logarithm 
of common logarithms, by Adrian Vlacq, 1628, has been 
the basis of every one since published. Abbreviated I. 
or log. Arithmetical complement of a logarithm. 
See arithmetical. Blnaxy logarithms. See biliary. 
Briggslan, common, or decimal logarithm. See above. 
Circular logarithm, an imaginary logarithm. Di- 
vision by logarithms, see </iV<Vm. Gaussian loga- 
rithms. See Gaussian. Logistic logarithm, the loga- 
rithm of a number of seconds subtracted from the loga- 
rithm of 3tiOO, the number of seconds in an hour. Natu- 
ral, hyperbolic, Neperian, or Napierian logarithm. 
See above. Negative index of a logarithm, one that 
Is affected with the negative sign. Such are the indices 
of the logarithms of all numbers less than unity. Para- 
bolic logarithm, a real logarithm. Quadratic loga- 
rithm, the exponent of a power of 2 which power of 
2 is itself the exponent of a power of the decimal anti- 
logarithm of 210, the power being the number of which 
the first exponent is the quadratic logarithm. That is, 
if a, = 102 -to and o2' = H, then a; is the quadratic loga- 
rithm of N, written LjN. 
logarithmetic (log"a-rith-met'ik), a. [< log- 
arithm + -et-ie, a,ttei' arithmetic.] Same as log- 
arithmic. [Bare.] 
logarithmetical (log"a-rith-met'i-kal), a. [< 
logarithmetie + -al.] Same as logarithmic. 
logarithmic (log-a-rith'mik), a. [< logarithm + 
-ic.] Of or pertaining to logarithms; consisting 
of logarithms. Logarithmic curvature, the ratio 
of the distances from the points of contact of two infi- 
nitely neighboring tangents to their point of intersection. 
This ratio is unity at an ordinary point, and on an al- 
gebraic curve is always rational. Logarithmic curve. 
See logistic curoe, under logistic. Logarithmic ellipse, 
hyperbola, etc. See the nouns. Logarithmic plus 
and tnimitt, two algebraic signs, J_ and T, such that a = 
J.T and a = STy signify that fog tan (ja + 450) = log 
tan (js + 450) i log tan (fa + 450), the upper sign for J.. 
and the lower for T. Logarithmic spiral, a curve- 
line somewhat analogous to the common logarithmic 
curve. It intersects all its radiants 
at the same angle, and the tangent 
of this angle is the modulus of the 
system of logarithms which the 
particular spiral represents. Its 
involute and evolute are also loga- 
rithmic spirals. Also called logistic 
spiral. 
logarithmical (log-a-rith'- 
mi-kal), a. [< logarithmic + 
-al.] Same as logarithmic. 
logarithmically (log-a-rith'- 
mi-kal-i), adv. By the use 
or aid of logarithms. 
Logarithmic Spiral. 
logarithmotechny (log-a-rith'mo-tek-ni), . 
[< E. logarithm (NGr. Aoyopifyiof) '+ Gr. TE^VJ?, 
art.] The art of calculating logarithms. 
logatt, n. See logget. 
log-beam (log'bem), . In a sawmill, the trav- 
eling frame which supports the log and feeds 
it to the saws. 
log-board (log'bord), . [< log 1 * + board.] 
A pair of boards shutting together like a book, 
formerly used instead of a log-slate. 
log-book (log'buk), n. [= Sw. logbok = Dan. 
logbog; as log* + book.] 1. The official record 
of proceedings on board ship: so called from the 
register which it includes of the indications of 
the log. It is a journal of all important items happen- 
ing on shipboard, contains the data from which the navi- 
gator determines his position by dead-reckoning (which 
seeX and is, when properly kept, a complete meteorologi- 
cal journal On board merchant ships the log is kept by 
the first officer ; on board men-of-war, by the navigator. 
2. In the board schools of Great Britain, a 
book for memoranda kept by the principal of 
the school, in accordance with the requirements 
of the Education Act. 
log-butter (log bot'to), . A heavy drag-saw 
used in squaring or butting the ends of logs. 
log-cabin (log'kab'in), n. See log cabin, under 
log 1 , a. 
log-chip (log' chip), n. The board, in the form 
of a quadrant, attached to a log-line. See log?. 
Also, erroneously, log-ship. 
log-Cock (log'kpk), n. The pileated woodpecker 
of North America, Hylotomws or Ceophkeus pile- 
atus, more fully called black log-cock. 
loget, and v. A Middle English form of lodge. 
log-fish (log 'fish), . The barrel-fish, Urus 
perciformui. Also called rudder-fish. 
log-frame (log'fram), . A sawmill machine 
for cutting timber into planks ; a deal-frame. 
loggan (log'an), n. [Also lor/an; < log^.] A 
logging-rock' or rocking-stone. 
loggatf, n. See logget. 
logget, . and i'. A Middle English form of lodge. 
logger 1 (log'er), n. [< log* + -er 1 .] A man 
employed in getting out logs or timber from 
the forest, and sometimes in getting them down 
rivers to market. [U. S. and Canada.] 
There were a couple of loggers on board, in red flannel 
shirts, and with rifles. Lowell, Fireside Travels, p. 110. 
Iogger 2 t (log'er), a. [< log 1 + -er, here used 
adjectively. Cf. loggij, logy.] Heavy ; stupid. 
Compare loggerhead. 
3504 
My head too heavy was and logger 
Even to make a Pettifogger. 
Cotton, Burlesque upon Burlesque. 
logger 3 (log'er), V. i. [Freq. of log 3 . Cf. Dan. 
logre, wag the tail.] To move irregularly, as 
a wheel that is loose on its axle. [Prov. Eng.] 
loggerhead (log'er-hed), . [< logger* + head.] 
1. A blockhead; a dunce; a dolt; athickskull. 
Now wae be to you, loggerheads, 
That dwell near Castlecarry, 
To let awa' sic a bonny lass, 
A Highlandman to marry. 
Lime Baillie (Child's Ballads, IV. 75). 
You in the mean time, you silly Logerhead, deserve to 
have your Bones well-thrash 'd with a Fool's staff, for think- 
ing to stir up Kings and Princes to War by such Childish 
Arguments. Milton, Ans. to Salmasius, Pref., p. 17. 
2. A spherical mass of iron with a long handle, 
used after being heated for various purposes, 
as to liquefy tar, to ignite the priming of a can- 
non, etc. Also called loggerheat. 
Here dozed a fire of beechen logs, that bred 
Strange fancies in its embers golden-red, 
And nursed the loggerhead whose hissing dip, 
Timed by nice instinct, creamed the mug of flip. 
Lowell, Fitz Adam's Story. 
3. A post in the stern of a whale-boat, with 
a bell-shaped head, around which the har- 
poon-line passes; a snubbing-post. 4. The 
hawk-billed turtle, a marine species of the 
genus Thalassochelys, as the American logger- 
head, T. caouana or caretta, or the Indian, T. 
olivacea ; also, the alligator-turtle of the south- 
ern United States, Macrochelys lacertina. 5. 
The small gray or Carolinian shrike, Lanius lu- 
dovicianus, a bird of the family Laniidai, resi- 
dent and abundant in the southern parts of the 
United States, and sometimes as far north as 
New England. It is about 8J inches long (the wing 
and tail each 4 inches), slate-colored above and white 
below, with the wings and tail black and white, the scapu- 
lars and upper tail-coverts bleached a little, and each side 
of the head marked by a black bar, the two bars meeting 
on the forehead. The bird is a geographical race of the 
common white-rumped shrike, L. excubitorides, and its 
habits are the same as those of other butcher-birds. 
6. A flycatcher. [West Indies.] 7. The chub. 
[Local, Eng.] 8. A kind of sponge found in 
Florida. 9. pi. The knapweed, Centaurea ni- 
gra; also, the blue-bottle, C. Cyanus At logger- 
heads, engaged in bickerings or disputes; contending 
about differences of opinion or the like. 
At last the divine and the poet, traditionally at logger- 
heads, have a common bond of suffering. 
Stedman, Viet. Poets, p. 13. 
To fall or go to loggerheads, to come to blows, 
loggerheaded (log'er-hed' / ed), a. [< loggerhead 
+ -erf 2 .] Dull; stupid; doltish. 
You logger-headed and unpolish'd grooms ! 
What, no attendance? Shak., T. of the S., iv. 1. 128. 
loggerheat (log'er-het), n. Same as logger- 
head, 2. 
loggett, [Also loggat, logat; dim. of log 1 .] 1. 
A small log or piece of wood. 
Now are they tossing of his legs and arms, 
Like loggete at a pear-tree. 
B. Jonson, Tale of a Tub, iv. 5. 
2. pi. An old English game, played by fixing a 
stake in the ground and pitching small pieces 
of wood at it, the nearest thrower winning; 
ekittle-pins. It was at one time prohibited by 
statute, under Henry VIII. 
Did these bones cost no more the breeding, hut to play 
at loggate with them? Shak., Hamlet, v. 1. 100. 
[I have seen it [loggats] played in different counties, at 
their sheep-shearing feasts, where the winner was entitled 
to a black fleece, which he afterwards presented to the 
maid to spin, for the purpose of making a petticoat, and 
on condition that she knelt down on the fleece to be kissed 
by all the rustics present. 
Steevens, note on the above passage. ] 
loggia (loj'a), n.; pi. loggie (-e). [It., = E. 
lodge, q. v.] In Italian arch.: (a) A gallery or 
arcade in a building, properly at the height of 
one or more stories, running along the front or 
part of the front of the building, and open on at 
least one side to the air, on which side is a 
series of pillars or slender piers. Such galleries af- 
ford an airy and sheltered resting-place or outlook, and are 
very characteristic of Italian palaces. Among famous loggie 
are those of the Vatican, decorated by Raphael and his 
scholars. Compare belvedere. See cut in next column. 
(A) A large ornamental window in the middle 
of the chief story of a building, often projecting 
from the wall, as seen in old Venetian palaces. 
logging 1 (log'ing), n. [Verbal n. of log 1 , .] 
The business of cutting and getting out logs or 
timber from a forest. [U. S. and Canada.] 
logging 2 !, A Middle English form of lodging. 
Ipgging-ax (log'ing-aks), n. A heavy ax used 
in cutting off logs. 
logging-bee (log'ing-be), . Same as log-roll- 
ing, 1. 
logic 
Loggia, Ospedale Maggiore, Milan. 
A logying-bee followed the burning of the fallow, as a 
matter of course. In the bush [Canada] where hands are 
few . . . these gatherings are considered indispensable 
[1832]. Susanna Moodie, Roughing it in the Bush, II. 58. 
logging-camp (log'ing-kamp), n. An encamp- 
ment of loggers or persons engaged in logging 
during winter. [U. S. and Canada.] 
logging-head (log'ing-hed), n. In a steam- 
engine, the working-beam. E. H. Knight. 
logging-rock (log'ing-rok), n. A rock so bal- 
anced on its base that it logs or rocks to and 
fro very easily, as by the force of the wind. 
log-glass (log'glas), n. A fourteen- or twenty- 
eight-second sand-glass, used with the log-line 
to ascertain the speed of a ship. See log*. 
loght, n. An obsolete form of loch 1 or lough 1 , 
and of low 3 . 
loghead (log'hed), re. A thick-headed or stupid 
person; a loggerhead. [Bare.] 
Not being born purely a Loghead (Dummkopf), thou 
hadst no other outlook. Carlisle, Sartor Resartus, p. 113. 
log-headed (log'hed"ed), a. Stupid. Dames. 
For well I knewe it was some mad-heded chyldo 
That invented this name, that the log-headed knave might 
be begilde. R. Edwards, Damon and Pythias. 
log-house (log'hous'), n. See log house, under 
log 1 , a. 
logic (loj'ik), re. and a. [Formerly logick, logique, 
< ME. logike, < OF. (and F.) logique = Sp. Ugica 
= Pg. It. logica, < L. logica, logice, < Gr. l.ayiidi 
(occurring first in Cicero), logic ; properly fern, 
of '/j>ytK.6$ (>L. logiciis), of or pertaining to speech 
or reason or reasoning, rational, reasonable, < 
Myof, speech, reason : see Logos.] I. n. 1. The 
science of the distinction of true from false 
reasoning, with whatever is naturally treated in 
connection therewith. See the phrases below. 
The definition of logic has been much disputed, and many 
definitions of the word have been given. There was much 
discussion in ancient and medieval times of the questions 
whether logic was a mode of knowing, or an instrument 
of science, or an art, or a practical science, or a specula- 
tive science. There was also a great diversity of opinion 
as to the subject-matter of logic, some holding that it had 
to do with words, others that It treated of the ens rationis, 
or that which has its existence in thought, and still others 
that it related to argumentations or some instrument of 
knowing. In modern times, especially since Kant, the 
real divergence of conception has been very much greater, 
one party holding that the main business of logic consists 
in developing the true theory of the process of cognition, 
and a second that its chief work is to separate inferences 
into classes distinguished by their form, while a third 
maintains that the form and the matter of thought have 
to be evolved together. 
Logike hath eke in his degree 
Betwene the trouth and the falshede 
The pleyne wordes for to shede. 
Sower, Conf. Amant., vli. 
He that knoweth reason to be in man, and the same 
geven by the greate might of God, must nedes confesse 
the Logique also is in man, and that onely by God. For 
there is none other difference betwixt the one and thother 
but that Logique is a Greke worde and Reason is an Eng- 
lishe woorde. . . . Logique is an arte to reason probably 
on bothe partes of al matiers that be putte i oorth, so ferre 
as the nature of every thing can beare. 
Sir T. Wilson, Rule of Reason (1562). 
[Dialectic and organon are generally synonyms of logic, 
though they have been variously distinguished at different 
times.] 
2. Beasoning, or power of reasoning; ratiocina- 
tion; argumentation; used absolutely, reason; 
sound sense. 
Ignorance in stilts, 
His cap well lined with logic not his own, 
With parrot tongue perform'd the scholar's part. 
Coicper, Task, ii. 737. 
Abstract logic, the general theory of logic (also called 
logica docens, general and theoretical logic) : opposed to 
concrete logic, or logic as an element of active thought in 
the prosecution of science (also called logica ittens, spe- 
cial and practical logic). The terais luyica iitrus :ind docenii 
