i82 
Mr. Ivory on a new Method of deducing 
= Ro' -j- qR® cos. X° cos. . e . p -j- p® 
r® = R® + 2R cos. X cos. (^ — ^) • p + 
r'" = R'" + 2R' cos. x' cos. c') . p f 
V = RR' cos. (e'— ^) + cos. X' cos. — ^ 
R' cos. X cos. (e' — ^) • ^ + cos. 7^^'. 
Cos. 7 denoting here the same thing as before. The first of 
these formLilas, which determines r""® when ^ is given, will 
enable us to compute ^ when the value of ^ is known or as- 
sumed, by means of this formula found above, viz. 
f sin. (Z)®~ 6) t' . B B 
? — ? ^ sin. (/y— Z>®) • T "* R^* 
Thus the values of the functions, r% r"- and V will depend only 
upon one unknown quantity, namely ^ ; which may therefore 
be found by the help of the same final equation as in the for- 
mer method. 
The preceding analysis leads us to the following method for 
determining the orbit of a comet, viz. 
1st. We must begin with computing the values of 0 , and 
i, as in the former method. We must then calculate 
cos. h = cos. X cos. (r — n') 
cos. ]f =z cos. x° cos. (c° — n') 
cos. h' ~ cos. x' cos. (r' — it) 
sin. (J) — h) t' 
^ sin. {h'—h^) * 
p cos. (g® — «) sin. If" cos. i sin. (e° — n) cos. l)° -q. 
i * Tm. (/y—h^~) * ^ 
cos. 7 =: cos. X cos. x' COS. — r) + sin. x sin. x'. 
2dly. We must reduce into numbers the several coefficients 
of the formulas, viz. 
/“"zz: Ro’' -{- 2R® COS. X° COS. (6°— 6° ) . g X ^ + g"" X 
