210 
11B into which it passes when e, = e, = — }e, and when e,——2e,. 
In the other case (7s w,) z varies from e, to e, and from e, to 
e,, While p changes from O to 2w, and from 2m, to 4m,. There 
are various cases: 
A. ¢, 24. 2 varies between —i and 2, p between g, and 4, for 
which 
—-4=?G¢9, + W‚) and 3 — PEP: + ,); 
p‚ lies between O and ow,, gy, between 0 and 2w, (vy, > ¥,). 7 changes 
between oo and a. This case corresponds to 114 and passes into 
it for 4, == 
B. e,S—1,e, <2. z varies between —+ and e,, p between gp, 
and 2w,; 7 changes from oo to a/(t He), a value between 2« and 
«. This corresponds to 11C, in which it passes for e, = e,, , then 
becoming infinite. 
C. es > —+,¢, <4. 2 varies between e, and e,, p between — oo 
and —+ oo; 7 changes from a/(t-+ e,), whieh may have all values 
> 3a, to a/4+e,), which may have all values between 2« and « 
The case corresponds to 110, in which it passes for e, =e, > 0; 
if e, <0 there is no corresponding degenerated case. 
Two roots are conjugate complex. The value which in (25) is 
possible for is is 0. Then z varies from oo to e, and back. So if 
eé, 22 this case is impossible. If —1 < e, < 2, z varies between 3 
and e,, p between a value g, for which 
PGP) =3 
(situated between O and 2w,) and 4m,—g,. 7 changes from a to 
aft + e,), which may have any value >a, and then returns to «. 
This case can pass into 10, if e, and e, approach to the same 
negative value: and, if e, becomes negative, it may divide itself 
into 1148 on the one hand and 110 or 11D on the other (11C if 
é< 1, 41D fe, 4). 
We now have a survey ofall possible motions. We must, however, 
remark that not all the motions take place with a velocity smaller 
than that of light, as in case of some of them (e.g. 114 and 124) 
A and so also ZL is negative. We have not separately mentioned 
all those cases. In 11 eg. a? <4, means that the velocities are 
smaller than that of light. In 12 for that purpose e, ¢, + @, 23 + €3 € 
has to be >—+4. 
18. It is now necessary to consider the place taken up in this 
survey by the well-known. motions of the planets and comets. These 
motions ail take place with small velocities; we will call a quantity 
