Part 6621

<i>Gwill.</i>

<h1>Loga\'d2dic</h1> <Xpage=865>

<hw>Log`a*\'d2d"ic</hw> <tt>(?)</tt>, <tt>a.</tt> <ety>[Gr. <?/; <?/ discourse, prose + <?/ song.]</ety> <fld>(Gr. Pros.)</fld> <def>Composed of dactyls and trochees so arranged as to produce a movement<-- ? ve illegible --> like that of ordinary speech.</def>

<h1>Logarithm</h1> <Xpage=865>

<hw>Log"a*rithm</hw> <tt>(?)</tt>, <tt>n.</tt> <ety>[Gr. <?/ word, account, proportion + <?/ number: cf. F. <ets>logarithme</ets>.]</ety> <fld>(Math.)</fld> <def>One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland (1550-1617), to abridge arithmetical calculations, by the use of addition and subtraction in place of multiplication and division. <note>The relation of <i>logarithms</i> to common numbers is that of numbers in an arithmetical series to corresponding numbers in a geometrical series, so that sums and differences of the former indicate respectively products and quotients of the latter; thus</def>

<table> <row>0 1 2 3 4 Indices or logarithms</row> <row>1 10 100 1000 10,000 Numbers in geometrical progression</row> </table>

Hence, the logarithm of any given number is the exponent of a power to which another given invariable number, called the <i>base</i>, must be raised in order to produce that given number. Thus, let 10 be the base, then 2 is the logarithm of 100, because <mathex>10<exp>2</exp> = 100</mathex>, and 3 is the logarithm of 1,000, because <mathex>10<exp>3</exp> = 1,000</mathex>.

<cs><col>Arithmetical complement of a logarithm</col>, <cd>the difference between a logarithm and the number ten.</cd> -- <col>Binary logarithms</col></mcol>. <cd>See under <er>Binary</er>.</cd> -- <mcol><col>Common logarithms</col>, &or; <col>Brigg's logarithms</col></mcol>, <cd>logarithms of which the base is 10; -- so called from Henry <i>Briggs<i>, who invented them.</cd> -- <col>Gauss's logarithms</col>, <cd>tables of logarithms constructed for facilitating the operation of finding the logarithm of the sum of difference of two quantities from the logarithms of the quantities, one entry of those tables and two additions or subtractions answering the purpose of three entries of the common tables and one addition or subtraction.</cd> They were suggested by the celebrated German mathematician Karl Friedrich <i>Gauss</i> (died in 1855), and are of great service in many astronomical computations. -- <mcol><col>Hyperbolic, &or; Napierian</col>, <col>logarithms</col><-- usually called 'natural logarithms' --></mcol>, <cd>those logarithms (devised by John Speidell, 1619) of which the base is 2.7182818; -- so called from <i>Napier<i>, the inventor of logarithms.</cd> -- <mcol><col>Logistic</col> &or; <col>Proportionallogarithms.</col></mcol>, <cd>See under <er>Logistic</er>.</cd></cs>

<h1>Logarithmetic, Logarithmetical</h1> <Xpage=865>

<hw><hw>Log`a*rith*met"ic</hw> <tt>(?)</tt>, <hw>Log"a*rith*met"ic*al</hw> <tt>(?)</tt>,<hw> <tt>a.</tt> <def>See <er>Logarithmic</er>.</def>

<h1>Logarithmetically</h1> <Xpage=865>

<hw>Log`a*rith*met"ic*al*ly</hw>, <tt>adv.</tt> <def>Logarithmically.</def>

<h1>Logarithmic, Logarithmical</h1> <Xpage=865>

<hw><hw>Log`a*rith"mic</hw> <tt>(?)</tt>, <hw>Log`a*rith"mic*al</hw> <tt>(?)</tt>,<hw> <tt>a.</tt> <ety>[Cf. F. <ets>logarithmique</ets>.]</ety> <def>Of or pertaining to logarithms; consisting of logarithms.</def>

<cs><col>Logarithmic curve</col> <fld>(Math.)</fld>, <cd>a curve which, referred to a system of rectangular co\'94rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa.</cd> -- <col>Logarithmic spiral</col>, <cd>a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See <er>Spiral</er>.</cd></cs>

<h1>Logarithmically</h1> <Xpage=865>

<hw>Log`a*rith"mic*al*ly</hw>, <tt>adv.</tt> <def>By the use of logarithms.</def>

<h1>Log-chip</h1> <Xpage=865>

<hw>Log"-chip`</hw> <tt>(?)</tt>, <tt>n.</tt> <fld>(Naut.)</fld> <def>A thin, flat piece of board in the form of a quadrant of a circle attached to the log line; -- called also <altname>log-ship</altname>. See 2d <er>Log</er>, <tt>n.</tt>, 2.</def>

<h1>Logcock</h1> <Xpage=865>

<hw>Log"cock`</hw> <tt>(?)</tt>, <tt>n.</tt> <def>The pileated woodpecker.</def>

<h1>Loge</h1> <Xpage=865>

<hw>Loge</hw> <tt>(?)</tt>, <tt>n.</tt> <ety>[F. See <er>Lodge</er>.]</ety> <def>A lodge; a habitation.</def> <mark>[Obs.]</mark>

<i>Chaucer.</i>

<h1>Loggan</h1> <Xpage=865>

<hw>Log"gan</hw> <tt>(?)</tt>, <tt>n.</tt> <def>See <er>Logan</er>.</def>

<h1>Loggat</h1> <Xpage=865>

<hw>Log"gat</hw> <tt>(?)</tt>, <tt>n.</tt> <ety>[Also written <ets>logget</ets>.]</ety> <p><b>1.</b> <def>A small log or piece of wood.</def> <mark>[Obs.]</mark>