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OF

MATHEMATICAL TABLES.

BY

THE REV. JOSEPH A. GALBRAITH, M.A.,

FELLOW OF TRINITY COLLEGE,
AND KRASMUS SMITH'S PROFESSOR OF NATURAL AND EXPERIMENTAL PHILOSOPHY

IN THE UNIVERSITY OF DUBLIN:

AND

THE REV. SAMUEL HAUGHTON, M. A., T.R.S.,

FELLOW OF TRINITY COLLEGE,
AND PROFESSOR OF GEOLOGY IN THE UNIVERSITY OF DUBLIN,

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LONGMAN, BROWN, GREEN, LONGMANS, & ROBERTS.

1860.

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CONTENTS.

PAGE

V

I

INTRODUCTION,
LOGARITHMS OF NUMBERS FROM I TO 1000,
LOGARITHMS OF 1001 TO 1100 TO SEVEN PLACES,

13 MULTIPLES OF THE NUMBERS 2 '302585 AND Oʻ434294,

FOR CONVERTING COMMON LOGARITHMS INTO NA-
PIERIAN LOGARITHMS, AND vice versa,

14 A TABLE OF MANTISSÆ OF THE LOGARITHMS OF NUMBERS FROM 1000 TO 10000,.-.

15 SOLUTION OF THE QUADRANO EQUATION 22 +px +9=0,

BY TRIGONOMETRICAL: TABLES,
LOGARITHMS OF SINES AND TANGENTS TO EVERY MI-
NUTE OF THE QUADRANT,

117 SOLUTION OF THE CUBIC EQUATION 7 px 9 = 0, BY TRIGONOMETRICAL TABLES,

208 Gauss's SUM AND DIFFERENCE LOGARITHMS,

209 TABLES OF USEFUL CONSTANTS WITH THEIR LOGARITHMS, 247

116

.

INTRODUCTION.

1. Definition of Logarithms.--2. The Common System.-3. Properties of Loga

rithms.-4. Logarithmic Tables.-5. Multiplication by Logarithms.-6. Division by Logarithms.-7. Involution by Logarithms.-8. Evolution by Logarithms.-9. Tables of Logarithmic Sines.-10. Gauss's Logarithms.

1. Definition of Logarithms.—Let any number a be raised to the power n, and let the result be N; then

an = N

In this equation n is said to be the logarithm of the number N to the base a; and therefore

n

loga N

2. The Common System. The base of the Common System, or, as it is sometimes called, Briggs' System, is 10. If this number be raised to the powers, 0, 1, 2, 3, 4, &c., we obtain the series of numbers, 1, 10, 100, 1000, 10000, &c. Thus:

100 = 1
101 = 10
102

= 100
103 = = 1000

&C.,

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= 2

&c. Therefore,

log 1
log 10
log 100
log 1000 = 3

&c., &c. It is evident that for numbers intermediate to these, the powers to which 10 must be raised, must lie between the numbers of the series,

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