LOGAN SPORT

a city of Indiana, in Ca co., of which it is the county seat. it is on the Wabash and other railroads and at the junction of the Wabash and Helrivers. Itis the chief trade center of a large farming region. Its industries “include fiour mills, paper mills, pump orks and plants for the making of galvanized iron, linseed oil and agricul- ‘tural implements. Logan sport is the iF seat of the Northern Indiana Hospital for the Insane. It has a large trade in _ tumber, pork and agricultural products. Pop. 1920, 21,696. t ¥ LOGARITHM. The common logarithm ofa number is the index to which - iQmust be raised to equal that number. _ Thus 10% equals 1000, so that the fogarithm of 1000 is3. Now 101!=10, _ it is well known that 10°=1, 10!=0.1, 102=0.01, etc. From this it follows that the logarithm t % problems of addition and subtraction of logarithms. Logarithms may be calculated from the Logarithmic Series— +n E+.) r et Been 1 4 +... ' These logarithms are known as Napierian or natural logarithms, and are used in all theoretical investigations. For purposes of computation, we require logs. to the base 10, which are known as common logarithms. It is usual to omit ‘the base 10 in writing. In common logarithms it is convenient to keep the decimal part always positive. Thus log. 0°3 is written 1°4771213 and not— 0°5228787. In this way the decimal part _ of the logarithms of all numbers consisting of the same digits in the same order is the same, and the logs. only differ in the integral part. When so written, _the decimal part is called the manti a, and may be obtained from tabies; the integral part is called the characterisivc, and may be written down by inspection by means of the following rules, decimal “notation being used: (1) The characterdstic of the log. of any number greater Ban unity is one le than the number of ci *, figures to the left of the decimal point. (2) The characteristic of the log. of any number le than unity is negative and ws one more than the number of ciphers immediately to the right of the decimal point, Log. tables are published giving to 7 or more places of decimals the manti of the logarithms of all numbers from 1 to 99,999. For numbers of more than 5 significant figures interpolation is nece ary, but for practical purposes it is sufficient to employ simple proportion in determining intermediate logarithms to those given in the tables.