Before the end of the first year of the H.S.C. course, a boy has dealt with the elementary theory of indices and logarithms and has been introduced to the exponential and logarithmic functions in Calculus. This introduction, the writer has suggested in a previous Note (1896), may well be intuitive and may be based upon the fact that if y = ax, then dy/dx = ky, the fact being established by reading off gradients and ordinates from a suitable graph. It is now suggested that when the H.S.C. course in Calculus is completed, a mathematically-minded boy may learn a great deal of mathematical technique from a treatment of the exponential and logarithmic functions of the kind outlined below.