152 Mr. Ivory on a new Method of deducing 
adding the constant logarithm 8.2355814 to the logarithm of 
T -j- r\ 
We must next compute the angles n and by the formulas 
investigated in No. 5: n being the longitude of one of the 
points in which a great circle drawn through the two extreme 
places of the comet cuts the ecliptic ; namely, the longitude 
of that intersection of the two circles which immediately pre- 
cedes the comet in longitude : and z being the inclination of 
the same great circle to the ecliptic. 
We must further make these computations, viz. 
cos. h — cos. X cos. (c — n) 
cos. h' = cos. x' cos. (c' — n) 
tan. (c* — n) 
tan. 0} = 
f . f Q X tan. > 
-sirrl 
tan. X® 
/3 = 
sin. i cos. (c® — n) — ^ 
sin.(w — T 
sin. (/&' — u) * T 
COS. y = COS. X COS. x' cos. [d — c) + sin. x sin. x'. 
2dly. We must reduce into numbers the following formulas, 
leaving p indeterminate, viz. 
= R'* -j- 2R cos. X cos. — c) . p 
d* = R''^ -|- 9,R'(3 cos. x' cos. (e'— c') . p -|- jQ* . p* 
V = RR' cos. e) I R /3 cos. x' cos. c') -j- R' cos. x 
cos. I . p -|- /3 cos. y . p*. 
3dly. We must determine p by means of these formulas, viz. 
6* = -j- ' — sV 
a" = + 2;''* 
In the trials necessary for approximating to the value of p. 
