514 



LOG LOGARITHM. 



censured both generals, Bonaparte, for taking a post 

 with an iinnit MM- su-rifire, of which, say they, he 

 might have been master, in twenty-four hours more, 

 with comparative ease; and Beaulieu, for having 

 evacuated the town of Lodi in sucii haste, as to 

 neglect breaking down the bridge, by which alone 

 the enemy could approach his position ; but it is idle 

 to dispute with Raphael about perspective. Lodi 

 remains one of the most striking military achieve- 

 ments of Napoleon; not merely from the personal 

 courage which he displayed, but from the boldness 

 with which the action was planned, and the energy 

 with which it was executed. At Lodi, Bonaparte 

 received the title of petit caporal (little corporal). 

 See Thiers's Histoire de la Revolution Fran^aise (vol. 

 8th); Botta's Histoire de f Italic de 1789 d 1814. 



LOG; a machine used to measure the rate of a 

 ship's velocity through the water. For this purpose, 

 there are several inventions, but the one most gen- 

 erally used is the following, called the common log. 

 It is a piece of thin board, forming the quadrant of a 

 circle of about six inches radius, and balanced by a 

 small plate of lead, nailed on the circular part, so as 

 to swim perpendicularly in the water; with the greater 

 part immersed. The log-line is fastened to the log 

 by means of two legs, one of which is knotted, through 

 a hole at one corner, while the other is attached to 

 a pin, fixed in a hole at the other corner, so as to 

 draw out occasionally. The log-line, being divided 

 into certain spaces, which are in proportion to an 

 equal number of geographical miles, as a half or 

 quarter minute is to an hour of time, is wound about 

 a reel. The whole is employed to measure the ship's 

 head-way in the following manner : The reel being 

 held by one man, and the half-minute glass by an- 

 other, the mate of the watch fixes the pin, and 

 throwa the log over the stern, which, swimming per- 

 pendicularly, feels an immediate resistance, and is 

 considered as fixed, the line being slackened over 

 the stern, to prevent the pin coming out. The knots 

 are measured from a mark on the line, at the distance 

 of twelve or fifteen fathoms from the log. The 

 glass is therefore turned at the instant that the mark 

 passes over the stern ; and, as soon as the sand in 

 the glass has run out, the line is stopped. The water, 

 then being on the log, dislodges the pin, so that the 

 board, now presenting only its edge to the water, is 

 easily drawn aboard. The number of knots and 

 fathoms which had run off at the expiration of the 

 glass, determines the ship's velocity. The half-min- 

 ute glass, and divisions on the line, should be fre- 

 quently measured, to determine any variation in 

 either of them, and to make allowance accordingly. 

 If the glass runs thirty seconds, the distance between 

 the knots should be fifty feet. When it runs more 

 or less, it should therefore be corrected by the fol- 

 lowing analogy : As thirty is to fifty, so is the num- 

 ber of seconds of the glass to the distance between 

 the knots upon the line. As the heat or moisture of 

 the weather has often a considerable effect on the 

 glass, so as to make it run slower or faster, it should 

 be frequently tried by the vibration of a pendulum. 

 As many accidents attend a ship during a day's sailing, 

 such as the variableness of winds, the different quan- 

 tity of sail carried, &c., it will be necessary to heave 

 the log at every alteration, and even if no alteration 

 be perceptible, yet it ought to be constantly heaved. 

 The inventor of this simple but valuable device is 

 not known, and no mention of it occurs till the year 

 1607, in an East India voyage, published by Purchas. 



LOG-BOARD ; two boards shutting together 

 like a book, and divided into several columns, con- 

 taining the hours of the day and night, the direction 

 of the winds, and the course of the ship, with all the 

 material occurrences that happen during the twenty- 



four hours, or from noon to noon, together with t!,p 

 latitude by observation. From this table, the officers 

 work the ship's way, and compile their journals. 

 The whole, being written with chalk, is rubbed out 

 every day at noon. 



LOG-BOOK ; a book into which the contents of 

 the log-board is daily transcribed at noon, together 

 with every circumstance, deserving notice, that may 

 happen to the ship, or within her cognizance, either 

 at sea, or in a harbour, &c. The intermediate di- 

 visions or watches of a log-book, containing four hours 

 each, are usually signed by the commanding officer 

 thereof, in ships of war or East Indiamen. 



LOG-LINE ; the line which is fastened to the log 



(q. v.). 



LOGAN, JAMES ; born at Lurgan, in Ireland, 

 Oct. 20, 1674, of Scottish parents. At the age ot 

 thirteen years, having learned Latin, Greek, and 

 some Hebrew, he was put apprentice to a linen- 

 draper in Dublin ; but, the country being involved in 

 much confusion by the war of the revolution (1688), 

 he returned to his parents, at Bristol, in England, 

 where he deroted all the time which he could com- 

 mand to the improvement of his mind. In his six- 

 teenth year, having happily met with a small book 

 on mathematics, he made himself master of it without 

 any manner of instruction. Having, also, further 

 improved himself in the Greek and Hebrew, he ac- 

 quired the French, Italian, and Spanish languages. 

 He was engaged in a trade between Dublin and 

 Bristol, when William Penn made proposals to him 

 to accompany him to Pennsylvania, as his secretary, 

 which he accepted, and landed, with the proprietor, 

 in Philadelphia, in the beginning of December, 1699. 

 In less than two years, William Penn returned to 

 England, and left his secretary invested with many 

 important offices, which he discharged with fidelity 

 and judgment. He filled the offices of provincial 

 secretary, commissioner of property, chief justice, 

 and, upon the demise of governor Gordon, governed 

 the province for two years as president of the council. 

 He had, for a long time, earnestly solicited from the 

 proprietary family a release from the fatiguing care 

 of their business ; but, even after this release, he 

 was constantly consulted and appealed to in difficulty. 

 Both the quiet and good government of the province, 

 for a number of years, was due to his prudence and 

 experience. He lived about twenty years at Stenton, 

 enjoying literary leisure, corresponding with eminent 

 men in various countries, and engaged in collecting 

 that library which he bequeathed to the public. He 

 was also the author of several learned works. His 

 Experimenta Meletemata de Plantarum Generatione 

 entitles its author to be ranked among the earliest 

 improvers of botany. It was written in 1739. He 

 corresponded with the great Swedish botanist. Mr 

 Logan died at Stenton, near Philadelphia, Oct. 

 31st, 1751, having just completed his seventy-seventh 

 year. 



LOGAN, REV. JOHN, an ingenious poet and ser- 

 mon writer, was born in the parish of Fala, Mid 

 Lothian, in 1748, and educated for the church, at 

 Edinburgh. Having been ordained, he became min- 

 ister of South Leith in 1773, previously to which he 

 had published a collection of poems, some his own 

 composition, and some the composition of his deceased 

 friend, Michael Bruce. He afterwards produced a 

 tragedy, entitled " Runnimede," which was acted at 

 Edinburgh, but with no great success. In 1786, he 

 removed to London, and became a writer in the 

 English Review. He died in 1788. His sermons, 

 which were published after his death, are much ad- 

 mired. 



LOGARITHM (from the Greek Xoyf, proportion, 

 and a^ftnt, number). " The logarithms of numbers 



