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by. the condition of the vibrator at the moment # at which the 
vibrations were given out, i.e. at the moment which precedes with 
a ‘ 
an interval of 2 = the moment, at which we want to know the 
way of motion. The equation of motion, which determines the motion 
of the vibrator, will therefore besides the electric moment of the 
vibrator and its fluctions at the moment ¢, contain the same quantities 
r 
at the moment t’=t— 2 ak 
Similar problems of a more intricate kind may occur in great 
numbers. First we may want to examine the influence which diffe- 
rent vibrators exercise on each other, in which case a set of simul- 
taneous differential equations is to be solved which show the pecu- 
liarity which we are discussing. 
Further the different bodies in question may move, which makes 
r and therefore the difference of time between ¢ and f variable. If 
we have e.g. a vibrator, which moves normally towards a reflecting 
plane, it will have been at the moment ¢’ at a distance from the 
wall which we call 7’, so that: 
Now it may be that we want to examine the ponderomotoric 
actions, so that the quantity 7, which occurs in #’ is at the same 
time the quantity, which is not given as function of t‚ but which 
we want to determine as function of ¢ by means of the differentia] 
equation. 
Similar problems are of course also found in the theory of sound. 
Though these problems are possibly not of so much importance, 
that it is worth while drawing up a complete theory of the equations 
in consideration, I will point out some particulars of the solutions, 
as they have never been discussed as far as I know. 
§ 2. In the physical problems there occur always differential 
equations. I will however begin with the simpler case in which 
the equation to be solved does not contain any differential quotients. 
In general such an equation may be represented by: 
Dia yc, 2) — 0. 
Here y' represents the value of y which is obtained by substi- 
