxes, we rise, by the aid of trigonometry, to
the knowledge of various parlticulart s recspecting the length and
breadthi of the slhadow and of th)e peCllnumbra. These being
known, vey next fhave recourse, to tlhe tables which contain all
tlhe nlecessary particulars respecting thle motions of thle sun and
mnoon, together with equations or corrections, to be applied for
all their irregularities. li'ence it is comparatively all easy task
to calculate with great accuracy an eclipse of tile moon.