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

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Page xvii - 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 xv - 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 former quotient, taken negatively, will be the characteristic to the fractional part of the quotient.

Page xxxii - ... setting in the latter ; double the time of his rising will be the length of the night, and double the time of his setting the length of the day.

Page x - Definition. — The integral part of a logarithm is called its characteristic, and the decimal part is called the mantissa.

Page xvii - 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 xi - Log. -78539 = 1-8950854 (d) If .the number whose Logarithm is sought contain six or seven figures : find the mantissa corresponding to the first five figures as directed in (c) ; then take the difference between this logarithm and the next higher in the table, which is the change in the logarithm corresponding to an increase of 1 or a unit in the fifth figure of the number. Now, the sixth figure is tenth parts of this unit, and the sixth and seventh are hundredth parts of this unit ; in other words,...

Page xvi - 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 xxxiii - 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 xxvi - CONVERSELY. (a) Find the degrees in the arc at the top of the page, and the minutes at the left-hand side ; then, under the degrees and opposite the minutes, is the length sought ; but if the angle contain seconds, to this result add the number opposite the seconds on the right-hand side of the page, and the sum will be the length...

Page xv - From the logarithm of the dividend subtract the logarithm of the divisor, and the remainder will be the logarithm of the quotient (Art.