384 
[471 
471. 
NOTE ON THE PROBLEM OF THE DETERMINATION OF A 
PLANET’S ORBIT FROM THREE OBSERVATIONS. 
[From the Monthly Notices of the Royal Astronomical Society, vol. xxix. (1868—1869), 
pp. 257—259.] 
The principle of the solution given in the Theoria Mot us may be explained very 
simply as follows : 
Consider three successive positions of C, C', G", of a planet revolving about the 
focus S; let n, n', n", denote the doubles of the triangular areas G'SG", CSC', and 
CSC" respectively (viz. the triangular area means the area of the triangle included 
between the two radius vectors and the chord joining their extremities), r the radius 
C" 
C 
vector SC'; 6", 6, the times of describing the arcs GO' and C'G" respectively, the 
units of time and distance being such that the time is equal to the double area 
divided by the square root of the half latus rectum (t — Zira^ for the Period in a 
circular or elliptic orbit). 
Then writing