## Mathematical Tables Consisting of Logarithms of Numbers 1 to 108000: Trigonometrical, Nautical, and Other Tables |

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Page 9 - Multiply the logarithm of the given number by the exponent of the power to which it is to be raised, and the product will be the logarithm of the required power.

Page 8 - But if the negative characteristic is not divisible by the divisor, add such a negative number to it as will make it divisible, and prefix an equal positive integer to the fractional part of the logarithm; then divide the increased negative exponent and the other part of the logarithm separately, and the...

Page 9 - Divide the logarithm of the given number by the exponent of the root which is to be extracted, and the quotient will be the logarithm of the required root.

Page 11 - By means of this table, the true amplitude is taken out by inspection, whereby the method of finding the variation of the compass, by comparing the magnetic with the true amplitude, is very much facilitated. The table is to be entered with the declination...

Page 6 - The characteristic, therefore, is the index of an index. 8. The index of the logarithm is always one less, than the number of integral figures, in the natural number whose logarithm is sought : or, the index shows how far the first figure of the natural number is removed from the place of units. Thus, the logarithm of 37 is 1.56820. Here, the number of figures being, two, the index of the logarithm is 1. The logarithm of 253 is 2.40312. Here, the...

Page 8 - Add together the logarithms of the second and third terms, and from their sum subtract the logarithm of the first, and the remainder will be the logarithm of the fourth term. (a) The arithmetical complement of a number is the remainder, after subtracting it from a number consisting of 1, with as many ciphers annexed as the number has of integers. When the index of a logarithm is less than 10, which is generally the case, its arithmetical complement is found by subtracting it from 10.

Page 8 - THE LOGARITHM OF THE FIRST TERM : THE REMAINDER WILL BE THE LOGARITHM OF THE FOURTH TERM, WHICH SEEK IN THE TABLES, AND FIND ITS CORRESPONDING NUMBER, OR DEGREES AND MINUTES.

Page 11 - NOTE. — If the time of the sun or a star's rising or setting be required in mean time, the equation of time taken from the Nautical Almanac must be applied to the apparent time, found as in the preceding examples.

Page 11 - For finding the Time of the Rising and Setting of a Celestial Object. This table exhibits half the time that a celestial object continues above the horizon when the declination and latitude are of the same name : or below, when they are of contrary names ; usually called its semidiurnal and seminocturnal arches, from whence the apparent time of its rising and setting may be computed.

Page 8 - ... used. MULTIPLICATION BY LOGARITHMS. 32. Add the logarithms of the factors ; and the sum will be the logarithm of their product (Art. 9). The term sum, here used, is to be understood in its algebraic signification. Therefore, since the characteristic alone of a logarithm is negative (Art. 15), whatever there is to be carried from the decimal part, in the operation, must either be added to a positive characteristic...