SMITHSONIAN MISCELLANEOUS COLLECTIONS V36

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLUME 3Resiearcl) 118 (WHOLE VOLUME) Corporation Jfunb SMITHSONIAN LOGARITHMIC TABLES TO BASE e AND BASE 10 Prepared by GEORGE WELLINGTON SPENCELEY, RHEBA MURRAY SPENCELEY, AND EUGENE RHODES EPPERSON Miami University, Oxford, Ohio (Publication 4054) CITY OF WASHINGTON PUBLISHED BY THE SMITHSONIAN INSTITUTION 1952 Z^t £or5 Q^afttmore (preeer BALTWOBB, HD., U B A PREFACE The tables here presented represent an adaptation of Hoiiel's factor- method of computing logarithms We became acquainted with Hoiiel's basic idea about 30 years ago, when we saw it explained and exemplified in Dr E R Hedrick's "Logarithmic and Trigonometric Tables." Fifteen years later we were using our own 20-place Hoiiel table of natural logarithms to compute the so-called "q's" used in preparing our "Smithsonian Elliptic Functions Tables" (published in 1947) At that time we conceived the idea embodied in the present tables and were so convinced of its possibilities that we carried out much of the early work in this izing secondary project simultaneously with the computation of the elliptic tables Originally we planned (i.e., to a table of natural logarithms only (i.e to base e), was decided to include common logarithms base 10) This doubled our work and necessitated some revi- but several years later it sion of computations already finished We feel that the completed design work and added expense While the tables were in preparation Miami University assigned four Paul Chifos, students to help in the work and paid them for their efforts Eugene Epperson, Steve Pizanis, and Russell Treon The loyal, painstaking, and efficient work of these young men was a continuing inspiration justifies the extra — to us, and all out of proportion to the remuneration they received In fact, Mr Epperson's work was so extraordinarily helpful that we have placed his name with ours on the title page Toward the end of our task of the manuscript to Dr A we sent photostatic copies of several pages J Thompson, computer and well-known editor of "Logarithmetica Britannica," for his expert appraisal, not for- getting to remind him that he himself had anticipated our idea by several His friendly and commendatory letter, including many suggested improvements, was a valuable aid and probably the deciding factor in the difficult task of promoting the publication of the tables We are deeply indebted to the Research Corporation of New York for the generous grant of funds to the Smithsonian Institution that made possible the publication of this book and also to Dr Alexander Wetmore, years Secretary of the Smithsonian, through whose interest and efforts the publiwas undertaken by the Institution Not only was Dr cation of the tables Wetmore tion, but chiefly responsible for negotiating the financing of the publica- he and his editorial volume through the staff have been most helpful in seeing the press G W S R M S Oxford, Ohio, June 24, 1951 CONTENTS Page Preface, by G W and R M Spenceley Introduction, by E R Epperson Logarithms Table Table of powers of 10 : Natural logarithms (to base e) : Common logarithms (to base 10) iii vii xii 203 392 xxxx LOGARITHMIC TABLES TO THE BASE 10 LOGARITHMIC TABLES TO THE BASE xxxx 10 393 394 xxxx LOGARITHMIC TABLES TO THE BASE 10 LOGARITHMIC TABLES TO THE BASE xxxx 10 395 396 xxxx LOGARITHMIC TABLES TO THE BASE 10 LOGARITHMIC TABLES TO THE BASE xxxx 10 397 398 xxxx LOGARITHMIC TABLES TO THE BASE 10 LOGARITHMIC TABLES TO THE BASE xxxx 10 399 400 xxxx LOGARITHMIC TABLES TO THE BASE 10 LOGARITHMIC TABLES TO THE BASE xxxx 10 401 402 xxxx LOGARITHMIC TABLES TO THE BASE 10 SMITHSONIAN INSTITUTION LIBRARIES 9088 01421 5057 55'?!!;!^'??x;^i)j?;^i;;ii!v''^?57'" smI ^*a!)rtVf>l^,';^WWM\'K(\;;i'.'o'\'>,