The Theory and Practice of Finding the Longitude at Sea Or Land: To which are Added, Various Methods of Determining the Latitude of a Place, and Variation of the Compass; with New Tables, Volume 2
sold, 1809 - Latitude - 8 pages
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Page 18 - JLjOGARITHM8 are a series of numbers so contrived, that the sum of the Logarithms of any two numbers, is the logarithm of the product of these numbers. Hence it is inferred, that if a...
Page 25 - Multiply the logarithm of the given number by the index of the power to which it is to be raised, and the product will be the logarithm of the power sought.
Page 22 - BY LOGARITHMS. RULE. From the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.
Page 25 - Divide the logarithm of the given number by the index of the root ; and the quotient will be the logarithm of the required root (Art.
Page 18 - ... decimals. In this form, the logarithm of 1 is 0, of 10, 1 ; of 100, 2 ; of 1000, 3 &c. Whence the logarithm of any term between 1 and 10, being greater than 0, but less than 1, is a proper fraction, and is expressed decimally. The logarithm of each term between 10 and 100, is 1, with a decimal fraction annexed ; the logarithm of each term between 100 and 1000 is 2, with a decimal annexed, and so on. The integral part of the logarithm is called the Index, and the other the decimal part. — Except...
Page 22 - NOTE 3. Otherwise, if one or both of the given terms are decimals, remove the decimal points till the factors contain whole numbers, and the dividend the greatest ; then if the dividend be more places removed than the divisor, remove the decimal point of the quotient as many places to the left hand, but if the divisor be more places removed, then remove the decimal point of the quotient as many places to the right hand. If the dividend and divisor be equally removed, the quotient is not to be altered....
Page 26 - RULE. If the vessel is a ship of war, let fall a perpendicular from the fore-side of the stem, at the height of the haus-e holes ; but if a merchantman, the perpendicular is to be let fall from that part of the fore-side of the stem which is at the same height above the keel, as the wing transom : also let fall another perpendicular from the back of the main post, at the height of the wing transom. Find the distance between these "two perpendiculars, from which subtract three-fifths of the extreme...
Page 19 - The decimal parts of the logarithms of numbers, consisting of. the same figures, are the same, whether the number be integral, fractional, or mixed. This is illustrated as follows...