on the Atmosphere of Venus. 327 
rent extent of the twilight ; but its true extent will only be 
the distance / g measured in degrees of a great circle. And it 
is sufficiently evident, that the smaller we assume the angle 
DcE, before or after an inferior conjunction, the more pointed 
of course will be its equal angle A c F, and hence also the longer 
the visible part of the twilight f c. It is likewise manifest, 
that when the elongation of the planet is equal to the angle 
D c C, the line DdB will represent the terminating surface 
of the dark and light hemispheres, whence the planet will, at 
its greatest elongation, be illuminated by the sun in the direc- 
tion C c, and the true extent of the twilight will coincide with 
the apparent one on the terminating plane A c. 
In order then to calculate in any, except the greatest, elon- 
gation, the arc fg, in t'.e right-angled spherical triangle/ eg, 
or to ascertain the true extent of the twilight in degrees of 
a great circle, it will be requisite to measure from T, the ap- 
parent prolongation of the twilight into the dark hemisphere 
/ c , and the apparent diameter of the planet. With these data 
it follows that, as the anglefgc isa right angle, the angle/c’o’ 
= AcF = DcE may be found by calculation, and the arc 
fg be thence easily deduced. 
But the angle fc g = D c E is equal to the complement of 
the angle S F T, fig. 6, on the planet, to 180°, orF ST -f- S TF, 
as is plainly illustrated by fig. 10, Tab. VII. Let S be the sun,T 
our earth, c the centre of Venus ; draw gcG perpendicular to 
S c K, and AcC perpendicular to T c: then is A c the projec- 
tion of the visible terminating plane, as seen from T, and the 
projection of the luminous border. S c T is the angle on the 
planet, K c B its complement to 180 s , and K c B = C c G ; 
Ull2 
