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

lprojection of thle shadow traversed by tlhe moon. Writh a
radius. equal to the semi-diameter of the shadow and thlat of
tihe moon (:'...t:,'16. I-.58'), and withl tile center A, mark the
two points c ald f oil the relative orbit, and they will be the
places of the center of tie moon at tie beginning and end of
thle eclipse. Tle perplendiculars cC, flF, give the times A.C
anl( A V of tlhe commencement and tlhe end of the eclipse, and
C:A: oVr i.V l gives half tlle duration. From thle cenlters c andi;
withl a radlius equlal to tile semi-diameter of tile mooll (16') deiscibcl circles, and they will each touch the shadow (Euc., 3, 12),
lndicating tile position of the m1oo11 at the bcgimiingl and en11d
of tie eclipse. If tlhe same circle described fiom m, is wholly
-w\itllin tile shadow, tile celipse will be total; if it is Only partly
withiln tile shadtow, tile eclipse will be. artial. Withl the
centter A, and radius equal to tile semli-diameter of the slladow
Ililnuts that of the 1noo01 (42'-.16':::26'), mark the two points c',
f', wltich will give the ptlaces of thie center of the mioon, at tile
beginnlilng and( ed of total darknlless, and M(', MtI:' will give
the corresponlding tillmes b)efore and after tile middle of tile
eclipse. tl'eir sum wll ill be tIle duration of total darkness.
260. If the foreg'oing p)rojection be accurately mnade from
a scale, tile required plarticullars of tile eclipse nmay be ascertained by llleasmllring, oil thle samel scale, tlhe lilles \wVlich l'0spl)c(tivcly represent trem; anld we shlould tthus obtailn a niear
approxilllation to the clemenits of tile eclipse. A. llmlre accurate ceterlllination of these elements may, however, be obtained by actual calelulation.'T.he general p)rinciples of tile
calculationl will be readily lunlderlstood.
I'irst,-llnowinlg ai (Fig. 53), tle lo0o's1 relative longitude,
and (h, h1cr latitude, we 1fi(1 tile anlgle dai, whlich is tile inclination of the mlool's relative orbit. But ai d::::aA.l; land,
in the triangle az, i, we harve the angle at A, and tile side Aa.,
be1ing thie 10oo1'sS latitude at the timle of oppositioln, whicll is
giveAll )y thell tables. [lence we call find tl side Am. 11l te10
trianllle.AmMs (Fig. 54), ilavilng thle side A.m. and tfle anglo
AtmMI.(:.:::a,8Am'), we call find AM:.:: tlhe are of relative lolngitulol
described by tile 1moon from tile timlle of tlle 1middle of the
eclipse to tile time of opposition; and knllowinlg tile oo11111
ltourly motioll in longitude, we can conlvert A. At into timle, and