dy CHC 4 
EL EE Oi 
dt 1 ( (0! ) y 2 ( 0 ) 
kk, +k ; 
ae ‘ley EHV FD AEC |» kyk, 0 
Suppose gd kt Vy ER AO = 2, 
De 0 
then 5 U — SRO cam = k 
dy 2 +4kC' 
and = a 
2k 7 
and when we call EEE == 
1 dt 2? + Ak C! 
ON de 2\@=2khz— Ae Oye Wk.) INC 
et Ak C! oF 
2° (Nkk, + 2k) z? +2 (NER, — UC — Nk, C,) 2 LANE EO 
Therefore : 
atpty=Nkk, + 2k (a); al Hay + By =2(NFE,—2kC'—NE,C,) (0); 
= apy = 4 NI KG on a RER) 
From (/) and (c) follows: 
28 (NIE, — 2k0’ — Nk?C,) + ANEL,C! 
aty= = 32 a = Sloane 
‘ 
ANRC’ 
a= — ET (e) 
vP 
From (a) and (d) follows: 
a? — (Nkk, + 2h)3? — 28(Nk%, — 2kC' — NIC) —ANEI,O . (fF) 
dz 
If there is equilibrium — ae becomes O and this happens when the 
( 
denominator of the above differential-equation becomes nought. The 
equation which we then obtain in z is the same as equation (/) in B, 
consequently @= 2, (the value of 2 in case of an equilibrium being 
x 
established). 
Again introducing the value for .V in equation (f) we obtain : 
f k. 5 
a3 — as 97.4 A2 ) sr yall “il 9: ee : 
p= lt INN ie I (9) 
ee Heb hee Ron 
(aar 7 me in i a 7 
