LOGANSPORT 



3485 



LOGGIA 



When ripe it has a rich, dark red color, and 

 sometimes is an inch and a quarter in length. 

 Its flavor is improved by cooking. It has been 

 widely distributed throughout America and Eu- 

 rope since 1893. If careful winter protection is 

 given, the plants can be grown as far north as 

 many parts of New England, Southern Canada 

 and the Middle States. 



LOGANSPORT, lND.,the county seat of Cass 

 County, in the northwestern part of the state, 

 is seventy-seven miles northwest of Indianapo- 

 lis and 117 miles southeast of Chicago. It is 

 situated at the junction of the Wabash and Eel 

 rivers, and is served by the Wabash Railroad 

 and several branches of the Pennsylvania and 

 Vandalia railroads and by interurban lines. 

 The population in 1910 was 19,052; in 1916 it 

 was 21,046 (Federal estimate). The area is 

 about four square miles. 



The principal buildings of the city are the 

 Federal building, courthouse, Carnegie Library, 

 Masonic Temple, high school building and 

 Saint Joseph's hospital. The Northern Indiana 

 Hospital for the Insane, located hete, is an in- 

 stitution occupying over thirty buildings and 

 300 acres of land valued at $725,000. Spencer 

 and Riverside parks together contain 240 acres. 



Logansport is an important railroad center 

 and a shipping point for grain, lumber, pork 

 and other farm produce. The railroad shops of 

 the Pennsylvania and Vandalia roads employ 

 more than 1,000 men. The chief manufactures 

 are lumber, automobiles, car trucks, machinery, 

 water wheels, radiators, kitchen cabinets, soaps, 

 brooms, and woodworking and foundry prod- 

 ucts. Limestone quarrying, water power and 

 natural gas are the industrial assets of the city. 



The town, which was established in 1828, was 

 named in honor of Captain Logan, a Shawnee 

 chief. It became the county seat of Cass 

 County in 1827, was incorporated in 1831 and 

 chartered as a city in 1838. J.D.D. 



LOGARITHMS, log'arith'mz, a system of 

 tables by reference to which the multiplication 

 and division of inconveniently long numbers 

 may be accomplished by addition and subtrac- 

 tion. 



A logarithm is what is known in algebra as 

 an exponent. The symbol x 2 expresses the 

 same thing as xXx. Since a logarithm is an 

 exponent, it follows the laws for exponents, and 

 the preparation of tables of logarithms de- 

 pends upon a principle used in algebra. This 

 principle may be expressed as follows: a x Xay= 

 a x+y . In algebra, in other words, quantities 

 may be multiplied by adding their exponents. 



If we say a* I and a y =p, then the quantities 

 x and y are the logarithms of the numbers I 

 and p to the base a. Each number in a table 

 of logarithms is accompanied by its logarithm. 

 Instead of multiplying two long numbers, the 

 calculator may simply add their logarithms; 

 the number in the table corresponding to the 

 new logarithm thus obtained is the product. In 

 like manner, if the problem be one of division, 

 the result is obtained by subtracting the loga- 

 rithm of the divisor from that of the dividend 

 and looking up the corresponding number in the 

 tables. 



In the common system of logarithms, the 

 base is 10. The expression 10 2 is equivalent to 

 10X10, and the product is 100. Here 2 is the 

 logarithm of 100 to the base 10. In like man- 

 ner 10 3 =1,000. The logarithm of 1,000 (writ- 

 ten log 1,000) is 3. 



To obtain the logarithm of the root of a 

 quantity, it is only necessary to divide the 

 logarithm of the given number by the figure 

 indicating the root to be taken. Suppose one 

 desires to find the cube root of 271. A refer- 

 ence to the table gives the logarithm of 271 as 

 2.4330. Divide by 3 and the result is 0.8110, 

 which is found to be the logarithm of 6.471. 

 Therefore, the cube root of 271 is 6.471. Simi- 

 larly, in raising a number to a given power, the 

 student multiplies the logarithm of that num- 

 ber by the exponent indicating the power. 



Logarithms are useful for all sorts of long 

 and complicated problems. They are used con- 

 stantly by scientists in their calculations and 

 particularly by astronomers and engineers. 

 They are indispensable in the study of trigo- 

 nometry, and their use is learned by students 

 while studying that branch of mathematics. 

 Their great practical utility was first shown by 

 John Napier, who published his tables in 1614. 

 Many high schools do not teach logarithms, 

 and boys and girls, as a rule, are never required 

 to become familiar with this branch of higher 

 mathematics. G.B.D. 



LOGGIA, lahj'a, or law' jia, an Italian word 

 meaning lodge or gallery, is used to denote any 

 roofed edifice open on one or more sides to the 

 weather. It is thus applied to well-known 

 buildings, such as the Loggia of the Vatican at 

 Rome, the great Loggia dei Lanzi and the Log- 

 gia del Bigallo at Florence. The name is also 

 given to an open arcade along the side of a 

 building, to the large, ornate windows, consist- 

 ing of several parts, found in old Venetian 

 palaces, and in America to a room open on one 

 side to the air. 



