The concept of a colloid as a set of layers is common in colloid chemistry \cite{Pechenyuk}, \cite{VFMarkov}. The layers will have one or another electrical moment in the case of rare metal oxyhydrates, since they are composed of electrically polar long molecules \cite{Fridrichsberg}.

It has been experimentally discovered that between electrodes placed in a colloidal substance and connected via a measuring device, a certain potential difference arises, and the device records a spontaneous electric current \cite{Sukharev1}. The diagram of the current's dependence on time appears chaotic, but the Fourier transform over time for a finite time interval (over the measurement interval) shows with high reliability the presence of harmonic oscillations of various frequencies. In this case, the frequencies are discrete and increase linearly with the frequency number.

The conclusion seems possible that the detected oscillations are a consequence of oscillations of long molecules having electric moments due to the layered structure of the colloidal substance, and the measuring device records these oscillations. Note that such an assumption is confirmed by the presence of long rod-shaped fragments in the rare metal colloid, visible at x1000 magnification.

The experimenter has access, at best, to the initial and final location of the fragment, since all measurements occur over a finite time interval. At the same time, the change in the shape of a long molecule is of considerable importance, since it can be used to draw conclusions about the chemical composition of the substance, its changes over time, the homogeneities and heterogeneities of the colloid, the flows of substances filtered by the fragments, the sorption properties of the gel, and much more.

Oscillations of structural units on a finite time interval with conditions at the initial and final moments are determined by the solution of the Dirichlet boundary value problem, which is ill-posed \cite{Ivanov}, \cite{Lavrentiev}. Therefore, a complexity arises from the fact that the solution of such a problem may not exist, be non-unique or unstable with respect to the initial data.