INTRODUCTION 



"To those who are continually using interpolation methods, the use of 

 factorizing methods with which they are unfamiliar may at first attempt appear 

 more lengthy. Such workers will find, however, that this is not so ; and that 

 after becoming familiar with them, they are at least as short for finding loga- 

 rithms, and distinctly shorter for finding antilogarithms." That is what A. J. 

 Thompson had to say in the introduction to part viii of his "Logarithmetica 

 Britannica" about the factorizing method for finding logarithms and antiloga- 

 rithms. The present volume is devoted exclusively to the factorizing method 

 and is composed of two parts, as follows : 



Table 1 : 23-decimal-place values of the natural logarithms of XXXX, 



l.O^XXXX, and 1.0' XXXX, the range of XXXX being from 



1 to 10,000. 

 Table 2 : 23-decimal-pIace values of the common logarithms of XXXX, 



l.O^XXXX, and l.O^XXXX, the range of XXXX being from 



1 to 10,000. 



These tables should be a welcome addition to the existing tables of loga- 

 rithms. 



The optimui number of significant figures has been chosen for the range 

 of the argument. Five significant figures would increase the number of tabular 

 values from the existing 60,000, for both tables, to 600,000. Thus two rela- 

 tively large volumes would be required. Further the number of decimal places 

 of the logarithm has been extended to 23. This number is the natural point 

 of departure permitting the computation ab initio of the logarithm of the 

 fourth factor l.O^^XXXX . . . with ease; for the second term of the series 

 /n(l +x) —x — x-/2-\- . . . will affect at most the twenty-third decimal place. 

 The need for a fourth column is therefore eliminated. 



The computation of the logarithms, to the base e, of the integers was per- 

 formed with the aid of Wolfram's table, which contains the natural logarithms 

 of the first 2,200 integers and of primes and certain composite numbers up 

 to 10,009 to 48 decimal places. The table actually used was the one given in 

 "Thesaurus Logarithmorum Completus" (1794) by George Vega. A complete 

 list of known errors in this table was supplied by Prof. Raymond Clare Archi- 

 bald, of Brown University, along with an invaluable suggestion. The tabular 

 values for the second and third columns were obtained with the aid of the series 

 ln(l+:K) =x — x-/2 + x^/3— . . . , and calculated to 28 decimal places. All 

 the tabular values for the logarithms, to the base 10, were obtained by multi- 

 plying the tabular values in the table of logarithms, to the base e, by the 

 modulus 0.43429 . . . , to 28 decimal places. These values were rounded to 

 23 decimal places. Both tables were tested by applying differencing tests. 

 Throughout the duration of this project hand-operated, calculating machines 

 with 10 columns of 10 keys were used for the computing and checking of the 

 tables. 



