80 Parabolic Orbits: Briinnow’s Method. 
D, B, L, are the distance, latitude and longitude of first comet's 
place as seen from third earth. 
Compute the number a and logarithm A from 
sin 6” = n* sin m 
cos 8” cos (ur L) == n cosm 
n cos (B—m) = cos 
D 
Compute the number r from 
ap Am. C 
= A-ac\4—-.0* = —— oi 
r tr/(A=c)?-C = al we put tan «= — 
c 
ris the heliocentric distance of comet at the first observation. 
e now seseie to find r’, which must be accomplished by a 
tentative proc 
sume a Sahie: A’, of the pe ania of third comet from third 
earth. Compute the number 7” from 
ad 
Al Pe 
With the rand r” thus = we compute logarithm x from 
Tt’s equation, as follow 
rl =a ten/ (AM —c!")2 0"? = ane ae we put tang = 
[85366114] ieee = 7 
(ate 
ne == sin’ 
3 si 
=" iP WV cos 38 cos 28 = mu 
log u is tabulated with argument 7. (See Davis's Gavss Theoria.) 
% = qu (r"-+r) 
If this value of # does not agree with that found from 
es 
z= = a/(a" oe a)?--A? = = ry er a 
ust then assume another aia, of A” and renew the com- 
Gatation of x. A few trials will give the required value of A”. 
# is the chord between the first and third places of the oa 
_ Weare now able to find the heliocentric distances r and 
: latitudes b and b”, and longitudes / and 2”, of the first and hd 
- positions of the comet, from the following form 
A cos 8 cos 40 2g at = r cos b cos (—O 
Acosfsin(A—©) = recosbsin (3 
4 sin 8 = rsinb 
if we put tanz = 
Sign of nis plus, 
