In a recent paper (these Proceedings (2), 6 (1939), 75–8), C. G. Lambe established, and gave some applications of, the formula

in which Ds is the symbol for the derivative of fractional order s. Lambe's proof of (1) is not quite rigorous and it does not bring out the conditions which have to be imposed upon f(x) in order to make (1) true. Furthermore this proof does not give any evidence as to the definition of fractional derivative which is to be used in connection with (1).