206 
If we now introduce a new variable 
= te Je 1 
b 2 — Lv eS 3 
putting 
= Lag 
é, = 4, zs 
=p ad 
Ee dz Sit 
i= £545 
we obtain 
— Gz 
dy = —— ike Se or 
V(z—e,)(z—e,)(z—e,) 
and we have 
e, t és + Ez |, . . e e * . e a (24) 
Now, introducing the P-funetion with the roots ¢,, e,, e,, we get 
z= P(ig+ C), 
where (C is a constant of integration, which may be complex; the 
real part is without signification as it only determines the direction 
in which y will be zero. We take 
PPG A 8) ar ee 
and then find 
a 
PENN 
From (14) now follows 
BAE i Ne Saal =—a’- deci 
ae aw (1—-«#) v(1 EV («—2,)(a—2,)\(a—a,) 
5 
or 
B -—dz 
= t= : == = (27) 
= 5 +4)*(3—<V (2 —e,)(z > e,)(2—é;) 
The problem under consideration gives rise to four constants of 
integration; two of which are e, and e,, the two others s (which 
can have only particular values) and a constant which arises after 
integration of (27) and is of no consequence as it only determines 
the moment at which ¢— 0. 
From (27) it now follows immediataly that the particle can never 
reach sphere r—a. For, if r became a, then z became $; (27) 
shows that tbis would require an infinitely long time. Sphere r= e, 
therefore, is never reached. 
It also follows from (27) that an infinitely long time is required 
for z to reach — 4. This is not at all strange, z= — 4 correspond- 
ing to ro. It may occur (if two e’s coincide) that there is still 
another value of + which cannot be attained, but is gradually 
approached; we will treat this case where it occurs. 
