LOG 



LOG 



The loci of all equations of the second 

 degree are conic sections or circles. 



LOCU'STA. In Botany, a spikelet, or 

 the partial inflorescence of certain grasses, 

 as the brome and the wheat. This term 

 is also applied to those other inflores- 

 cences, in which the flowers are sessile, 

 and arranged upon a lengthened axis, 

 which is permanent ; it is thus distin- 

 guished from the catkin, which is deci- 

 duous. 



LOCU'STIC ACID. An acid procured 

 from the locusta, or grasshopper, differ- 

 ing little from acetic acid. 



LOCU'STIDiE {locusta, a locust). The 

 Locust tribe; a group of Orthopterous 

 insects, belonging to the class Saltatoria, 

 remarkable for their migratory habits 

 and devastating powers. 



LODE. A technical term for a metallic 

 or mineral vein. Live lodes are those 

 which contain metallic ores ; dead lodes, 

 those which contain only stony matters. 



LOESS, or LOSS. A German desig- 

 nation of a peculiar loamy deposit in the 

 valley of the Rhine, occurring in patches 

 between Cologne and Basle. The term 

 is sometimes applied in this country to 

 a peculiar yellow loam with calcareous 

 concretions. 



LOG and LOG-LINE. The Log, in 

 sea-language, is the name of a piece of 

 wood in the form of the sector (usually a 

 quadrant) of a circle of five or six inches 

 radius. It is about a quarter of an inch 

 thick, and so balanced by means of a plate 

 of lead nailed upon the circular part, as to 

 swim perpendicularly in the water with 

 about two-thirds immersed under the 

 surface. The Log-line is a small cord of 

 about one hundred fathoms in length, 

 one end of which is fastened (by means of 

 two legs) to the centre and to the arched 

 part of the Log, while the other is wound 

 round a reel in the gallery of the ship. 

 The Log thus poised keeps its place in 

 the water while the line is unwound from 

 the reel by the ship's sailing; and the 

 length of line unwound in a given time 

 gives the rate of the ship's course. This 

 is calculated by knots made on the line 

 at between forty and fifty feet distance, 

 while the time is measured by a sand- 

 glass of a certain number of seconds. 

 The length between the knots is so pro- 

 portioned to the time of the glass, that 

 the number of knots unwound shows the 

 number of miles which the ship is sailing 

 in the hour. 



LO'GARITHM (X^TOf, a ratio, &pid- 

 fxoi, number). Logarithms are a series 

 201 



of numbers adapted in a certain way to 

 a series of natural numbers, to facilitate 

 the processes of numerical computation. 

 A simple idea of this system may be ac- 

 quired by taking a set of numbers, as 

 1,2, 3, 4, 5, 6, having for their common 

 difference the first number of the series ; 

 and placing under them another set of 

 numbers, which proceed by continued 

 multiplication by the first number of the 

 series, as 2, 4, 8, 16, 32, 64. The former 

 set are the logarithms of the latter, which 

 are called natural numbers. Thus, 



1, 2, 3, 4, 5, 6, &c. 



2, 4, 8, 16, 32, 64, &c. 



1. If now we add together any two of 

 the upper set, and note the number be- 

 neath their sum in the lower set, this 

 number represents the product arising 

 from multiplying together the numbers 

 of the lower set corresponding with the 

 numbers of the upper set which were 

 added together. Thus, on adding 2 to 4, 

 we have 6 in the upper set, beneath 

 which is 64 ; and this is the product of 

 4 and 16 in the lower set, opposite to 2 

 and 4 in the upper. So that, instead of 

 multiplying the natural numbers, we add 

 their logarithms together, and at once find 

 the product. 



2. In like manner, if we subtract one 

 of the upper numbers from another, and 

 note the number beneath their difference 

 in the lower set, this number represents 

 the quotient arising from the division of 

 one of the lower numbers by another, 

 both corresponding with the upper num- 

 bers which were subjected to the process 

 of subtraction. Thus, on subtracting 4 

 from 6, we have 2 in the upper set, be- 

 neath which is 4 ; and this is the quotient 

 arising from the division of 64 (the num- 

 ber beneath 6) by 16 (the number beneath 

 4). So that, instead of dividing the natu- 

 ral numbers, we subtract their logarithms, 

 and at once find the quotient. 



3. By the aid of logarithmic tables, 

 time and labour are saved to an extraor- 

 dinary degree. Supposing, for instance, 

 we had to multiply a number, consisting 

 of seven figures by itself, and this pro- 

 duct again by the original number, we 

 shall have to multiply seven places of 

 figures by an equally large number, and 

 then fourteen places of figures by seven 

 places, till at last we reach a product 

 of twenty-one places. But, by the aid of 

 logarithms, we have only to take three 

 times the logarithm of the original num- 

 ber, and that gives the logarithm of the 



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