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

this subtracted from th th time of opposition gives us ftle time of
the middle of the eelip6se.
Secondly, joining Ac (I)'ig. 5t:), not represented in the figrn)c, we calculate m.Ae, in fle triangle AreN; thelln A (::::::
mIA).M c..:.A(.. hec=::::. Ielnce, in tlhe triangle ACe, we can determine AC, and ttherefore.OAC AMl::::: MC, wllicl changlled
into time as before, gives us, whlven subtracted firomtt the time
of the middlle of the eclipse, the time of the beginntting of the
ectipyse, or, whlen added to tlhat of the middle, the, ti'e of tthe
en7d of the ecli2pse. The stlum of the two equals the ole ralion.
Thllilrdly, by a similar metlhod -we calcuhlte the value of AMO'>
which converted into time), and subtracted fr'om the time of tlte
middle of the celipsc, gives the eommei cement.ofV totil (larkness, or when addelcd gives the end of total (artnc88. Their
sum is the (d1'rattio)n of tottl (datkness.
FIourthly, the qtaelutitdy qf the ectipse is determined by supposing the diameter of thle moon livided into twelve equal
parts called Digits, and finding how many suchl parts lie'within the slhadow, at the time whlenl the centers of. the omoo n
and tlhe shadow are nearest to each other. Even whenll the
3moonl lies whlolly Aithllil thle sladow, the quantity of the
eclipse is still expressed by the iunlber of digits contained in
that part of the line whlich joins the center of the shadow and
fthe center of th0e 0 moo n, which is intercepted between the edge
of the shadow and the inner edge of the Iloonl. Tillus ill figure
no Ao...... An
54, thoe Inuber of digits eclipsed, equals............. -
Ao..(Am.....)
A...... (-.. an exprl'ession containing only known quantitles.
261. The for'cgoing will. serve as an explanation of tld ge~neral prinec)ies, on wlichl proceeds tfhe calculation of a lunar
eclipse. AThe actual methotds practiced employ mlany expedients to facilitate the process, and to insure the greatest possible
accuracy, the nature of wvhich arl explained and exemplified
in M ason's Supplement to this work.
262. The leadling particulars respecting an ]eIEPwSI.: oF TIM}