180 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1914. 
purpose, which made of them a work almost without rival for its 
beauty. 
Finally, it is known that the distinguished professor of astronomy 
at the Sorbonne, Prof. Andoyer, has now undertaken the task of 
recalculating a complete table of logarithms, which im this branch 
of learning, will remain as the most important work of our epoch. 
Let us add, as a matter of curiosity, that certain. tables, of very 
restricted length, have been published with a very great number of 
decimals for the extremely precise calculations exacted by certain 
purely theoretical questions. We may cite in this connection the 
Wolfram tables with 48 decimals; those of Sharp with 61 decimals; and 
finally, those of Adams with 260 decimals. These last contain only 
the natural logarithms of the numbers 2, 3, 5, 7, 10, and that of the 
factor (modulus) which permits passing from these logarithms to the 
common logarithms. 
In the above remarks concerning the process used by Prony in the 
calculation of his tables, it has been shown that the greatest part of 
the work is reduced to simple addition required by the application of 
what mathematicians call the method of differences. This im- 
mediately brings up the possibility of entrusting the preparation of 
the tables of logarithms to calculating machines, of the type called 
“for differences.’ This is not a matter of fiction, for a machine of 
this type invented by the Swedes, Schentz, father and son, and shown 
at the Universal Exposition in Paris in 1855, has been found adapted 
to such an operation. And not only does it effect the calculation of 
logarithms, but it also stamps the results as depressions in a lead 
plate after the method of stereotyping, calculating and stereotyping 
at the same time two and a half pages of tables in the same time that 
a good compositor would need to set up a single page. Through the 
liberality of a wealthy. American merchant, Mr. Rathbone, this 
machine became the property of the Dudley Observatory at Albany, 
N. Y., and has there effectively served to calculate tables of which 
some examples were put on sale in Paris in 1858. 
However invaluable the tables of logarithms may be to calculating 
humanity, they do not in themselves constitute the entire benefit 
derived from the ingenious invention of Napier. Indeed, scarcely 
had this invention come to light when it was transformed by the 
Englishman, Gunter, into the logarithmic scale, on which the functions, 
at least for certain numbers, are at distances from the origin propor- 
tional to the logarithms of these numbers. This simple scale of 
Gunter, a kind of graphic representation of Napier’s table, was in its 
turn to become the source of a number of improvements in the 
organization of means by which the calculator could more and more 
simplify his task. It was in fact Gunter’s scale which gave birth to 
the slide rules or calculating circles whose use is to-day so widely 
