( 541 ) 
§ 5. As an example of an application of this kind of differential 
equations I shall take the problem which Gatirzin ') has solved, 
without taking into account the difference between tand ¢'. In order 
to get a simpler representation, I shall modify his suppositions 
slightly, without changing the essential properties of the problem. 
I take, namely, two Hertz’s vibrators, which are at rest in the 
points P, and P,. Both vibrate in the same direction, normal to the 
line which joins them. I shall take the line passing through the 
vibrators as axis of 2, and the direction in which they vibrate as 
axis of z. If we call the distance between them # = 2, — #9, then 
we have 
Let us represent the moments of the vibrators by a, and a, and 
their distances from an arbitrary point Q by 7 and 79, and let us put : 
The electric force emitted by the vibrator in P, has a component 
in the direction of the z-axis, which in an arbitrary point Q 
amounts to: 
In the point Po, where y = 0, this component has the value of: 
Pda 1 da 
A VAA Ered Pica NS 
ha, >. at? Vv dt +7 i ‘ 
Let us further assume that the vibration in each vibrator sepa- 
rately is determined by a force proportional to the deviation, and 
; ; ; ds 
that moreover a damping exists proportional to — qo then the problem 
is reduced to the solution of two equations of the following form: 
da, da, 
+ 4, T+ Agar + A (GE) 44, ( 
TE) 4 Ay (as) = 0. (1) 
1) Wied. Ann. B, 56, H. 1. 1895, P. 89—94, 
