Log board(Naut.), a board consisting of two parts shutting together like a book, with columns in which are entered the direction of the wind, course of the ship, etc., during each hour of the day and night. These entries are transferred to the log book. A folding slate is now used instead.Log book, or Logbook(Naut.), a book in which is entered the daily progress of a ship at sea, as indicated by the log, with notes on the weather and incidents of the voyage; the contents of the log board.Log cabin, Log house, a cabin or house made of logs.Log canoe, a canoe made by shaping and hollowing out a single log.Log glass(Naut.), a small sandglass used to time the running out of the log line.Log line(Naut.), a line or cord about a hundred and fifty fathoms long, fastened to the log-chip. See Note under 2d Log, n., 2.Log perch(Zoöl.), an ethiostomoid fish, or darter (Percina caprodes); — called also hogfish and rockfish.Log reel(Naut.), the reel on which the log line is wound. Log slate. (Naut.) See Log board Rough log(Naut.), a first draught of a record of the cruise or voyage.Smooth log(Naut.), a clean copy of the rough log. In the case of naval vessels this copy is forwarded to the proper officer of the government.To heave the log(Naut.), to cast the log-chip into the water; also, the whole process of ascertaining a vessel's speed by the log.

(Log), v. t. [imp. & p. p. Logged ; p. pr. & vb. n. Logging ] (Naut.), To enter in a ship's log book; as, to log the miles run. J. F. Cooper.

(Log), v. i.

1. To engage in the business of cutting or transporting logs for timber; to get out logs. [U.S.]

2. To move to and fro; to rock. [Obs.]

(Log"an) n. A rocking or balanced stone. Gwill.

(Log`a*œd"ic) a. [Gr. logaoidiko`s; lo`gos discourse, prose + 'aoidh` song.] (Gr. Pros.) Composed of dactyls and trochees so arranged as to produce a movement like that of ordinary speech.

(Log"a*rithm) n. [Gr. lo`gos word, account, proportion + 'ariqmo`s number: cf. F. logarithme.] (Math.) One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland to abridge arithmetical calculations, by the use of addition and subtraction in place of multiplication and division. 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,

3. Hence: The record of the rate of ship's speed or of her daily progress; also, the full nautical record of a ship's cruise or voyage; a log slate; a log book.

4. A record and tabulated statement of the work done by an engine, as of a steamship, of the coal consumed, and of other items relating to the performance of machinery during a given time.

5. (Mining) A weight or block near the free end of a hoisting rope to prevent it from being drawn through the sheave.

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.

  By PanEris using Melati.

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