102 
mt;. j. h. jeans on the EQTTILTBPJUM 
There is tlierefore a rout at about r = I'Jo, but it is clear that we are already in 
the region at which the ap])roximatioii ceases to be satisfactory, and that we are close 
u])on the region in which the series become actually divergent. 
The smallness of (J^/dv indicates that somewhere in the neighbourhood of the point 
just calcidated we come to a point at wliich there is a pair of equal roots for r, and 
therefore a “minimum” in the value f)f This is the “neck” of which the first 
signs are apjrarent in fig. 5. Let us refer to all the matter to the left of this “ neck ” 
as tlie “ primary,” to all that to the right as the “ satellite.” Let the exact line of 
division l)e a vertical line at a distance 2 from the origin. 
The 2)rimary has been drawn with fair accuracy ; the satellite must be cLawn in 
the manner adopted in the difficult region of the former curve. 
The area of the primary was found to be 
11778 sq. millims., 
and this leaves 1312 sq. millims. to be accounted for by the satellite and the error in 
drawing. The centre of gravity of tlie primary was found to be 4v millims. to the 
left of the origin. Distributing the error as equally as possible, I have arrived at the 
curve of fig. 6. The area r)f primary and satellite are respectively 
11778 and 881 sq. millims., 
the error in area is a defect of 431 sq. ]nilli]ns., and tliat in the moment about (^ = 7r/2 
is that of an excess of 431 sq. millims. at the point v — 125 millims., (f) = 0. The 
error in the whole curve is therefore ahout 3 per cent. ; that in the satellite is 
unfortunately of the same order of magnitude as the satellite itself 
§ 32. Tlie following table sums up the results which have been obtained, and also 
ci.intains some new results. The moments of momentum of the last curves were 
obtained by a })recess of counting on squared papei', and are not carried to any great 
accuracy. 
Curve. 
Area. 
.■) 
(t>- 
•2-p ' 
Angular momentum 
^omitting factor 
(1) 
Circle .... 
1 
0 
0 
( 2 ) 
19 .... 
— 
1 
•43 
oo 
(3) 
J9 .... 
Point of bifurcation . 
1 
•5 
•35 
(4) 
Ellipse .... 
Ratio of axes v^S : 1 . 
1 
•43 
•44 
(5) 
„ fig. 4 . . 
Point of bifiu’cation : ratio 
of axes 3 : 1 
1 
•375 
•51 
(6) 
Fig. 5 . . . . 
= 4 . 
1 
•39 
•53 
(D 
Fig. 6 . . . . 
? ^ .... 
02=1. 
1 
•421 
•551 
(8) 
Separation of fluid into 
primary and satellite 
1 
•431 
•571 
(9) 
1 I'he tvo parts f 
Primary. 
•931 
•431 
•401 
(10) 
J of curve (8) { 
Satellite. 
•07 « 
•431 
•1711 
