1^6 Mr. Ivory 07 i a new Method of deducing 
Where x® and which denote what x and ~ become at the 
dx 
dr 
dr 
epoch, are the arbitrary quantities necessary to complete the 
fluent: and the same things are to be understood in the ex- 
pressions of y and 2;. 
2. Of three observations which are necessary to determine 
a comet's orbit, let the epoch, or the instant from which the 
time is reckoned, be made to fall on the middle one ; and let 
— T denote the interval between the first and second obser- 
vations, which precedes the epoch ; and + t', the interval 
between the second and third observations, which follows the 
epoch; and further let x,y, z and r express the coordinates 
and radius vector of the comet at the first observation ; y\ 
z"", arid r®, the same quantities at the second observation; and 
x\y*, z\ and r\ those at the third : finally, let the values of 
the series denoted by 5 and o- (Equat. 2 and 3) be taken for 
the intervals — t and -j- “r' ; that is, let 
5=1 
X 2L^tL 
3 • 2ros 
pT* 
i_x 
^ — * 3 • roJ ' 2ros 
= — ■>■+ 673 + 
■then, on account of the equations (4), we shall get, 
0 dx° 
= sx 
b 
i 
dy^ 
= sy 
dz° 
= sz 
