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

lhorizontal parallax at tlec moon, is, since she is nearler to the
sul,) about Wo16 greater than at the earth; but on account of
1her inferior size it is. - less than at the earth. lene, illncreafsing the sun's horizontal parallax at the carth by the for400
mer firaction, and diminishing it by the latter, we have 3- X
X 9."::::". 5t.::: the slun's horizontal parallax at tile moon.
T.Ilerefore, the scmli-angle of the cone of tlhe moon's shbadow,
whlliclt, as appears above, equals SDXI)I -— )..RK, equals 16' 3".9,."'.5..:161' 1".//4, whiclh so nearly equals the sun's al))parent
semi-diameter, as seen fr'om thte earth, that we may adopt tlh6
latter as the value of the semi-angle of the shadow. lience,
sin 10' 1".5': 1080 (1:B1)):: Rnad::)I:(::231i 90. IBut t~ho
mcan distance of the moon from the surface of the earth is
238545..... — 3956:::: 23934589, whichl exceeds a little the imean Ilength
of the shadow as above.
lBut cwhen thle 1moonl is nearpst thle carthl, her distance fiom
the center of the Carth is only 2g21,14-S miles; and w\\eln the
earth is furthest from the sun, tite sunl's lapparent semi-diamete i's only 15' 45".5. 13y employing this numbler in tlhe foregoing estimate, wc slhall find the lengt1h of the shadow 235,630
mniles; andii 235G30 22.1148::::-14482, the distance whichl thi
mnoon's shadow 1nmaty reach beyond the center of thle earlth.
266. Tedii Sameter of the lmoo'$ s]hadow where it traverses
the earth,,is, at its nmafeim.umi, tabout 170 milets.*x
Iln tlhe triantgle JI K, the angle at l-:.:15' t:f5".5 (Art. 265),
thfe sid;e Te:.39,,,and T:1(- 14482.
Or, 3956:,14482:: sin 15' 45".5: sin 57' 41/".5.
And 57' 41".V5-15' 45".5:.i 1~ 13' 27"t:.:-d.Te, or the are (de.
And 2de::::: 26' 546::e..
lience 360: 2.45 (==2~ 26' 5.4"): 24899.,: 1710 (nearly).
267. ['he greatest portion of the earth's sufatce ever covered
by the,moon's penlumbra, is about 4393 miles.
Io T'his fiupposes the conjunction to take place at the node, and the shadow to
strike the earth I'petlndicularly to its surfaco; whelro it strikes obliquely, tho
scCtion may be gr'cater th)ta thtis.
t The equatorial ci rcumference.