476] 
ORBIT OF A PLANET FROM THREE OBSERVATIONS. 
403 
7. I say that in the first of the cases above considered the locus of the orbit- 
pole is a separator; in the second case the orbit-pole is a point B; in the third case 
the locus is the regulator; and in the fourth case the orbit-pole is a point A. 
8. In the absence of models, the spherical figure must be represented by a pro 
jection ; the stereographic projection is convenient for facility of description; and it has 
the very great advantage that we can by means of it exhibit, no matter how large 
a portion of the spherical surface. In the figures called “ spherograms,” afterwards 
referred to, the representation of a hemisphere is all that is required; but, to give a 
more distinct general idea, I annex a figure representing a larger portion of the 
surface; the data are those belonging to the particular symmetrical case referred to as 
intended to be specially considered: and the regulator conic is accordingly a pair of 
opposite small circles, the points A and B being related to it symmetrically; but, 
disregarding these specialities, the figure is adapted to the illustration of the general 
Fig. 1. 
A 
case (at least if the point S be situate within the hyperboloid), and it is here given 
for that purpose. The circle marked “ Ecliptic ” does not properly belong to the figure: 
it is added as showing the boundary of a hemisphere, so that, by omitting all that 
lies outside this circle, the figure would be limited to the representation of a hemi 
sphere ; and the orbit-pole be in every case represented, no longer as a pair of opposite 
points, but as a single point; we should have the separators each as a half circle, and 
the regulator as a single small circle; the separators would intersect in pairs, in the 
three points B, and would touch the regulator in the three points A, &c. 
9. The figure constructed as above, but omitting so much of it as lies outside 
the ecliptic circle, is the representation of a hemisphere—say of the northern hemi- 
51—2