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

4
DEF. The integral part of a logarithm is named its characteristic,
the decimal part its mantissa.'
In all arithmetical computations by logarithms, the mantissa is
always positive, but the characteristic may be positive or negative.
6. Pnor. To explain the advantages of that system of logaritfhms wtiose
base is 10, the same as the radix of the scale of notation.
By considering logo(10\.n) and log, 10;
log10I0.u} = log, lO1+logl,^ = 2n logo,10 + loglou = n + log,1c,
and log, { '1 } = logot - logilO" - logol 0+ loglou= - + logot;
That is, the logo{1lO.u} and logo { o } are found from logio i,
by simply ine;-easing or diminishing the characteristic of log,0o by n.
Hence, the logarithms of all numbers consisting of the same significant figures, whether integral, decimal, or partly integral and
partly decimal, have the same mantissa; the only difference being in
the value of the characteristic.
7. PROP. To find the law of the characteristics of that system of loga#oithnzs whose base is 10.2
Let any integral number A consist of n digits.
It lies between 10"1- and 10";
The word mcantissa appears to be a Tuscan word, formerly employed in commerce,
and meaning over-measure or over-weight, "additamentum quod ponderi adjicitur."
The following logarithms of the prime numbers less than 100 are here given to
enable the student to obtain numerical results in the exercises. In the printed
tables of logarithms, the characteristics are omitted, and only the decimal parts are
given without the decimal point. Of the Mathematical tables published by Dr.
Hutton, one table calculated to seven places of decimals contains the logarithms of
trhe natural numbers from 1 to 100,000. In the table published by Mr. Babbage, the
logarithms of the numbers are extended from 1 to 108,000, and very great care was
taken by Mr. Babbage to secure the accuracy of them.
Nos. Logarithms. Kos. Logarithm Nos. Loaitms..
2 3010300 29 4623980 61 7853298
3 4771213 31 4913617 67 8260748
7 8450980 37 5682017 71 8512583
11 0413927 41 6127839 73 8633229
13 1139434 43 6334685 79 8976271
17 2304489 47 6720979 83 9190781
19 2787536 53 7242759 89 9493900
23 3617278 59 7708520 97 9867717
If,he number assumed for the base of a system'of logarithms be the same as the
radix of the system of notation employed, a great advantage arises; as in the system
of notation whose radix is 10, the mantissa of any number composed of the same
digits will have the same mantissa, whether the number be integral, or decimal, or