Modal classifications of common volcanic rocks are expensive, difficult, or impossible to attain. As a consequence, these classified using the chemical composition. However, existing classificatory diagrams unable identify all 16 families rocks; most used is total alkali-silica (TAS) diagram that identifies six families. Rocks not in TAS misclassified with other rock names; their names evolving...

This papet studies the connections between the smoothness of a function and its degree of approximation by Chebyshevian splines. This is accomplished by proving companion direct and inverse theorems which give a characterization of smoothness in terms of degree of approximation. A determination of the saturation properties is included.