906 LOG 
fitted points at the diftance of the interval betwixt I and 
io, and a moveable point be made to range betwixt them 
'always to indicate the antecedent; then, if the confequent 
fixed point fall without the ruler, the other fixed point will 
always denote the divifion on which it would have fallen 
had the ruler been prolonged; and this contrivance may 
eafily be adapted to any arrangement of parallel lines 
whatever. The arrangement of right lines, however, 
ought always to be difpoled in fuch a manner as to oc¬ 
cupy a right-angled parallelogram, or the crofs line al¬ 
ready mentioned ought always to be at right angles to the 
length of the ruler. 
Fig. 9. is a ruler confifting of ten parallel lines. Fig. xo, 
a beam-compafs for meafuring the intervals. E, A, C, 
are the parts which apply to the furface of the ruler; the 
middle one, A, being moveable fidewife in a groove in 
the piece DE, fo as always to preferve its parallelifm to 
the external pieces BC, which are fixed at a diftance equal 
to the length of the ruler, and have their edges placed in 
fuch a manner as to form with the.parallel lines which 
they interfefil a ratio, which by compofition is which 
in the prefent cafe requires them to be at right angles to 
the length. The piece DE is applied to the edge FG of 
the ruler. The edges or border, H, I, K, L, are more 
conveniently made of tranfparent horn, or tortoiie-fiiell, 
than of any opaque matter. In ufing this ruler, apply 
the edge of either B or C to the confequent, and Hide the 
piece A to the antecedent; obferving the difference be¬ 
tween the numbers on the pieces denoting the lines they 
are found on: then, applying the fame edge of A to any 
other antecedent, the other piece B or C will interfed a 
confequent in the fame ratio upon that line, having the 
fame fituation with regard to the antecedent that the line 
of the former confequent had to its antecedent. But if B 
be the confequent piece, and fall without the ruler, the 
piece C will fhow the confequent one line lower; or if C, 
in like manner, fall without the ruler, then B will (how 
the confequent one line higher. “It might be conveni¬ 
ent (fays Mr. Nicholfcn), for the purpofe of computation, 
to make inftruments of this kind with one hundred or 
more lines ; but, in the prefent inltrument, the numbers 
on the pieces will anfwer the fame purpofe; for, if a con¬ 
fequent fall upon a line at any given number of intervals 
without the ruler, it will be found on that line of the ar¬ 
rangement which occupies the fame number of intervals 
reckoned inwards from the oppofite edge of the ruler.” 
Fig. ii. is an inrtrument on the plan of a Gunter’s fcale 
of 28^ inches long, invented by the late Mr. Robertfon. 
There is a moveable piece AB in the Aider GH, acrofs 
which is drawn a fine line; the Aider having alfo lines 
CD, EF, drawn acrofs it at diftances from each other equal 
to the length of the ruler AB. In ufing the inArument, 
the line CD or EF is to be placed at the confequent, and 
the line in AB at the antecedent; then, if the piece AB 
be placed at any other antecedent, the fiune line CD or 
EF will indicate its confequent in the fame ratio taken 
the fame way; that is, if the.antecedent and confequent 
lie on the fame fide of the Aider, all other antecedents and 
confequents in that ratio will be in the fame manner; and 
the contrary- if they do not. But, if the confequent line 
fall without the ruler, the other fixed line on the Aider 
will fhow the confequent, but on the contrary fide of the 
Aider to that where it would elfe have been feen by means 
of the firft confequent line. 
Fig. 12 is a circular inftrument equivalent to the for¬ 
mer; confifting of three concentric circles engraved and 
graduated upon a plate of an inch and qn half diameter. 
Two legs A and B proceed from the centre, having right- 
LOG 
lined edges in the direction of radii; and are moveable ei¬ 
ther lingly or together. In ufing the inftrument, place 
one of the edges at the antecedent and the other ..t the 
confequent, and fix them at the angle. Move the two 
legs then together; and, having placed the antecedent leg 
at any other number, the other will give the confequent 
one in the like pofition on the lines. If the line CD hap¬ 
pen to lie between the legs, and B be the confequent leg, 
the number fought will be found one line farther from 
the centre than it would otherwife have been; and on the 
contrary it will be found one line nearer in the like cafe, 
if A be the confequent leg. “This inftrument (fays Mr. 
Nicholfon), differing from that reprefenced fig. 11 only in 
its circular form, and the advantages refulting from that 
form, the lines muft be taken to fucceed each other in 
the fame manner laterally; fo that numbers which fall ei¬ 
ther within or without the arrangement of circles, will be 
found on fuch lines of the arrangement as would have oc¬ 
cupied the vacant places if the fucceftion of lines had been 
indefinitely repeated fidewife. I approve of this conftruc- 
tion as fuperior to every other which has yet occurred to me, 
not only in point of convenience, but likewife in the pro¬ 
bability of being better executed ; becaufe fmall arcs may 
be graduated with very great accuracy, by divifions tranf- 
ferred from a larger original. The inftrument, fig. 11. 
may be contained conveniently in a circle of about four 
inches and an half diameter. The circular inftrument 
is a combination of the Gunter’s line and the fefitor, with 
the improvements here pointed out. The property of the 
feftor may be ufeful in magnifying the differences of the 
logarithms in the upper parts of the line of fines, the 
middle of the tangents, and the beginning of the verfed 
fines. It is even poffible, as mathematicians will eafily 
conceive, to draw fpirals, on which graduations of parts, 
every where equal to each other, will fhow the ratios of 
thofe lines by moveable radii, fimilar to thofe in this in¬ 
ftrument.” 
LOG'ATEZ. See Loitsch. 
LO'GE, a town of Germany, in the county of Hoya : 
twenty miles fouth-weft of Nienburg. 
LOGEFOUGEREU'SE, a town of France, in the de¬ 
partment of the Vendee: three miles fouth-eafl of La 
Chataigneraye. 
LO'GENWASSER, a river of Silefia, which runs into 
the Staritz in the principality of Neifle. 
LOG'GATS, f.—Loggats is the ancient name of a play 
or game, which is one of the unlawful games enumerated 
in the thirty-third ftatute of Henry VIII. It is the fame 
which is now called kittle-pins, in which boys often make 
ufe of bones inftead of wooden pins, throwing at them 
with another bone inftead of bowling. Hanmer. —Did thefe 
bones coft no more the breeding, but to play at loggats 
with them ? Shahefpeare’s Hamlet. 
LOG'GERHEAD,yi [logge, Dut. ftupid, and head.-, or 
rather from log, a heavy motionlefs mafs, as blockhead j A 
dolt; a blockhead ; athickfcul.—Says this loggerhead, What 
have we to do to quench other people’s fires ? VEf range. 
To fall or go to Loggerheads, tofeuffle; to fight with¬ 
out weapons.— A couple of travellers that took up an afs 
fell to loggerheads which fiiould be his mafter. VEJlrange. 
LOG'GERHEAD KE'Y, or El Contoy.s fmall ifland 
in the bay of Honduras, near the coali of Yucatan. Lat. 
21,25 N. Ion. 87. 45. W. 
LOG'GERHEADED, adj. Dull; ftupid; doltifh.-— 
You loggerheaded and unpolifti’d groom, what! no attend¬ 
ance ? Shakejpeare's Taming of the Shrew. 
LOG'GERIIEAT, J. in fea-language, a large round 
ball of iron, with a long handle, for heating pitch. 
INDEX 
