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

Let S be tthe place of an observer ol the eart,t and sluppose a
line ES to be drawn to tile sun; then NlAl S is tlhe elongathon
of the p)oilnt 21t friom thle suln, whlich is determined by ol)se\rvation.'The angle 1EMMS ca n never differ so much as 9' fri'o the
Fig. 46.
E: $'K /
A
supp)lement of AE.S, on account of the grleat distance of the
sla comnpared with AEM, which is about 4.00 to 1:. tBut to obtain EIM15AS accurately, 400: I:sisn:TMES: sill ES, lwhich
angle subtracted from tlhe supplement of lMES, leaves EMS.
Let MEG;O, thi visual angle between the mountain top1) and tlhe
termini torl be mneasu red by a micrometer. J.Then, as the (distance friom the eartI to the mioon is known, the isosceles triangle INE:GO gives the lelngth of )ON..As E is very small, thel
alngles at IN may be considered righlt angles; hienee, tle righltangled triancile:MN, in whlichl (G)IN and At are knownl, gives
M:. Finally, friom the known sides 0O and GOM, in tihe riglhtanogled triangle O)G, C l: is obtained; afnd 0 beingl subtractedl fron it, we find l(lt', the heigllt of the mountllain.
207. A.s GOAMt is very small complaredl with OCO,'I A[ is 1both
lmore easig anll more (tccrtedl/q fotund by taking the thlird
proportiontal to 2 an)(i and ()GM. l:or, su1l0ose a p)crpelllicldar
dtrawn ftiro- F to OC; then GOCM may be called equal to IF(O),
antlld Mt'A to the versed sillne; hentce 200:):: Ml O: FM.
T. lte whole work tnay be finistced by logaritlms, wittout tatkinlgE