It is known that the surface of a solid body and its volume part are different forms of the same substance. There is a hypothesis about the presence of a transition fractional-dimensional layer, which is the "limiter" of the volume from the surface. It is assumed that this layer is able to store information about changes in the surface and internal structures of the solid. The origin of defects, leading to destruction, in most cases begins in the surface and surface layers of the metal. In this regard, the existence of fractional-dimensional layer as a subsurface structure, which has information about the properties of the whole solid, is of particular importance in the detection of possible critical defects. In order to test this hypothesis, an experiment was conducted based on measuring the magnetic field strength of a steel plate (25x25x2 mm) when its thickness was changed. With the help of sandpaper, one side of the plate was swamped, and the second remained unchanged. The measurements of the magnetic field strength components were carried out on both sides with the plate thickness decreasing by 0.08-0.1 mm from 2.0 to 0.3 mm. Applying a linear approximation to the obtained dependence of the average tangential component of the magnetic field on the plate thickness, it was found that the extrapolated approximation line comes to a point close to zero (0.01 mm). It was assumed that the value 0.01 determines the preliminary value of the fractional-dimensional layer. Such an experiment was carried out for the first time, so the results obtained so far will undoubtedly become the basis for further research in this area.