468 
ON THE DETERMINATION OE THE 
[476 
between the inner circular region and the three outer regions, but it must be recol 
lected that for certain given values of the parameter, the points A may be isolated 
points on the isoparametric line. 
115. It is sometimes necessary (more particularly as regards the Time-spherogram 
and isochronic lines) to distinguish from each other the several points A and B; and 
for this purpose I consider the several points, as situated in the spherogram, to be 
accented in the following manner: 
i? IV B' B 
A' A 
B "> ß" 
B y 
so that the inner triangle is B'B"B"’ and the outer triangles are BB'B", B'B 1V B'" and 
B'"B Y B" respectively; this distinction has been already partially made in Fig. 10. 
Article Nos. 116 to 122. The e-spherogram and I seccentric Lines, See Plate IV. 
116. Constructing a blank spherogram as above, we may from the tables for 
planograms Nos. 1 and 2 lay down numerically the values of the eccentricity at the 
several points of each meridian for the longitudes 0°, 30°,.. 330°, viz. 
Longitudes 
0°, 60°, 120°, 180°, 240°, 300°. 
Planogram No. 2 shows that e increases from 0 at 
the centre to oo at 60°, then, 60° to 63° 26' (shaded 
region), it diminishes from oo to 4*912; on passing 63° 26' 
it changes abruptly to 1*853; thence diminishes to a 
minimum = *628 at 59°, and again increases to 1*018 at 
90°. 
Longitudes Planogram No. 1, part 1, shows that e increases 
10°, 210°, 330°. from 0 at the centre to oo at 60°, then, 60° to 73° 54' 
(shaded region), it diminishes from oo to 2*309, this last 
value being at a point B, the termination of the sphero 
gram. 
Longitudes Planogram No. 1, part 2, and for values over 90°, 
30°, 150°, 210°. part 1, shows that e increases from 0 at the centre to 
*264 at 60° (point A), *869 at 90°, and 2*309 at 100° 6', 
point B. 
It will be recollected that, although e has the same value, 2*309 at the two 
opposite points B, yet there is an abrupt change of orbit, indicated by the change of 
sign of A (= + e). 
117. Planogram No. 3 
iseccentric lines. Planogram 
shows the directions at the points A of the several 
No. 4, if the calculations were completed, would give the