of the Georgian planet . 347 
angle at S is a right one ; and the arch PN, being the mea- 
sure of the angle of position of that point of the ecliptic where 
the planet is situated, may be had by Table LIII, published 
in Dr. Maskelyne’s first volume of Observations. 
To find what alteration has taken place in the situation of 
the parallel with regard to the point p, we calculate the posi- 
tion of this point for any given time by the following analogy. 
(1 ) cos P : rad : : tan PS : tan Pp ; and the difference between 
PN and Pp will give Np ; the complement of which is the 
position of p, with regard to the parallel. When Pp is greater 
than PN, the position of P being north following, that of p 
will be north preceding ; but when Pp is less than PN, it 
will be north following. 
To find the inclination of the plane of the satellite’s orbit 
to the plane of projection, we have only to calculate the dis- 
tance of the poles of these planes ; and since the place of the 
planet is the pole of the projecting plane, and since also the 
situation of the pole of the orbits is known, which is in longi- 
tude 15 degrees 30 minutes of Gemini, and latitude south 
ii° 2', therefore in the right angled triangle figure 3, of 
which GL is the distance of the planet from the longitude of 
the pole, and PL the given latitude of the pole, we have the 
analogy ( 2 ) rad : cos GL : : cos PL : cos GP ; which is the 
required inclination of the two planes to each other. 
To find the distance of the point p, or zero of the projected 
ellipsis from the ascending node, by figure 2 we have the 
analogy (3) rad : sin PS : : tan P : tan Sp ; and go 0 -f- S^>, 
before the node, and go° — Sp, after it, will give the distance 
of p, or zero point of the inner circle from the ascending 
node. 
Yy 2 
