666 
Let us now try to find the condition that the real root is negative. 
Let us for this purpose follow the course of the values in the left- 
hand member. We put: 
a 
1 
mre emg) 
foryp = — % y= — 0 
a 
Ned eh y=—— A, 
q 
t 
If the real root must be negative, tens A must be positive or: 
q 
a> Ag ol. 8. Oe 
which also appears in the first remark on the energy below. 
Finally the condition that the real part mentioned must be nega- 
tive; it becomes: 
1 3 
Voss VD+4"—4Q—VD>0.. (LI) 
dsx 
energy, but also that with regard to the force q —. For I interpret the whole 
dt? 
lefthand member of the equation (1) as a set of forces that keep each other in 
equilibrium : 
dr : 
ae force of D'ALEMBERT for the motion 
Ch 
xq at frictional force 
(a—Aq) x quasi elastic force and 
On : 
q-—— another elastic force. 
dts 
A second remark should be made on the limiting cases. As point of issue we 
have equation (1) of § 2, in which 
bt 
RI Pien igs 
When we make q approach zero, and A approach oo, we get: 
t 0 
de HEEE RS 
tea q uae(yafe ads = + x(t) Aq 
calling lim Aq= Bf, we get: 
: Sn 
de + (e—8)2=0, 
the equation for the ordinary periodic motion. — This equation is, indeed, imme- 
diately found when we take equation (2), multiply both members by gq, and then 
substitute q =O and Aq= 8. 
Let us finally treat equation (1) of § 2 with the general U (t— 7) approximating 
