This is a presentation of research into the inductive solution to the problem on the internal constitution of stars. The solution is given in terms of the analytic study of regularities in observational astrophysics. Conditions under which matter exists in stars are not the subject of a priori suppositions, they are the objects of research. In the first part of this research we consider two main correlations derived from observations: "mass-luminosity" and "period - average density of Cepheids". Results we have obtained from the analysis of the correlations are different to the standard theoretical reasoning about the internal constitution of stars. The main results are: (1) in any stars, including even super-giants, the radiant pressure plays no essential part - it is negligible in comparison to the gaseous pressure; (2) inner regions of stars are filled mainly by hydrogen (the average molecular weight is close to 1/2); (3) absorption of light is derived from Thomson dispersion in free electrons; (4) stars have an internal constitution close to polytropic structures of the class 3/2. The results obtained, taken altogether, permit calculation of the physical conditions in the internal constitution of stars, proceeding from their observational characteristics L, M, and R. For instance, the temperature obtained for the centre of the Sun is about 6 million degrees. This is not enough for nuclear reactions. In the second part, the Russell-Hertzsprung diagram, transformed according to physical conditions inside stars shows: the energy output inside stars is a simple function of the physical conditions. Instead of the transection line given by the heat output surface and the heat radiation surface, stars fill an area in the plane of density and temperature. The surfaces coincide, being proof of the fact that there is only one condition - the radiation condition. Hence stars generate their energy not in any reactions. Stars are machines, directly generating radiations. The observed diagram of the heat radiation, the relation "mass-luminosity-radius", cannot be explained by standard physical laws. Stars exist in just those conditions where classical laws are broken, and a special mechanism for the generation of energy becomes possible. Those conditions are determined by the main direction on the diagram and the main point located in the direction. Physical coordinates of the main point have been found using observational data. The constants (physical coordinates) should be included in the theory of the internal constitution of stars which pretend to adequately account for observational data. There in detail manifests the inconsistency of the explanations of stellar energy as given by nuclear reactions, and also calculations as to the percentage of hydrogen and helium in stars. Also considered are peculiarities of some sequences in the Russell-Hertzsprung diagram, which are interesting from the theoretical viewpoint.