Four figure mathematical tables: comprising logarithmic and trigonometrical tables, and tables of squares, square roots, and reciprocals ..

1905·3.6 MB·English

by  Bottomley, J. T. (James Thomson), 1845-1926

OUR
laCURE
MATHEMATIOAL TABLES
OTTOMLEY
MEMORIAM
IN
FLORIAN CAJO
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» • • I U. > U • A,^ B 11-
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FOUR FIGURE
MATHEMATICAL TABLES.
f
FOUR FIGURE
MATHEMATICAL TABLES
COMPRISING LOGARITHMIC AND TRIGONOMETRICAL TABLES, AND
TABLES OF SQUARES, SQUARE ROOTS, AND RECIPROCALS.
BY
T. BOTTOMLEY, M.A, LL.D., D.Sc,
J.
F.R.S., F.R.S.E., F.C.S.,
LATE LECTURER IN NATURAL PHILOSOPHY IN THE UNIVERSITY OF GLASGOW.
MACMILLAN AND
CO., Limited
NEW YORK THE MACMILLAN COMPANY
:
1905
A/i rights reserved
First Edition 18S7.
Reprinted 1890, 1893, 1894, 1S96, i?97, 1899(twice), 1900, 1901,
1902, 1903(twice). With additions 1904, 1905 (twice).
CAJORI
GLASGOW PRINTED AT THE UNIVERSITY PRESS
:
BY ROBERT MACLEHOSE AND CO. LTD.
' > >' J 1 ) J * ' »
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EXPLANATIONS AND » >R)>U.J LES
FOR THE
USE OF THE ACCOMPANYING TABLES.
The logarithm of a number consists in general of two parts, an
integer part and a decimal. The integer part is called the Index or
Characteristic; the decimal part is called the Mantissa.
RULE I, The Index of the logarithm of a number greater than
unity is the number which is less by one than the number of digits in
the integral part of the given number.
Thus, the index ofthe logarithm of 47320 is 4.
473-2 is 2.
4732 is o.
RULE n. The Index ofthe logarithm of a number less than unity,
and reduced to the form of a decimal fraction, is negative, and is a
higher number by one than the number of zeros that follow the decimal
point of the given number.
Thus, the index of the logarithm of '4732 is - i
-
•004732 is 3
To denote that the index is negative the sign minus is often
written above it ; thus T, 3.
RULE III. To find the mantissa of the logarithm of a given number
—
consisting of four figures. Find the Jirst two figures in the left hand
column of the table. Pass along the corresponding horizontal line and
take the number in the vertical column headed by the third figure.
To this number add the number found in the difference columns under
the fourth figure of the given number. The sum with a decimal point
prefixed is the required mantissa.
911380
—
•
MATHEMATICAL TABLES.
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Example. Find the mantissas corresponding to the sequences of
figures 4732 and 6985.
473 -': - - - - 6749
: ;
'2.from dif. col. - - 2
;
.CC C,f«CC I •
•6751
•»
698 8439
5 from dif. coL - - 3
•8442
RULE IV. To find the logarithm of a given number consisting of
four figures.—Find themantissa corresponding to the givenfourfigures,
and to it prefix the proper index. The number thus obtained is the
required logarithm.
Exa//:p/es.
log 47320 - - - is 4-6751
log 47-32 - - - is 1-6751
log 6-985 - - - is 0-8442
log 0-006985 - - - is 3 8442
A^o^e.—A logarithm whose index is negative really consists of a
positive mantissa with a negative index algebraically added to it.
Thus:— 7-8442= +0-8442- I. It is important to bear this in mind
in numerical operations on logarithms. For example, in taking the
square root of 0-6985, the logarithm of that number is divided by 2,
and in taking the cube by 3. The simplest way of doing this is
as follows
: |(-8442- i)=1(1-8442 -2)=-9221 -I
IC8442- =^2-8442 -3;= -9481 - I
RULE V. To find the anti-logarithm of a given logarithm, i.e., the
—
number corresponding to the given logarithm. Find in the table of
anti-logarithms, proceeding as in Rule III., the sequence of figures cor-
responding to the man/issa of the given logarithm. To these figures
place a decimal point, in the position indicated by the index of the
given logarithm, prefixing or affixing zeros, if necessary. (See Rules I.
and II.) The number thus obtained is that required.
Examples. Given the logarithm 27834 find the anti-logarithm.
783 6067
4 from dif col. - - 6
6073
Hence the number whose logarithm is 2-7834 is 607-3.