Six-figure logarithms, cologarithms and antilogarithms [antikvár]

PREFACE The tables of logarithms and antilogarithms in this work were formerly published with logarithmic trigonometrical functions, because logarithms of trigonometrical functions are useless unless logarithms of numbers are available. Calculations are more straightforward if antilogarithms are available as well. These two tables are now published separately, to provide flexibility now that the book is one of a series, and the opportunity has been taken to include a table of cologarithms to supplement the table of logarithms. Few tables of logarithms are available to six-figure accuracy; antilogarithm tables are even less common and cologarithms are virtually unobtainable except in this work. Cologarithms simplify one of the most frequent kinds of calculation, by enabling combined multiplication and division to be replaced by a single addition. Interpolation by mean proportional parts is little used in con- junction with tables to more than five-figure accuracy yet this is the simplest of all methods of interpolation. The method is inherently less accurate than interpolation based on actual differences so the compiler must take special care to keep errors under control and, as with all methods of interpolation, he should indicate the maximum error that can occur. Accuracy may be considerably enhanced by providing mean proportional parts on each page, so that entries in the table are averaged in groups of five instead of ten. As far as is known, this is the first time mean proportional parts have been provided in this form but the principle is, of course, the same as that used in smaller table books, when a row is split into two halves, on separate lines, and mean proportional parts are provided for each line. Mean proportional parts have acquired an undeserved reputa- tion because this method of interpolation has hitherto been confined to small works, where compilers have sometimes allowed the method to give grossly misleading results. The