LOG 



last product of the 21 places of figures, 

 •without any further multiplication. 



4. The index or characteristic of the 

 logarithm of a number is one less than 

 the number of integral figures of the 

 number. Thus, if the number contain 

 five integral figures, the index is 4 ; if it 

 contain four,. the index is 3; and so on. 

 "When the number has no integral figures, 

 the index of its logarithm is negative, 

 and is one more than the number of ci- 

 phers immediately after the decimal 

 place; that is, the number of prefixed 

 ciphers. Thus, if there is no cipher after 

 the decimal, the index is — I ; if there is 

 one prefixed cipher, the index is — 2 ; and 

 so on. The negative sign is placed over 

 the index, thus : T^ "2^ &c. 



5. The logarithm of a number to a given 

 base is the quantity expressing the power 

 to which the base must be raised to be- 

 come equal to the number. 



6. Logarithmic Curve and Logarithmic 

 Spiral. " The former has for its rectan- 

 gular equation g^a", and its most re- 

 markable property is that its subtangent 

 is the same at every point of the curve. 

 The latter has r = ca^ for its polar equa- 

 tion, and its tangent always makes the 

 same angle with its radius vector ; whence 

 it is called the equiangular spiral." — Pen. 

 Cycl. 



LOGIC {XoyiKt] Texvrif the art of rea- 

 soning). Logic, in its most extensive 

 application, is the science, as well as the 

 art, of reasoning. So far as it institutes 

 an analysis of the process of the mind in 

 reasoning, it is strictly a science; while, 

 so far as it investigates the principles on 

 ■which argumentation is conducted, and 

 furnishes rules to secure the mind from 

 error in its deductions, it may be called 

 the art of reasoning. — Whately. 



LONDON CLAY. An extensive de- 

 posit of a bluish clay, except near the 

 surface, where it has the usual appearance 

 of clay. It abounds in Middlesex, Essex, 

 Suffolk, and part of Norfolk. It occa- 

 sionally includes beds of sandstone, and 

 of a coarse argillaceous limestone, from 

 ■which Parker's Roman cement is made. 

 It contains also the bones of the crocodile, 

 the turtle, &c. 



LONGICO'RNES {longus, long, comu, 

 a horn). A family of the tetramerous 

 Coleoptera, characterized by the great 

 development of the antennae, which 

 are often longer than the body of the 

 animal. 



LONGIPE'NNES {longus, long, penna, 

 a feather). A family of long-winged 

 202 



LOO 



oceanic birds, comprising the albatross, 

 the petrel, &c. 



LONGITUDE {longitudo, length). 1. 

 The longitude of a heavenly body is 

 measured on an arc of the ecliptic, inter- 

 cepted between the vernal equinoctial 

 point and a great circle passing through 

 the body, and perpendicular to the 

 ecliptic. 2. The longitude of a place on 

 the earth's surface is the inclination of 

 its meridian to that of some fixed station 

 referred to as a point to reckon from. 

 English astronomers and geographers 

 use the observatory at Greenwich for this 

 station ; foreigners, the principal ob- 

 servatories of their respective nations. 

 The terms longitude and latitude were 

 employed in Geography from an idea 

 of the ancients that the earth was longer 

 from east to west than from north to 

 south ; the former dimension was called 

 its length, the latter its breadth. 



1. Proposed Change of Expression. As 

 latitude is reckoned north or south, so 

 longitude is usually said to be reckoned 

 west or east. "It would add greatly, 

 however, to systematic regularity, and 

 tend much to avoid confusion and am- 

 biguity in computations, were this mode 

 of expression abandoned, and longitudes 

 reckoned invariably westward from their 

 origin round the whole circle from to 

 360°. Thus, the longitude of Paris is, 

 in common parlance, either 2° 20' 22" 

 east, or 357° 39' 38" west of Greenwich. 

 But the latter is its proper designation." 

 — Herschel. 



2. Longitude in Time. Longitude is 

 reckoned in time at the rate of 24 hours 

 for 360°, or 15° per hour. Thus the 

 longitude of Paris is 23h. 50m. 38^s. 

 Hence, by longitude in time is denoted 

 the difference in time in which two 

 places, situated east and west of each 

 other, see the same heavenly bodies : a 

 place 15° east of us sees the sun and 

 stars an hour earlier than we do ; at the 

 same distance west, an hour later. 



LONGITU'DINAL {longitudo, length). 

 Lengthwise ; that which has a perpen- 

 dicular direction from the apex to the 

 base of a body, as contradistinguished 

 from the term "transverse," which de- 

 notes a direction across its breadth. 



LONGITUDINAL VALLEYS. The 

 name given by Saussure to the great 

 valleys which separate the mountain- 

 chains, and give passage to rivers, as 

 that of the Danube, those of the Rhine 

 and the Rhone, &c. 

 LOOKING-GLASSES. Plain mirrors 



