LOG 



LOG 



watch fixes the pin, and throws the log 

 over the sLcrn, which, .swimming 1 perpen- 

 dicularly, 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 mea- 

 sured from a mark on the line, at the dis- 

 tance 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 minute glass and divisions on the 

 line should be frequently measured, to 

 determine any variation in either of 

 them, and to make allowance according- 

 ly. 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 

 following analogy. As thirty is to fifty, 

 so is the number 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 vibrations of a pendulum. As many 

 accidents attend a ship during a day's 

 sailing, such as the variableness of wind, 

 the different quantity of sail carried, &c. 

 it will be necessary to heave the log at 

 every alteration; but if none of these al- 

 terations be perceptible, yet it ought to 

 be constantly heaved. In ships of war 

 and East ludiamen, it is usaal to heave 

 the log once every hour, and in all other 

 vessels once in two hours; and if at any 

 time of the watch the wind has increased 

 or abated in the intervals, so as to affect 

 the ship's velocity, the officer generally 

 makes a suitable allowance for it at the 

 close of the watch. 



LOG board, a table generally divided into 

 five columns, in the first of which is en- 

 tered the hour of the day; in the second, 

 the course steered ; in the third, the num- 

 ber of knots run off the reel each time of 

 heaving the log; in the fourth, from what 

 point the wind blows ; and in the fifth, 

 observations on the weather, variation of 

 the compass, 8cc. 



Lo'; botjk a book ruled in columns like 

 the log-board, into which the account on 

 the log-board is transcribed every day at 



noon ; from whence, after it is corrected, 

 &c. it is entered into the journal. 



LOR tvood, in the arts, is derived from 

 a low prickly tree, Avhich is found in great 

 plenty at Campeachy, in the bay of Hon- 

 duras, and is denominated " hsematoxy- 

 lon campechianum." It comes to Europe 

 in large logs, cleared from the bark, and 

 is very hard, compact, heavy, and of a red 

 colour. It is in high request among 

 dyers, especially in dyeing black. It gives 

 out the colour both to water and alcohol ; 

 the liquor at first assumes a fine red co- 

 lour with a shade of purple. The infu- 

 sion becomes gradually deeper, and at 

 last almost black. To cloth previously 

 boiled in alum and tartar, it gives a beau- 

 tiful violet colour, which, however, will 

 not stand. Alkalies render the colour 

 darker, acids change it to yellow. From 

 a variety of experiments it is found, that 

 the colouring matter of log-\vood bears 

 in many respects a strong analogy to tan- 

 nin, but in others it differs from it, 



LOGARITHMIC, in general, some- 

 thing belonging to logarithms. See LO- 

 GARITHMS. 



LO&.IBITKHIC curve. If on the line A N 

 (Plate VIII. Miscel. fig. 12) both ways in- 

 definitely extended, be taken A C, C E, 

 E G, G I, I L, on the right hand. And 

 also A 5-, g P, &c. on the left, all equal to 

 one another. And, if at the points P, _-. 

 A, C, E, G, I, L, be erected to the right 

 line, A N, the perpendiculars P S, g d, 

 A B, C 1), E F, G H, I K, L M, which let 

 be continually proportional, and repre- 

 sent numbers, viz. A B, 1, C 1), 10, E F, 

 100, 8cc. then shall we have two progres- 

 sions of lines, arithmetical and geometri-- 

 cal .- for the lines A C, A E, A G, &c. are 

 in arithmetical progression, or as 1, 2, 3, 

 4, 5, Sec. and so represent the logarithms 

 to which the geometrical lines A B, CD, 

 E F, Sec. do correspond. For since A G 

 is triple of the right line A C, the number 

 G II shall be in the third place from unity, 

 if C D be in the first : so, likewise, shall 

 L M be in the fifth place, since A L = 

 5 A C. If the extremities of the propor- 

 tionals S d, B, D, F, &c. be joined by 

 right lines, the figure S B ML will become 

 a polygon, consisting of more or less sides, 

 according as there is more or less terms in. 

 the progression. 



If the parts A C, C E, E G, &c. be 

 bisected in the points c, e, g> i, /, and there 

 be again raised the perpendiculars c d, ef, 

 gh, ik, lm, which are mean proportion- 

 als between A B, C D; C D, E F, &c. then 

 there will arise a new series of proper- 



