Elementary arithmetic, with brief notices of its history... by Robert Potts.

8

LOGARITHMS.

he thought that the change ought to be effected in this way-that 0;
should be made the logarithm of 1; and 10,000,000,000 the logarithm~
of the whole sine, which I could not but acknowledge was by far the,
most convenient of all. Therefore, rejecting those which I had before
prepared, I began at his exhortation to ponder seriously about the
calculation of these tables, and in the following summer I went again
to Edinburgh, and showed him the principal part of those tables
which are here published, and I was about to do the same the third
summer, if it had pleased God to spare him so long."
This workl contains the logarithms (1 being the logarithm of 10,
and 0 of 1) of numbers from 1 to 20,000, and from 90,000 to 100,000,
all to 15 places of figures, with a method of finding the logarithms of
the intermediate numbers. It may be noted that in some copies of the
" Arithmetica Logarithmica " there is found a table of the logarithms,
of the numbers 100,000 to 101,000, which appears to have been addedc
after the former tables had been printed. From the time of explaining the "Canon Mirificus" in his lectures till the publication of his
great work, he always regarded Napier as his guide. Both the
character of Napier, his friendly intercourse with Briggs, and the
respect with which they both wrote of each other, are scarcely in
unison with the opinion expressed by Dr. Hutton in the introduction
to his "Tables of Logarithms."
" Upon the whole matter, it seems evident that Briggs, whether
he had thought of this improvement in the construction of logarithms,
of malking 1 the logarithm of the ratio of 10 to 1, before Lord Napier
or not (which is a secret that could be known only to Napier himself), was the first person who communicated the idea of such an improvement to the world; and that he did this in his lectures to hi:3
auditors at Gresham College in the year 1615, very soon after hi3
perusal of Napier's ' Canon Mirificus Logarithmorum' in the year
1614. He also mentioned it to Napier, both by letter in the same
year, and on his first visit to him in Scotland, in the summer of the
year 1616, when Napier approved the idea, and said it had alreadyr
occurred to himself, and that he had determined to adopt it. It would
therefore have been more candid in Lord Napier to have told tho
world, in the second edition of this book, that Mr. Briggs had mentioned this improvement to him, and that he had thereby been confirmed in the resolution he had already taken, before Mfr. Briggs'scommunication with him (if, indeed, that was the fact), to adopt it iii
that his second edition, as being better fitted to the decimal notation
of arithmetic which was in general use. Such a declaration would
have been but an act of justice to Mr. Briggs; and the not having,
made it, cannot but incline us to suspect that Lord Napier was
desirous that the world should ascribe to him alone the merit of this
very useful improvement of the logarithms, as well as that of havingoriginally invented them; though, if the having first communicated an
invention to the world be sufficient to entitle a man to the honourof having invented it, Mr. Briggs had the better title to be called.
the first inventor of this happy improvement of logarithms."
The same kindly feelings existed between Briggs and Ptobert.
1 The title-page of the work bears these words:-" os numeros primus invenit
Clarissimus Vir Johannes Neperus, Baro Merchistonii; eos autem ex ejusdem
sententia mutavit, eorumque ortum et usumn illustravit Henricus Briggius, in
Celeberrima Academia Oxoniensi, Geometrie Professor Savilianus."