While in recent years the market has been flooded with small books of mathematical tables, each of which reproduces most of the defects of the others, there are few tables, if any, which meet all requirements when it is necessary to use logarithms for operations involving both multiplication and division. In such cases logarithms of reciprocals are constantly needed. Few tables contain these, a notable exception being the tables at the end of Carson and Smith's Algebra. On the other hand, tables of reciprocals are often given, which are rarely of use except in geometrical optics, and only confusion is occasioned by the separation of the tables for logarithms and antilogarithms, and of those for sines and cosines. Either the table of antilogarithms or that of logarithms may be banished with advantage.

If we retain the table of logarithms, it is impossible to obtain logarithms of reciprocals without performing an additional operation, which increases the work and the risk of error. Further, in the lowest parts of the scale the differences are large, and it is difficult to pick out the number which represents the logarithm correctly to four or five places of decimals as the case may be.