a Problem in physical Astronomy . 
559 
given above in Art. 3, 4, and 5, of this paper, is very obvious. 
In a subsequent Article, these values will be inserted. 
8. And the product of the two factors in the value of B, in 
Art. 1b, may also be exchanged for a more convenient expres- 
sion, by a like process. 
p -j- a-cc -{- tC* * 
which expression also is more accurate than that from which 
it is derived, as well as more simple. The numerical values of 
l and m, which are evidently given from those of p, <r, and r, 
will be inserted a little further on, when we come to an example 
of calculating the values of A and B in numbers. 
■9* The numerical calculation of the other member also, in 
which * enters, may be facilitated and abridged, by the follow- 
ing considerations. 
If c be put for the sine of an angle, radius being 1, then will 
1 + v/ ( 1 — be the versed-sine of the supplement of that angle, 
and r +v / (l _ 6 . 6 .) will be = the tangent of half that angle; from 
■which it follows, that the reciprocal of this quantity, viz. 
i + \/( 1 — cc) . . 
c 1S ^ co-tangent of half the angle of which the 
sine is c. The common logarithm of may therefore 
be taken out fromTAYLOR's excellent Tables,* and quickly con- 
verted into an hyperbolic logarithm, by Table XXXVII. of 
Dodson's Calculator. 
* These valuable Tables are computed to every second of the quadrant. 
1 
c c 
2 
p + 
- ±pcc 
= p + / c c -f ?n c 4 , &c. 
