HISTORICAL NOTE ON THE DIFFERENTIATION OF A 



LOGARITHM. 



BY FLOKIAN CAJORI. 



The preface of Olney's Calculus contains the following pass- 

 age: "In conclusion I must do myself the pleasare to acknowl- 

 edge my indebtedness to my accomplished colleague and friend, 

 Prof. J. C. Watson, Ph. D., for the original, direct, and simple 

 method for demonstrating the rule for differentiating a logar- 

 ithm .... ivhich banishes from the Calculus ihe last 

 necessity for resort to series to establish any of its fundamental 

 operations.'^ Statements to this effect are also found in a few 

 more recent American works on the Calculus. 



Dr. E. W. Davis has called my attention to the fact that a 

 method of proving the rule for differentiating logarithmic 

 expressions without resorting to infinite series is given in De 

 Morgan's Calculus. I see that such a method is found also in 

 John Rowe's "Introduction to the Doctrine of Fluxions," 

 Fourth Edition, London, 1809. The first edition was printed in 

 1751. Doubtless other old books with similar methods of 

 demonstration which do not involve infinite series can be found. 

 The credit of first banishing from the Calculus " the last neces- 

 sity of resort to series to establish aiiy of its fundamental oper- 

 ations " can, therefore, not be ascribed to Watson. 



