Carbon, hydrogen, sulfur, nitrogen, volatile matter content, and higher heating value of 6-21 samples for each of 11 U.S. coal sorts was checked for linearity versus ash content in order to learn how well they fit the two-phase model of coals. The linear relationship is very strong for carbon content and heating value within each seam, with correlation coefficients better than -0.998 in most cases, and with relative mean square errors (mse/mean) between 0.5% and 1.5%. The relationship is good for H, N, and VM content, with mse/mean of a few percent and poor for sulfur content, with mse/mean around 40%. Except for sulfur content, for which a pronounced inhomogeneity of samples is obvious, coal behaves as being formed of two "homogeneous phases": the maceral phase and the mineral phase, each one containing wellmixed individual maceral and mineral particles of small size as compared to the mass of the sample. Within a certain area of a given seam, the only variable is the ratio between the two phases, which changes with the location in the seam, while the composition of each of the mineral phase and the maceral phase is unchanged, explaining the linearity with ash content. Extrapolation of any coal property to the ash content of pure mineral phase, i.e., to nil organic carbon content, results in the respective property of the pure mineral phase (mineral matter minus inorganic oxides of the maceral ions), which cannot be evaluated by any other means, without inducing compositional changes. For the studied coals the following properties of the mineral phase were calculated, using the linear relationships: ash, volatile matter, carbon, hydrogen, sulfur contents, and higher heating value, as well as carbon dioxide and water emerged by ashing. Mineral sulfur content relates linearly to heating value of the mineral phase, with a slope close to the heating value of pyrite.