The paper aims to provide new insights into the mechanism of adsorption of nitrogen at 77 K in the submonolayer range, by means of analysis of the isotherm derivative d[N(p)]/dp. For this purpose, a series of isotherms of adsorption on different types of carbons are analyzed. In order to investigate deterministic isotherms, a series of isotherms of adsorption in slit-shaped micropores, calculated by Lastoskie er al., are analyzed by the same method. It is shown that the derivatives can always be fitted to power laws, i.e., d[N(p)]/dp proportional to p(v) where -2 less than or equal to v less than or equal to 0. For carbons,several regimes, characterized by different v values are evidenced. In contrast, for silicas, a single power law (-1 less than or equal to v less than or equal to -0.5) is evidenced over a broad range of relative pressures (10(-6)-0.2). It yields a Freundlich equation after integration, whereas more than one equation is needed to describe adsorption on carbons. Depending on v, integration yields Henry, Freundlich, or Temkin equations or a new one ("C-type"), involving a negative exponent for p. Dubinin-Radushkevich plots, largely used for carbons, are also shown. The comparison with the derivatives provides explanation for the usual deviations from the DR equation. The exponent v is related to a fractal dimension D by means of the following relation : v (D - 4)/2. The physical meaning of D is discussed. When the solid surface is fractal, the upper value of D-s, which is deduced from v, is compared to the ones obtained by other methods. This work also provides a theoretical background for some usual empirical isotherm equations.