ADVERTISEMENT 



The Smithsonian Institution has maintained for many years a group of 

 publications in the nature of handy books of information on geographical, 

 meteorological, physical, and mathematical subjects. These include the 

 Smithsonian Geographical Tables (third edition, reprint, 1918); the Smithsonian 

 Meteorological Tables (fourth revised edition, 1918); the Smithsonian Physical 

 Tables (seventh revised edition, 1921); and the Smithsonian Mathematical 

 Tables: Hyperbolic Functions (second reprint, 1921). 



The present volume comprises the most important formulae of many branches 

 of applied mathematics, an illustrated discussion of the methods of mechanical 

 integration, and tables of elliptic functions. The volume has been compiled by 

 Dr. E. P. Adams, of Princeton University. Prof. F. R. Moulton, of the Univer- 

 sity of Chicago, contributed the section on numerical solution of differential 

 equations. The tables of elliptic functions were prepared by Col. R. L. Hippisley, 

 C. B., under the direction of Sir George Greenhill, Bart., who has contributed the 

 introduction to these tables. 



The compiler, Dr. Adams, and the Smithsonian Institution are indebted to 

 many physicists and mathematicians, especially to Dr. H. L. Curtis -and col- 

 leagues of the Bureau of Standards, for advice, criticism, and cooperation in 

 the preparation of this volume. 



CHARLES D. WALCOTT, 

 Secretary of the Smithsonian Institution. 

 May, 1922. 



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