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

14f-','1'zI: MOON.
tal parallax being 8 ".O, 6.:.:11 5' 5 2". 1and ] B 3956.n
IIcnc%3
Sin 15' 53": tRad: 3956. 856,275.
Since the distance of the moon fri'o tihe earith is 238,54t5
miles, tle shtladow extends abouti 3.6 timells s af1' as the nlooln,
-aulu colscquenltly the moon passes the;lhadtow toward its broadest part, whelre itss breadtht is mliuch more than sufficient to
cover thte 1mo ns0011 disk.
244). T1:e average, breadthz. qf tle cartAh's stadow, where it
eclises Ilte'moon, is atmost til/ee times tIke mtoon's diameter'.
Let m.im' ('Flig. 5 ) replresent a section of the carth's slhadow
whV1re tile moon p)asses tlrough it, AM being' the center of the
circular section.'T.hlen the anlgle NI.AEIm will be the angular
breadth of half thle shtadow.:Buht,
ME t 1.... 1|mE.1......... (CE; that is, since] mEl is tile t1ooon's Ilo]izonftal parallax (Art.. 82), and IC ()e, equthals tile sun's semi(diametoer mlins ]his lorizontal parallax (d -.- ), telrcefore, putting' filr thle mloon's hlorizontal parallax, we hlave.M n(.i2 6 --- -'):t.)-I-p,- tlhat is, sinlce 1P:_ 57' 1.", and
6 -.-...p:::.. 15-' E52".9, tlhrceforle 5"i'" I"...-.. 15' 51".9.:::. 4.. 1' 8".1, whlich
is nearlt y) three times 15' 33", tile semi-dinameter of the mooln.
Ti111us it: is seenl ]lo 1,3' t;}le aid of geoellctry, we learn to estimate various particulars respecting tle eartlhl's shIadow, by
1Qmeans of si lnple data derived firom observation.
250. Thlle distance friom the node to the center of tie earltl's
shadow, whllen so situalted thlat the m0oonll Nwould mnerely toulch
it att opp)ositionl, is calledt thie lu.nar ect/iptic limit; and the solar
ccli]tic limit is tle (listante f'om the nolde to the center of thle
su1nl's diskt, when tle oon tapparently touches it ill )assing the
conjunction. All cclipses of tlhe moon and suntl occur within
tlhese limits rcspectively.
25 1. I'kTe i.unar t cli. ptie;il'nit is wearl/y 12 tdegrees.
Let ON (Fig. 52!) be the sn's patll, N the moon's, ald N
the node. Let Ca be thlie semi-diameter of thle cartlh's shadow,
andl'A[at thlle semi-diamleter of thle moon. Since (ct and Maf, are
known quanttiies, thellir sum CM.lt is also known. The alngle at
N is known, being tie inclination of the lunar orbit to the