PREFACE 



The original object of this collection of mathematical formulae was to bring 

 together, compactly, some of the more useful results of mathematical analysis 

 for the benefit of those who regard mathematics as a tool, and not as an end in 

 itself. There are many such results that are difficult to remember, for one who 

 is not constantly using them, and to find them one is obliged to look through a 

 number of books which may not immediately be accessible. 



A collection of formulae, to meet the object of the present one, must be 

 largely a matter of individual selection; for this reason this volume is issued 

 in an interleaved edition, so that additions, meeting individual needs, may be 

 made, and be readily available for reference. 



It was not originally intended to include any tables of functions in this 

 volume, but merely to give references to such tables. An exception was made, 

 however, in favor of the tables of elliptic functions, calculated, on Sir George 

 Greenhill's new plan, by Colonel Hippisley, which were fortunately secured for 

 this volume, inasmuch as these tables are not otherwise available. 



In order to keep the volume within reasonable bounds, no tables of indefinite 

 and definite integrals have been included. For a brief collection, that of the 

 late Professor B. O. Peirce can hardly be improved upon; and the elaborate 

 collection of definite integrals by Bierens de Haan show how inadequate any 

 brief tables of definite integrals would be. A short list of useful tables of this 

 kind, as well as of other volumes, having an object similar to this one, is appended. 



Should the plan of this collection meet with favor, it is hoped that suggestions 

 for improving it and making it more generally useful may be received. 



To Professor Moulton, for contributing the chapter on the Numerical 

 Integration of Differential Equations, and to Sir George Greenhill, for his Intro- 

 duction to the Tables of Elliptic Functions, I wish to express my gratitude. 

 And I wish also to record my obligations to the Secretary of the Smithsonian In- 

 stitution, and to Dr. C. G. Abbot, Assistant Secretary of the Institution, for the 

 way in which they have met all my suggestions with regard to this volume. 



E. P. ADAMS 

 PRINCETON, NEW JERSEY 



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