fastened to the log, by means of two legs, Log board, a table generally divided into 
one of which is knotted through a hole at five columns, in the first of which is entered 
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 geo- 
graphical 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 another, the mate of the 
watch fixes the pin, and throws the log over 
the stern, which swimming peipendicularly, 
feels an immediate resistance, and is consi- 
dered 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 fif- 
teen 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 pre- 
senting only its edge to the water is easily 
drawn aboard. The number of knots and 
fathoms which had run otf 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 de- 
termine any variation in either of them, 
and to make allowance accordingly. If the 
glass runs thirty seconds, the distance be- 
tween 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 ef- 
fect on the glass, so as to make it run slow'er 
or faster, it should be frequently tried by 
the vibrations of apendiilum. As many ac- 
cidents attend a ship during a day’s sailing, 
such as the variableness of wind, the diffe- 
rent quantity of sail carried, &c. it will be 
necessary to heave the log at every altera- 
tion ; but if none of these alterations be 
'perceptible, yet it ought to be constantly 
heaved. In ships of w'ar and East India- 
men, it is usual 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 inter- 
vals, so as to affect the ship’s velocity, the 
officer generally makes a suitable allowance 
for it at the close of the watch. 
VOL. IV. 
the hour of the day ; in -the second, the 
course steered ; in the third, the number of 
knots run off the reel each time of heaving 
the log ; in the fourth, from w'hat point the 
wind blows ; and in the fifth, observations on 
the weather, variation of the compass, &c. 
Log book, 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. 
Log wood, in the arts, is derived from a 
low prickly tree, which is found in great 
plenty at Campeacliy, in the bay of Hon- 
duras, and is denominated “ hsematoxylon 
campechianuni.” It comes to Europe in 
large logs, cleared from the bark, and is 
very bard, compact, heavy, and of a red 
colour. It is in high request among dyers, 
especially in dying black. It gives out 
the colour both to water and alcohol ; the 
liquor at first assumes a fine red colour with 
a shade of purple. The infusion becomes 
gradually deeper, and at last almost black. 
To cloth previously boiled in alum and tar- 
tar, it gives a beautiful 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-wood bears 
in many respects a strong analogy to tannin, 
but in others it differs from it. 
LOGARITHMIC, in general, something 
belonging to logarithms. See Logarithms. 
Logarithmic curve. If on the line A N 
(Plate VIII. Misccl. fig. 12 ) both ways in- 
definitely extended, be taken, AC, C E, 
EG, GI, I L, on the right hand. And 
also Ag, g P, &c. on the left, all equal to 
one another. And, if at the points P, g, 
A, C, E, G, I, L, be erected to the right 
line, AN, the perpendiculars P S, g d, A B, 
CD, E P, GH, I K, L M, which let be 
continually proportional, and represent num- 
bers, viz. A B, 1, C D, 10, E P, 100, &c. 
then shall we have two progressions of lines, 
arithmetical and geometrical : for the lines 
A C, A E, A G, &c. are in arithmetical pro- 
gression, or as 1, 2, 3, 4, 5, &c. and so re- 
present the logarithms to which the geome- 
trical lines A B, CD, E P, &c. do cor- 
respond. Por since A G is triple of the 
right line A C, the number G H 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 proportionals S d, 
