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

190 T11M, PLAN1E$.
fore the triangles VA13 and Vab are simlilar; and ANV:::
All: (b. ]But AB is known\; also the ratio of AV\: aV (Art.
308); hlenee ab, thie distance l)etwecnl thel points at which the ttwo
obserlvets see IV pl)rojcted on the snl's disk, is known11 inl miles.
We nceld now to obttiln the antgular value of ab. The observers
carefully note the ilstant when'Venus touches the, disk, at tlhe
bc(-gimlninl of flthe tra-sit, and also at the end. Thus the ti-/me
of mtakilng thle transit, as seen by each ol scervcr, is accuratltely
obtained. But since the angular motion per1 hour, hoth otf thle
planet and of tlhe sun, is known, this time of croSilng the di(isk
can be chlianged into anll arc; andl we thus have the number of
minutes of a (legree in the chord cd, and also the number in;f,
anld of courlse in their halves ca and cb. lBut cS and fS, the
angular semi-.diamneter of the sun at the samel time is known
hence, in the riglt-angled triangles cSat, Sb4, we readily find
the minltes ill Sa, Sb, the diflerence betxween vrwhich is the
angular value of (ab. AWe lv\r, therefore, ascertained wlhat
angle is subtended by a line of given length, wh\!n placed at
tlhe sill and viewed froml the carth; or, 1which is the salme
thing', pllaced at the earth and viewed fi'om tlhe sunl; and
th.erefore we know whlat angle (at tihe sunll is subteinded by the
earth's semi-diameter,) which is the sun's ]horizontal parallax.
The observers ctanl not, probtabtly, be at points diametrically
opposite, nor can they remttain stationary during the transit, on
account of di'urnal motion; therefore allowance imust be mt ade
for thles circumstances. The.l line aib will be mlore accurately
imacsuired, according- as the transit occurs nearer to the edg( of
thle sun's disk, because of the greater inecqt!ality in the length
of thte chordsal. Thle solar parallax is so small thtat several stations should be occupied, so as to obtain a number of in(lependillt resullts. lhe p)arallax of the sun, as Imeaslured in 1769),
is 8" 576.*''
\rVcMl1s wlhen on the side of her inferior COlljunctiol, and
MiTars when lltar hlis opl)osition, eacht comes comlpar.atively near
to thie earth, and at these tilles exhlibits a large horizontal
parallax. I'lhat of Venus, especially, may be obtaittlltcd w\ith
great accuracy when she is near1 her greatest elongation; and
* 1)clambre, t. ii; Vince, Complete Syst., vol. i.; Woodhiousc, p. 754; ITcrschcl'$s Outltics, p. 255.