747
D* = (/ - Vf + (k - k‘f . cos. 1 I
=(/- + (--£)'““-‘'h
/. D = (/ — l'). sec. 0,
making tan. 6 =
k - k'
l - l'
. cos. 1.
The latter expression for the value of D is easily deducible
jy i _ j i
from the former, by substituting in the former—, -, &c.
’ •' e 2 2
"’stead of their sines, which may be done with inconsiderableerr °r, by reason of the smallness of those angles, during thecontiguity of the Moon and star, 8tc.
The first term of the expression for sin. 2 D , (see p. 746,)
' s siii.* ^—-—J . In which expression I, l', arc the apparent
latitudes, therefore if 5, 5', were the parallaxes, and A the differ-e "ce of the true latitudes, we should have
l -1‘ = A +5-3'.
Suppose now one of the bodies (that to which the latitude l'belongs) to have no parallax in latitude, but the other to have aParallax equal to 5 — S', then, still as before,
l- l' = A + (5 - S f ),
a "d a similar result will hold good with regard to sin. 2
therefore, if the coefficient of this latter term, instead of beingCos - I . cos. V, were a constant quantity a, for instance, (or in-v °lved merely the difference of the parallaxes), the distance D' v °uld result precisely of the same value sin. 2 D from the expression
sin.
2
D
2
sin.
I - l'2
+
instead of assigning to each body its proper parallax, we suppose0Me to be entirely without, and attributed to the other an ima-ginary parallax in latitude and longitude, equal to the difference