Parabolic Orbits: Briinnow’s Method. 79 
Arr. VIIL— On the Improvement of the Elements of a Comet’s 
Orbit: Briinnow’s method ; communicated by C. ABBE. 
Tae following method of conducting the computation of the 
elements of a parabolic orbit was taught by Dr. Briinnow in lee- 
tures at the University of Michigan in 1858; it is here faithfully 
reproduced from my notes taken at that time, and whatever of 
merit it possesses is of course due to my instructor. The form- 
ule are thrown into the natural order of computation, and the 
exact observations, and is not limited to the use of three places. 
The intervals ¢’—? and ¢’—t are not restricted. 
¢ 
tances R, R’, R’. From our previous knowledge of the orbit 
We shall have been able to correct our observations for velocity 
of light, aberration and parallax; they should be referred by 
Proper corrections for nutation and precession to the same 
equinox, 
We first may prepare the angles 
"#—@©, 4—E, M-O, 
the number R, and the logarithm of ¢’—2 
Compute the number g and angle G from 
R” cos (O”—O)—R = g cos (G@—O) 
R” sin (QO”-O) =g sin (G—QO) : 
g and G are the distance and longitude of the first place of the 
earth as seen from the third. : ° 
Compute the numbers c and ¢” and logarithms C and C” from 
cos y Sees _— os 6” cos (”— ©”) = cos py’ 
Sap6 A Nid ag! cos 3 eM Re 
Rsiny=C R” sin y” == C” 
¥ and w’’ are the angles at the earth between the sun and comet 
at the first and third observations. : 
fom our previous knowledge of the orbit we now assume 
two values a and A, of the distance between the comet and 
€arth at the time ¢. It will be a little more convenient and ele- 
gant to assume log a and logA+z. The following computation 
48 to be made for “each assumption. Compute log D and angles 
Band L from 
A cos 8 cos (A—G) + g = D cos B cos (LG) 
A cos 8 sin 8) = D cos B sin (L—G) 
A sin 8 = D sin B 
