IN connection with the correspondence on this subject in NATURE, attention may be directed to the attempts made by C. Benedicks (Zeit. f. anorg. Chem., vol. xlvii., p. 455, 190s; Ann. d. Phvsik, vol. xlii., p. 153, 1913) to relate the hardness (H) to the other phvsical properties of the substance. He suggested that H is inversely proportional to the atomic volume (V) and to the coefficient of expansion (α), and therefore HVα is constant for different elements. This result includes the relation given by Mr. J. Innes (NATURE, November 18). Benedicks also proposed a new formula for the characteristic frequency (v) of an element of atomic weight A in the solid state. He assumed that the frequency is proportional to √(H/A), and hence to √(1/VαA). If the further assumption be made that the frequency so determined is identical with the frequency given by one or other of the formulae summarised by Mr. V. T. Saunders (NATURE, December 23), other relations between the physical constants may be obtained. For example, according to the Sutherland-Lindemann formula ν is proportional to √(Ts/AV/2/3), where Ts is the melting point on the Absolute scale. Combining this with the previous result, we find αV1/3/Ts = a constant, a relation given by Pictet in 1879.