It is shown how a simple change of variable allows analysis of adsorption isotherms from an angle which is very different from the traditional one and eventually yields very simple equations characterizing the growth mechanism of the adsorbed molecule clusters in terms of fractal dimensions. The variable experimentally measured is the relative gas pressure p = P/P-0. The variable involved in most equations describing the variation of the number of adsorbed molecules N is p or the chemical potential mu, which is proportional to In(p). In the present approach, the variable is a length delta related to the mean free path (proportional to P-1) of molecules in the gas phase, at a constant temperature, by means of the following relation: delta = lambda. - lambda(0). It is shown that the derivative dN/d delta determined from the experimental data obtained for very different samples of silica or carbon materials and several adsorbates consists of one, two, or more power law regimes over the whole domain investigated, corresponding to p values ranging between 10(-6) and 1. The exponents can be related to a fractal dimension which characterizes the growth of the adsorbed molecule cluster, which is governed by the molecule-molecule and molecule-solid interactions, the surface heterogeneity, the surface fractal dimension, and the diffusion on the solid surface. It follows that the whole adsorption isotherm can be described by one, two, or more equations having all the same analytical form and describing the particular mechanism involved in each regime. It is shown that this new approach can be used to analyze any type of isotherm of adsorption on solid surfaces. However, in the particular case of adsorption on microporous solids characterized by a type I isotherm, which was previously investigated and which will not be considered in the present paper, the physical meaning of the results may be somewhat different. Examples of adsorption of nitrogen and argon on silica and carbon materials are presented and discussed. In the multilayer coverage domain, the results are compared to those obtained with the fractal Frenkel-Halsey-Hill equation.