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 Log·a·rithm n.  Math. 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 logarithms 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,
 0    1    2     3      4       Indices or logarithms
 1   10   100  1000  10,000     Numbers in geometrical progression
 Hence, the logarithm of any given number is the exponent of a power to which another given invariable number, called the base, must be raised in order to produce that given number. Thus, let 10 be the base, then 2 is the logarithm of 100, because 10² = 100, and 3 is the logarithm of 1,000, because 10³ = 1,000.
 Arithmetical complement of a logarithm, the difference between a logarithm and the number ten.
 Binary logarithms. See under Binary.
 Common logarithms, or Brigg's logarithms, logarithms of which the base is 10; -- so called from Henry Briggs, who invented them.
 Gauss's logarithms, 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.  They were suggested by the celebrated German mathematician Karl Friedrich Gauss (died in 1855), and are of great service in many astronomical computations.
 Hyperbolic logarithm or Napierian logarithm or Natural logarithm, a logarithm (devised by John Speidell, 1619) of which the base is e (2.718281828459045...); -- so called from Napier, the inventor of logarithms.
 Logistic logarithms or  Proportional logarithms, See under Logistic.
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 Bi·na·ry a.  Compounded or consisting of two things or parts; characterized by two (things).
 Binary arithmetic, that in which numbers are expressed according to the binary scale, or in which two figures only,  0 and 1, are used, in lieu of ten; the cipher multiplying everything by two, as in common arithmetic by ten. Thus, 1 is one; 10 is two; 11 is three; 100 is four, etc. --Davies & Peck.
 Binary compound Chem., a compound of two elements, or of an element and a compound performing the function of an element, or of two compounds performing the function of elements.
 Binary logarithms, a system of logarithms devised by Euler for facilitating musical calculations, in which 1 is the logarithm of 2, instead of 10, as in the common logarithms, and the modulus 1.442695 instead of .43429448.
 Binary measure Mus., measure divisible by two or four; common time.
 Binary nomenclature Nat. Hist., nomenclature in which the names designate both genus and species.
 Binary scale Arith., a uniform scale of notation whose ratio is two.
 Binary star Astron., a double star whose members have a revolution round their common center of gravity.
 Binary theory Chem., the theory that all chemical compounds consist of two constituents of opposite and unlike qualities.