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 AND THE REV. SAMUEL HAUGHTON, M. A., F. R. S., FELLOW OF TRINITY COLLEGE, AND PROFESSOR OF GEOLOGY IN THE UNIVERSITY OF DUBLIN. LONGMAN, BROWN, GREEN, LONGMANS, & ROBERTS. 181. c.86. MULTIPLES OF THE NUMBERS 2.302585 AND 0*434294, FOR CONVERTING COMMON LOGARITHMS INTO NA- 14 A TABLE OF MANTISSE OF THE LOGARITHMS OF NUM- 15 SOLUTION OF THE QUADRATIC EQUATION x2+px+9=0, BY TRIGONOMETRICAL TABLES, 116 LOGARITHMS OF SINES AND TANGENTS TO EVERY MI NUTE OF THE QUADRANT, 117 SOLUTION OF THE CUBIC EQUATION +px+9=0, BY TRIGONOMETRICAL TABLES, 208 GAUSS'S SUM ANd Difference LOGARITHMS, 209 TABLES OF USEFUL CONSTANTS WITH THEIR LOGARITHMS, 247 INTRODUCTION. 1. Definition of Logarithms.-2. The Common System.-3. Properties of Logarithms. 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, o, 1, 2, 3, 4, &c., we obtain the series of numbers, 1, 10, 100, 1000, 10000, &c. Thus: 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, |