34 $ Dr. Herschel’s observations oj the satellites 
third is an alteration in the distance between the ascending 
node and the extreme point of the transverse axis of the 
ellipsis, into which the orbit is projected. 
In figure 1, (PL XVI.) suppose the circle PSFN to represent 
the plane of the orthographic projection, in which the angles of 
position are counted from the parallel P and F towards SandN, 
and expressed by the number of degrees 10, 20, 30 to 90 in 
each quadrant. Then let there be a moveable circle within 
the former, of which the degrees should be marked in suc- 
cession, 10, 20, 30 continued to 360. The inner circle being 
moveable, the line from 180 to 360 will express, by its dif- 
ferent situations, the position of the transverse axis of the 
ellipsis into which the orbits of the satellites at any given 
time are projected. The conjugate extending from 90 to 
270, and the lines parallel to it, will point out the direction in 
which the orbits will be more or less contracted according to 
the different inclinations of their planes to the plane of the 
projection. 
In a triangle PS p, figure 2, let P be the pole of the ecliptic. 
S, a point in the orbit of the satellite, 90 degrees distant from 
the ascending node, p , the point of the greatest northern 
elongation of the satellites, which on the moveable circle is 
marked 360. It is the zero of the ellipsis into which the 
orbits of the satellites are projected, and its calculated situa- 
tion will regulate the adjustment of the moveable circle. N, 
a point in a meridional direction, 90 degrees distant from the 
geocentric place of the planet. The arch PS then being the 
complement of the inclination of the satellite’s orbit to the 
ecliptic, is therefore given ; and the angle at P is equal to the 
distance of the longitude of the planet from the node. The 
