156 Mr, Ivory on a new Method of deducing 
easy to prove from the nature of the parabola, they will be 
equal to the angles which the chord h makes with the axis of 
the orbit. From the angles thus found, the true anomalies 
are immediately deduced: for d is equal to the difference of <p 
and 4 ^; and u', to the difference of (p' and 4 ^'. Further, the time 
of passing the perihelion will be between the two extreme 
observations, when 4^ and are both greater than cp and cp' 
respectively : otherwise the time of passing the perihelion will 
be before, or after, both the observations, according as r, the 
radius vector at the first observation is less, or greater, than r', 
the radius vector at the third observation. But these rules 
suppose that the angular motion of the comet in its orbit, in 
the interval between the extreme observations, is less than 
180°; which, in fact, will comprehend all the cases that can 
occur in applying the method. 
The true anomalies of r and r', being known, the perihelion 
distance, denoted by D, will be found by either of these for- 
mulas, viz. 
D = r cos."" — 
2 
D = r' cos."" — . 
2 
To find the time of passing the perihelion, we must take 
the times corresponding to u and v from a table of the motion 
in a parabola ; these times, being multiplied by D^, will give 
the intervals between the two extreme observations and the 
time of passage. 
In order to determine the position of the orbit in the hea- 
vens, it is best to begin with seeking the heliocentric latitudes : 
let these latitudes be / and /' ; then 
sin. / = ~ , sin. x ; sin, /' z= ^ . sin. 
