Chapter VII: Part 7

_Double Blackwall Hitch_ (fig. 15).--Pass the end _a_ twice round the
hook and under the standing part _b_ at the last cross.

_Cat's-paw_ (fig. 16).--Twist up two parts of a lanyard in opposite
directions and hook the tackle in the eyes _i_, _i_. A piece of wood
should be placed between the parts at _g_. A large lanyard should be
clove-hitched round a large toggle and a strap passed round it below
the toggle.

_Marling-spike Hitch_ (fig. 17).--Lay the end _a_ over _c_; fold the
loop over on the standing part _b_; then pass the marline-spike
through, over both parts of the bight and under the part _b_. Used for
tightening each turn of a seizing.

_Fisherman's Bend_ (fig. 18).--Take two turns round a spar, then a
half-hitch round the standing part and between the spar and the turns,
lastly a half-hitch round the standing part.

_Studding-sail Halyard Bend_ (fig. 19).--Similar to the above, except
that the end is tucked under the first round turn; this is more snug.
A _magnus hitch_ has two round turns and one on the other side of the
standing part with the end through the bight.

_Timber Hitch_ (fig. 20).--Take the end _a_ of a rope round a spar,
then round the standing part _b_, then several times round its own
part _c_, against the lay of the rope.

_Carrick Bend_ (fig. 21).--Lay the end of one hawser over its own part
to form a bight as _e_´, _b_; pass the end of another hawser up
through that bight near _b_, going out over the first end at _c_,
crossing under the first long part and over its end at _d_, then under
both long parts, forming the loops, and above the first short part at
_b_, terminating at the end _e_´´, in the opposite direction
vertically and horizontally to the other end. The ends should be
securely stopped to their respective standing parts, and also a stop
put on the becket or extreme end to prevent it catching a pipe or
chock; in that form this is the best quick means of uniting two large
hawsers, since they cannot jam. When large hawsers have to work
through small pipes, good security may be obtained either by passing
ten or twelve taut racking turns with a suitable strand and securing
each end to a standing part of the hawser, or by taking half as many
round turns taut, crossing the ends between the hawsers over the
seizing and reef-knotting the ends. This should be repeated in three
places and the extreme ends well stopped. Connecting hawsers by
bowline knots is very objectionable, as the bend is large and the
knots jam.

_Sheet Bend_ (fig. 22).--Pass the end of one rope through the bight of
another, round both parts of the other, and under its own standing
part. Used for bending small sheets to the clews of sails, which
present bights ready for the hitch. An ordinary net is composed of a
series of sheet bends. A _weaver's knot_ is made like a sheet bend.

_Single Wall Knot_ (fig. 23).--Unlay the end of a rope, and with the
strand a form a bight. Take the next strand _b_ round the end of _a_.
Take the last strand _c_ round the end of _b_ and through the bight
made by _a_. Haul the ends taut.

_Single Wall Crowned_ (fig. 24).--Form a single wall, and lay one of
the ends, _a_, over the knot. Lay _b_ over _a_, and _c_ over _b_ and
through the bight of _a_. Haul the ends taut.

_Double Wall and Double Crown_ (fig. 25).--Form a single wall crowned;
then let the ends follow their own parts round until all the parts
appear double. Put the ends down through the knot.

_Matthew Walker_ (figs. 26, 27).--Unlay the end of a rope. Take the
first strand round the rope and through its own bight; the second
strand round the rope, through the bight of the first, and through its
own bight; the third through all three bights. Haul the ends taut.

_Inside Clinch_ (fig. 28).--The end is bent close round the standing
part till it forms a circle and a half, when it is securely seized at
_a_, _b_ and _c_, thus making a running eye; when taut round anything
it jams the end. It is used for securing hemp cables to anchors, the
standing parts of topsail sheets, and for many other purposes. If the
eye were formed outside the bight an _outside clinch_ would be made,
depending entirely on the seizings, but more ready for slipping.

_Midshipman's Hitch_ (fig. 29).--Take two round turns inside the
bight, the same as a half-hitch repeated; stop up the end or let
another half-hitch be taken or held by hand. Used for hooking a tackle
for a temporary purpose.

_Turk's Head_ (fig. 30).--With fine line (very dry) make a clove hitch
round the rope; cross the bights twice, passing an end the reverse way
(up or down) each time; then keeping the whole spread flat, let each
end follow its own part round and round till it is too tight to
receive any more. Used as an ornament variously on side-ropes and
foot-ropes of jibbooms. It may also be made with three ends, two
formed by the same piece of line secured through the rope and one
single piece. Form with them a diamond knot; then each end crossed
over its neighbour follows its own part as above.

_Spanish Windlass_ (fig. 31).--An iron bar and two marling-spikes are
taken; two parts of a seizing are twisted like a cat's-paw (fig. 16),
passed round the bar, and hove round till sufficiently taut. In
heaving shrouds together to form an eye two round turns are taken with
a strand and the two ends hove upon. When a lever is placed between
the parts of a long lashing or frapping and hove round, we have what
is also called a Spanish windlass.

_Slings_ (fig. 32).--This is simply the bight of a rope turned up over
its own part; it is frequently made of chain, when a shackle (bow up)
takes the place of the bight at _s_ and another at _y_, connecting the
two ends with the part which goes round the mast-head. Used to sling
lower yards. For boat's yards it should be a grummet with a thimble
seized in at _y_. As the tendency of all yards is to cant forward with
the weight of the sail, the part marked by an arrow should be the
fore-side--easily illustrated by a round ruler and a piece of twine.

_Sprit-Sail Sheet Knot_ (fig. 33).--This knot consists of a double
wall and double crown made by the two ends, consequently with six
strands, with the ends turned down. Used formerly in the clews of
sails, now as an excellent stopper, a lashing or shackle being placed
at _s_ and a lanyard round the head at _l_.

_Turning in a Dead-Eye Cutter-Stay fashion_ (fig. 34).--A bend is made
in the stay or shroud round its own part and hove together with a bar
and strand; two or three seizings diminishing in size (one round and
one or two either round or flat) are hove on taut and snug, the end
being at the side of the fellow part. The dead-eye is put in and the
eye driven down with a commander.

_Turning in a Dead-Eye end up_ (fig. 35).--The shroud is measured
round the dead-eye and marked where a throat-seizing is hove on; the
dead-eye is then forced into its place, or it may be put in first. The
end beyond _a_ is taken up taut and secured with a round seizing;
higher still the end is secured by another seizing. As it is important
that the lay should always be kept in the rope as much as possible,
these eyes should be formed conformably, either right-handed or
left-handed. It is easily seen which way a rope would naturally kink
by putting a little extra twist into it. A shroud whose dead-eye is
turned in end up will bear a fairer strain, but is more dependent on
the seizings; the under turns of the throat are the first to break and
the others the first to slip. With the cutter-stay fashion the
standing part of the shroud gives way under the nip of the eye. A rope
will afford the greatest resistance to strain when secured round large
thimbles with a straight end and a sufficient number of flat or
racking seizings. To splice shrouds round dead-eyes is objectionable
on account of opening the strands and admitting water, thus hastening
decay. In small vessels, especially yachts, it is admissible on the
score of neatness; in that case a round seizing is placed between the
dead-eye and the splice. The dead-eyes should be in diameter 1½ times
the circumference of a hemp shroud and thrice that of wire; the
lanyard should be half the nominal size of hemp and the same size as
wire: thus, hemp-shroud 12 in., wire 6 in., dead-eye 18 in., lanyard 6
in.

_Short Splice_ (fig. 36).--The most common description of splice is
when a rope is lengthened by another of the same size, or nearly so.
Fig. 36 represents a splice of this kind: the strands have been
unlaid, married and passed through with the assistance of a
marling-spike, over one strand and under the next, twice each way. The
ends are then cut off close. To render the splice neater the strands
should have been halved before turning them in a second time, the
upper half of each strand only being turned in; then all are cut off
smooth. _Eye Splice._--Unlay the strands and place them upon the same
rope spread at such a distance as to give the size of the eye; enter
the centre strand (unlaid) under a strand of the rope (as above), and
the other two in a similar manner on their respective sides of the
first; taper each end and pass them through again. If neatness is
desired, reduce the ends and pass them through once more; cut off
smooth and serve the part disturbed tightly with suitable hard line.
Uses too numerous to mention. _Cut Splice._--Made in a similar manner
to an eye splice, but of two pieces of rope, therefore with two
splices. Used for mast-head pendants, jib-guys, breast backstays, and
even odd shrouds, to keep the eyes of the rigging lower by one part.
It is not so strong as two separate eyes. _Horseshoe Splice._--Made
similar to the above, but one part much shorter than the other, or
another piece of rope is spliced across an eye, forming a horseshoe
with two long legs. Used for back-ropes on dolphin striker, back stays
(one on each side) and cutter's runner pendants. _Long Splice._--The
strands must be unlaid about three times as much as for a short splice
and married--care being taken to preserve the lay or shape of each.
Unlay one of the strands still further and follow up the vacant space
with the corresponding strand of the other part, fitting it firmly
into the rope till only a few inches remain. Treat the other side in a
similar manner. There will then appear two long strands in the centre
and a long and a short one on each side. The splice is practically
divided into three distinct parts; at each the strands are divided and
the corresponding halves knotted (as shown on the top of fig. 38) and
turned in twice. The half strand may, if desired, be still further
reduced before the halves are turned in for the second time. This and
all other splices should be well stretched and hammered into shape
before the ends are cut off. The long splice alone is adapted to
running ropes.

_Shroud Knot_ (fig. 37).--Pass a stop at such distance from each end
of the broken shroud as to afford sufficient length of strands, when
it is unlaid, to form a single wall knot on each side after the parts
have been married; it will then appear as represented in the figure,
the strands having been well tarred and hove taut separately. The part
_a_ provides the knot on the opposite side and the ends _b_, _b_; the
part _c_ provides the knot and the ends _d_, _d_. After the knot has
been well stretched the ends are tapered, laid smoothly between the
strands of the shroud, and firmly served over. This knot is used when
shrouds or stays are broken. _French Shroud Knot._--Marry the parts
with a similar amount of and as before; stop one set of strands taut
up on the shroud (to keep the parts together), and turn the ends back
on their own part, forming bights. Make a single wall knot with the
other three strands round the said bights and shroud; haul the knot
taut first and stretch the whole; then heave down the bights close: it
will look like the ordinary shroud knot. It is very liable to slip. If
the ends by which the wall knot is made after being hove were passed
through the bights, it would make the knot stronger. The ends would be
tapered and served.

_Flemish Eye_ (fig. 38).--Secure a spar or toggle twice the
circumference of the rope intended to be rove through the eye; unlay
the rope which is to form the eye about three times its circumference,
at which part place a strong whipping. Point the rope vertically under
the eye, and bind it taut up by the core if it is four-stranded rope,
otherwise by a few yarns. While doing so arrange six or twelve pieces
of spun-yarn at equal distances on the wood and exactly halve the
number of yarns that have been unlaid. If it is a small rope, select
two or three yarns from each side near the centre; cross them over the
top at _a_, and half-knot them tightly. So continue till all are
expended and drawn down tightly on the opposite side to that from
which they came, being thoroughly intermixed. Tie the pieces of
spun-yarn which were placed under the eye tightly round various parts,
to keep the eye in shape when taken off the spar, till they are
replaced by turns of marline hove on as taut as possible, the hitches
forming a central line outside the eye. Heave on a good seizing of
spun-yarn close below the spar, and another between six and twelve
inches below the first; it may then be parcelled and served; the eye
is served over twice, and well tarred each time. As large ropes are
composed of so many yarns, a greater number must be knotted over the
toggle each time; a 4-in. rope has 132 yarns, which would require 22
knottings of six each time; a 10-in. rope has 834 yarns, therefore, if
ten are taken from each side every time, about twice that number of
hitches will be required; sometimes only half the yarns are hitched,
the others being merely passed over. The chief use of these eyes has
been to form the collars of stays, the whole stay in each case having
to be rove through it--a very inconvenient device. It is almost
superseded for that purpose by a leg spliced in the stay and lashing
eyes abaft the mast, for which it is commonly used at present. This
eye is not always called by the same name, but the weight of evidence
is in favour of calling it a Flemish eye. _Ropemaker's Eye_, which
also has alternative names, is formed by taking out of a rope one
strand longer by 6 in. or a foot than the required eye, then placing
the ends of the two strands a similar distance below the disturbance
of the one strand, that is, at the size of the eye; the single strand
is led back through the vacant space it left till it arrives at the
neck of the eye, with a similar length of spare end to the other two
strands. They are all seized together, scraped, tapered, marled and
served. The principal merit is neatness. _Mouse on a Stay._--Formed by
turns of coarse spun-yarn hove taut round the stay, over parcelling at
the requisite distance from the eye to form the collar; assistance is
given by a padding of short yarns distributed equally round the rope,
which, after being firmly secured, especially at what is to be the
under part, are turned back over the first layer and seized down
again, thus making a shoulder; sometimes it is formed with parcelling
only. In either case it is finished by marling, followed by serving or
grafting. The use is to prevent the Flemish eye in the end of the stay
from slipping up any farther.

_Rolling Hitch_ (fig. 39).--Two round turns are taken round a spar or
large rope in the direction in which it is to be hauled and one
half-hitch on the other side of the hauling part. This is very
useful, as it can be put on and off quickly.

_Round Seizing_ (fig. 40).--So named when the rope it secures does not
cross another and there are three sets of turns. The size of the
seizing line is about one-sixth (nominal) that of the ropes to be
secured, but varies according to the number of turns to be taken. An
eye is spliced in the line and the end rove through it, embracing both
parts. If either part is to be spread open, commence farthest from
that part; place tarred canvas under the seizing; pass the line round
as many times (with much slack) as it is intended to have under-turns;
and pass the end back through them all and through the eye. Secure the
eye from rendering round by the ends of its splice; heave the turns on
with a marling-spike (see fig. 17), perhaps seven or nine; haul the
end through taut, and commence again the riding turns in the hollows
of the first. If the end is not taken back through the eye, but pushed
up between the last two turns (as is sometimes recommended), the
riders must be passed the opposite way in order to follow the
direction of the under-turns, which are always one more in number than
the riders. When the riders are complete, the end is forced between
the last lower turns and two cross turns are taken, the end coming up
where it went down, when a wall knot is made with the strands and the
ends cut close; or the end may be taken once round the shroud. _Throat
Seizing._--Two ropes or parts of ropes are laid on each other parallel
and receive a seizing similar to that shown in figure 35--that is with
upper and riding but no cross turns. As the two parts of rope are
intended to turn up at right angles to the direction in which they
were secured, the seizing should be of stouter line and short, not
exceeding seven lower and six riding turns. The end is better secured
with a turn round the standing part. Used for turning in dead-eyes and
variously. _Flat Seizing._--Commenced similarly to the above, but it
has neither riding nor cross turns.

_Racking Seizing_ (fig. 41).--A running eye having been spliced round
one part of the rope, the line is passed entirely round the other
part, crossed back round the first part, and so on for ten to twenty
turns, according to the expected strain, every turn being hove as
tight as possible; after which round turns are passed to fill the
spaces at the back of each rope, by taking the end _a_ over both parts
into the hollow at _b_, returning at _c_, and going over to _d_. When
it reaches e a turn may be taken round that rope only, the end rove
under it, and a half-hitch taken, which will form a clove-hitch; knot
the end and cut it close. When the shrouds are wire (which is half the
size of hemp) and the end turned up round a dead-eye of any kind, wire
seizings are preferable. It appears very undesirable to have wire
rigging combined with plates or screws for setting it up, as in case
of accident--such as that of the mast going over the side, a shot or
collision breaking the ironwork--the seamen are powerless.

_Diamond Knot_ (figs. 42, 43).--The rope must be unlaid as far as the
centre if the knot is required there, and the strands handled with
great care to keep the lay in them. Three bights are turned up as in
fig. 42, and the end of _a_ is taken over _b_ and up the bight _c_.
The end of _b_ is taken over _c_ and up through _a_. The end _c_ is
taken over a and through _b_. When hauled taut and the strands are
laid up again it will appear as in fig. 43. Any number of knots may be
made on the same rope. They were used on man-ropes, the foot-ropes on
the jibboom, and similar places, where it was necessary to give a good
hold for the hands or feet. Turk's heads are now generally used.
_Double Diamond._--Made by the ends of a single diamond following
their own part till the knot is repeated. Used at the upper end of a
side rope as an ornamental stopper-knot.

_Stropping-Blocks._--There are various modes of securing blocks to
ropes; the most simple is to splice an eye at the end of the rope a
little longer than the block and pass a round seizing to keep it in
place; such is the case with jib-pendants. As a general rule, the
parts of a strop combined should possess greater strength than the
parts of the fall which act against it. The shell of an ordinary block
should be about three times the circumference of the rope which is to
reeve through it, as a 9-in. block for a 3-in. rope; but small ropes
require larger blocks in proportion, as a 4-in. block for a 1-in.
rope. When the work to be done is very important the blocks are much
larger: brace-blocks are more than five times the nominal size of the
brace. Leading-blocks and sheaves in racks are generally smaller than
the blocks through which the ropes pass farther away, which appears to
be a mistake, as more power is lost by friction. A clump-block should
be double the nominal size of the rope. A single strop may be made by
joining the ends of a rope of sufficient length to go round the block
and thimble by a common short splice, which rests on the crown of the
block (the opposite end to the thimble) and is stretched into place by
a jigger; a strand is then passed twice round the space between the
block and the thimble and hove taut by a Spanish windlass to cramp the
parts together ready for the reception of a small round seizing. The
cramping or pinching into shape is sometimes done by machinery
invented by a rigger in Portsmouth dockyard. The strop may be made the
required length by a long splice, but it would not possess any
advantage.

_Grummet-Strop_ (fig. 44).--Made by unlaying a piece of rope of the
desired size about a foot more than three times the length required
for the strop. Place the centre of the rope round the block and
thimble; mark with chalk where the parts cross; take one strand out of
the rope; bring the two chalk marks together; and cross the strand in
the lay on both sides, continuing round and round till the two ends
meet the third time; they are then halved, and the upper halves
half-knotted and passed over and under the next strands, exactly as
one part of a long splice. A piece of worn or well-stretched rope will
better retain its shape, upon which success entirely depends. The
object is neatness, and if three or multiples of three strops are to
be made it is economical.

_Double Strop_ (fig. 45).--Made with one piece of rope, the splice
being brought as usual to the crown of the block _t_, the bights
fitting into scores some inches apart, converging to the upper part,
above which the thimble receives the bights _a_, _a_; and the four
parts of the strop are secured at _s_, _s_ by a round seizing doubly
crossed. If the block be not then on the right slew (the shell
horizontal or vertical) a union thimble is used with another strop,
which produces the desired effect; thus the fore and main
brace-blocks, being very large and thin, are required (for appearance)
to lie horizontally; a single strop round the yard vertically has a
union thimble between it and the double strop round the block. The
double strop is used for large blocks; it gives more support to the
shell than the single strop and admits of smaller rope being used.
Wire rope is much used for block-strops; the fitting is similar. Metal
blocks are also used in fixed positions; durability is their chief
recommendation. Great care should be taken that they do not chafe the
ropes which pass by them as well as those which reeve through.

_Selvagee Strop._--Twine, rope-yarn or rope is warped round two or
more pegs placed at the desired distance apart, till it assumes the
requisite size and strength; the two ends are then knotted or spliced.
Temporary firm seizings are applied in several places to bind the
parts together before the rope or twine is removed from the pegs,
after which it is marled with suitable material. A large strop should
be warped round four or six pegs in order to give it the shape in
which it is to be used. This description of strop is much stronger and
more supple than rope of similar size. Twine strops (covered with
duck) are used for boats' blocks and in similar places requiring
neatness. Rope-yarn and spun-yarn strops are used for attaching
luff-tackles to shrouds and for many similar purposes. To bring to a
shroud or hawser, the centre of the strop is passed round the rope and
each part crossed three or four times before hooking the "luff"; a
spun-yarn stop above the centre will prevent slipping and is very
necessary with wire rope. As an instance of a large selvagee
block-strop being used--when the "Melville" was hove down at Chusan
(China), the main-purchase-block was double stropped with a selvagee
containing 28 parts of 3-in. rope; that would produce 112 parts in
the neck, equal to a breaking strain of 280 tons, which is more than
four parts of a 19-in cable. The estimated strain it bore was 80 tons.

_Stoppers_ for ordinary running ropes are made by splicing a piece of
rope to a bolt or to a hook and thimble, unlaying 3 or 4 ft., tapering
it by cutting away some of the yarns, and marling it down securely,
with a good whipping also on the end. It is used by taking a
half-hitch round the rope which is to be hauled upon, dogging the end
up in the lay and holding it by hand. The rope can come through it
when hauled, but cannot go back.

_Whipping and Pointing._--The end of every working rope should at
least be whipped to prevent it fagging out; in ships of war and yachts
they are invariably pointed. Whipping is done by placing the end of a
piece of twine or knittle-stuff on a rope about an inch from the end,
taking three or four turns taut over it (working towards the end); the
twine is then laid on the rope again lengthways contrary to the first,
leaving a slack bight of twine; and taut turns are repeatedly passed
round the rope, over the first end and over the bight, till there are
in all six to ten turns; then haul the bight taut through between the
turns and cut it close. To point a rope, place a good whipping a few
inches from the end, according to size; open out the end entirely;
select all the outer yarns and twist them into knittles either singly
or two or three together; scrape down and taper the central part,
marling it firmly. Turn every alternate knittle and secure the
remainder down by a turn of twine or a smooth yarn hitched close up,
which acts as the weft in weaving. The knittles are then reversed and
another turn of the weft taken, and this is continued till far enough
to look well. At the last turn the ends of the knittles which are laid
back are led forward over and under the weft and hauled through
tightly, making it present a circle of small bights, level with which
the core is cut off smoothly. Hawsers and large ropes have a becket
formed in their ends during the process of pointing. A piece of 1 to
1½ in. rope about 1½ to 2 ft. long is spliced into the core by each
end while it is open: from four to seven yarns (equal to a strand) are
taken at a time and twisted up; open the ends of the becket only
sufficient to marry them close in; turn in the twisted yarns between
the strands (as splicing) three times, and stop it above and below.
Both ends are treated alike; when the pointing is completed a loop a
few inches in length will protrude from the end of the rope, which is
very useful for reeving it. A hauling line or reeving line should only
be rove through the becket as a fair lead. _Grafting_ is very similar
to pointing, and frequently done the whole length of a rope, as a
side-rope. Pieces of white line more than double the length of the
rope, sufficient in number to encircle it, are made up in hanks called
foxes; the centre of each is made fast by twine and the weaving
process continued as in pointing. Block-strops are sometimes so
covered; but, as it causes decay, a small wove mat which can be taken
off occasionally is preferable.

_Sheep-Shank_ (fig. 46).--Formed by making a long bight in a
topgallant back-stay, or any rope which it is desirable to shorten,
and taking a half-hitch near each bend, as at _a_, _a_. Rope-yarn
stops at _b_, _b_ are desirable to keep it in place till the strain is
brought on it. Wire rope cannot be so treated, and it is injurious to
hemp rope that is large and stiff.

_Knotting Yarns_ (fig. 47).--This operation becomes necessary when, a
comparatively short piece of junk is to be made into spun-yarn, or
large rope into small, which is called twice laid. The end of each
yarn is divided, rubbed smooth and married (as for splicing). Two of
the divided parts, as _c_, _c_ and _d_, _d_, are passed in opposite
directions round all the other parts and knotted. The ends e and f
remain passive. The figure is drawn open, but the forks of A and B
should be pressed close together, the knot hauled taut and the ends
cut off.

_Butt Slings_ (fig. 48).--Made of 4-in. rope, each pair being 26 ft.
in length, with an eye spliced in one end, through which the other is
rove before being placed over one end of the cask; the rope is then
passed round the opposite side of the cask and two half-hitches made
with the end, forming another running eye, both of which are beaten
down taut as the tackle receives the weight. Slings for smaller casks
requiring care should be of this description, though of smaller rope,
as the cask cannot possibly slip out. _Bale Slings_ are made by
splicing the ends of about 3 fathoms of 3-in. rope together, which
then looks like a long strop, similar to the double strop represented
in fig. 45--the bights _t_ being placed under the cask or bale and one
of the bights _a_, _a_ rove through the other and attached to the
whip or tackle.

For a complete treatise on the subject the reader may be referred to
_The Book of Knots, being a Complete Treatise on the Art of Cordage,
illustrated by 172 Diagrams, showing the Manner of making every Knot,
Tie and Splice_, by Tom Bowling (London, 1890).

_Mathematical Theory of Knots._

In the scientific sense a knot is an endless physical line which cannot be deformed into a circle. A physical line is flexible and inextensible, and cannot be cut--so that no lap of it can be drawn through another.

The founder of the theory of knots is undoubtedly Johann Benedict Listing (1808-1882). In his "Vorstudien zur Topologie" (_Göttinger Studien_, 1847), a work in many respects of startling originality, a few pages only are devoted to the subject.[1] He treats knots from the elementary notion of twisting one physical line (or thread) round another, and shows that from the projection of a knot on a surface we can thus obtain a notion of the relative situation of its coils. He distinguishes "reduced" from "reducible" forms, the number of crossings in the reduced knot being the smallest possible. The simplest form of reduced knot is of two species, as in figs. 49 and 50. Listing points out that these are formed, the first by right-handed the second by left-handed twisting. In fact, if three half-twists be given to a long strip of paper, and the ends be then pasted together, the two edges become one line, which is the knot in question. We may free it by slitting the paper along its middle line; and then we have the juggler's trick of putting a knot on an endless unknotted band. One of the above forms cannot be deformed into the other. The one is, in Listing's language, the "perversion" of the other, i.e. its image in a plane mirror. He gives a method of symbolizing reduced knots, but shows that in this method the same knot may, in certain cases, be represented by different symbols. It is clear that the brief notice he published contains a mere sketch of his investigations.

The most extensive dissertation on the properties of knots is that of Peter Guthrie Tait (_Trans. Roy. Soc. Edin._, xxviii. 145, where the substance of a number of papers in the _Proceedings_ of the same society is reproduced). It was for the most part written in ignorance of the work of Listing, and was suggested by an inquiry concerning vortex atoms.

Tait starts with the almost self-evident proposition that, if any
plane closed curve have double points only, in passing continuously
along the curve from one of these to the same again an even number of
double points has been passed through. Hence the crossings may be
taken alternately over and under. On this he bases a scheme for the
representation of knots of every kind, and employs it to find all the
distinct forms of knots which have, in their simplest projections, 3,
4, 5, 6 and 7 crossings only. Their numbers are shown to be 1, 1, 2, 4
and 8. The unique knot of three crossings has been already given as
drawn by Listing. The unique knot of four crossings merits a few
words, because its properties lead to a very singular conclusion. It
can be deformed into any of the four forms--figs. 51 and 52 and their
perversions. Knots which can be deformed into their own perversion
Tait calls "amphicheiral" (from the Greek [Greek: amphi], on both
sides, around, [Greek: cheir], hand), and he has shown that there is
at least one knot of this kind for every even number of crossings. He
shows also that "links" (in which two endless physical lines are
linked together) possess a similar property; and he then points out
that there is a third mode of making a complex figure of endless
physical lines, without either knotting or linking. This may be called
"lacing" or "locking." Its nature is obvious from fig. 53, in which it
will be seen that no one of the three lines is knotted, no two are
linked, and yet the three are inseparably fastened together.

The rest of Tait's paper deals chiefly with numerical characteristics
of knots, such as their "knottiness," "beknottedness" and
"knotfulness." He also shows that any knot, however complex, can be
fully represented by three closed plane curves, none of which has
double points and no two of which intersect. It may be stated here
that the notion of beknottedness is founded on a remark of Gauss, who
in 1833 considered the problem of the number of inter-linkings of two
closed circuits, and expressed it by the electro-dynamic measure of
the work required to carry a unit magnetic pole round one of the
interlinked curves, while a unit electric current is kept circulating
in the other. This original suggestion has been developed at
considerable length by Otto Boeddicker (_Erweiterung der Gauss'schen
Theorie der Verschlingungen_ (Stuttgart, 1876). This author treats
also of the connexion of knots with Riemann's surfaces.

It is to be noticed that, although every knot in which the crossings
are alternately over and under is irreducible, the converse is not
generally true. This is obvious at once from fig. 54, which is merely
the three-crossing knot with a doubled string--what Listing calls
"paradromic."

Christian Felix Klein, in the _Mathematische Annalen_, ix. 478, has
proved the remarkable proposition that knots cannot exist in space of
four dimensions. (P. G. T.)

FOOTNOTE:

[1] See P. G. Tait "On Listing's _Topologie_," _Phil. Mag._, xvii.
30.

KNOUT (from the French transliteration of a Russian word of Scandinavian origin; cf. A.-S. _cnotta_, Eng. knot), the whip used in Russia for flogging criminals and political offenders. It is said to have been introduced under Ivan III. (1462-1505). The knout had different forms. One was a lash of raw hide, 16 in. long, attached to a wooden handle, 9 in. long. The lash ended in a metal ring, to which was attached a second lash as long, ending also in a ring, to which in turn was attached a few inches of hard leather ending in a beak-like hook. Another kind consisted of many thongs of skin plaited and interwoven with wire, ending in loose wired ends, like the cat-o'-nine tails. The victim was tied to a post or on a triangle of wood and stripped, receiving the specified number of strokes on the back. A sentence of 100 or 120 lashes was equivalent to a death sentence; but few lived to receive so many. The executioner was usually a criminal who had to pass through a probation and regular training; being let off his own penalties in return for his services. Peter the Great is traditionally accused of knouting his son Alexis to death, and there is little doubt that the boy was actually beaten till he died, whoever was the executioner. The emperor Nicholas I. abolished the earlier forms of knout and substituted the pleti, a three-thonged lash. Ostensibly the knout has been abolished throughout Russia and reserved for the penal settlements.

KNOWLES, SIR JAMES (1831-1908), English architect and editor, was born in London in 1831, and was educated, with a view to following his father's profession, as an architect at University College and in Italy. His literary tastes also brought him at an early age into the field of authorship. In 1860 he published _The Story of King Arthur_. In 1867 he was introduced to Tennyson, whose house, Aldworth, on Blackdown, he designed; this led to a close friendship, Knowles assisting Tennyson in business matters, and among other things helping to design scenery for _The Cup_, when Irving produced that play in 1880. Knowles became intimate with a number of the most interesting men of the day, and in 1869, with Tennyson's co-operation, he started the Metaphysical Society, the object of which was to attempt some intellectual _rapprochement_ between religion and science by getting the leading representatives of faith and unfaith to meet and exchange views.

The members from first to last were as follows: Dean Stanley, Seeley,
Roden Noel, Martineau, W. B. Carpenter, Hinton, Huxley, Pritchard,
Hutton, Ward, Bagehot, Froude, Tennyson, Tyndall, Alfred Barry, Lord
Arthur Russell, Gladstone, Manning, Knowles, Lord Avebury, Dean
Alford, Alex. Grant, Bishop Thirlwall, F. Harrison, Father Dalgairns,
Sir G. Grove, Shadworth Hodgson, H. Sidgwick, E. Lushington, Bishop
Ellicott, Mark Pattison, duke of Argyll, Ruskin, Robert Lowe, Grant
Duff, Greg, A. C. Fraser, Henry Acland, Maurice, Archbishop Thomson,
Mozley, Dean Church, Bishop Magee, Croom Robertson, FitzJames Stephen,
Sylvester, J. C. Bucknill, Andrew Clark, W. K. Clifford, St George
Mivart, M. Boulton, Lord Selborne, John Morley, Leslie Stephen, F.
Pollock, Gasquet, C. B. Upton, William Gull, Robert Clarke, A. J.
Balfour, James Sully and A. Barratt.

Papers were read and discussed at the various meetings on such subjects as the ultimate grounds of belief in the objective and moral sciences, the immortality of the soul, &c. An interesting description of one of the meetings was given by Magee (then bishop of Peterborough) in a letter of 13th of February 1873:--

"Archbishop Manning in the chair was flanked by two Protestant bishops
right and left; on my right was Hutton, editor of the _Spectator_, an
Arian; then came Father Dalgairns, a very able Roman Catholic priest;
opposite him Lord A. Russell, a Deist; then two Scotch metaphysical
writers, Freethinkers; then Knowles, the very broad editor of the
_Contemporary_; then, dressed as a layman and looking like a country
squire, was Ward, formerly Rev. Ward, and earliest of the perverts to
Rome; then Greg, author of _The Creed of Christendom_, a Deist; then
Froude, the historian, once a deacon in our Church, now a Deist; then
Roden Noel, an actual Atheist and red republican, and looking very
like one! Lastly Ruskin, who read a paper on miracles, which we
discussed for an hour and a half! Nothing could be calmer, fairer, or
even, on the whole, more reverent then the discussion. In my opinion,
we, the Christians, had much the best of it. Dalgairns, the priest,
was very masterly; Manning, clever and precise and weighty; Froude,
very acute, and so was Greg. We only wanted a Jew and a Mahommedan to
make our Religious Museum complete" (_Life_, i. 284).

The last meeting of the society was held on 16th May 1880. Huxley said that it died "of too much love"; Tennyson, "because after ten years of strenuous effort no one had succeeded in even defining metaphysics." According to Dean Stanley, "We all meant the same thing if we only knew it." The society formed the nucleus of the distinguished list of contributors who supported Knowles in his capacity as an editor. In 1870 he became editor of the _Contemporary Review_, but left it in 1877 and founded the _Nineteenth Century_ (to the title of which, in 1901, were added the words _And After_). Both periodicals became very influential under him, and formed the type of the new sort of monthly review which came to occupy the place formerly held by the quarterlies. In 1904 he received the honour of knighthood. He died at Brighton on the 13th of February 1908.

KNOWLES, JAMES SHERIDAN (1784-1862), Irish dramatist and actor, was born in Cork, on the 12th of May 1784. His father was the lexicographer, James Knowles (1759-1840), cousin-german of Richard Brinsley Sheridan. The family removed to London in 1793, and at the age of fourteen Knowles published a ballad entitled _The Welsh Harper_, which, set to music, was very popular. The boy's talents secured him the friendship of Hazlitt, who introduced him to Lamb and Coleridge. He served for some time in the Wiltshire and afterwards in the Tower Hamlets militia, leaving the service to become pupil of Dr Robert Willan (1757-1812). He obtained the degree of M.D., and was appointed vaccinator to the Jennerian Society. Although, however, Dr Willan generously offered him a share in his practice, he resolved to forsake medicine for the stage, making his first appearance probably at Bath, and playing Hamlet at the Crow Theatre, Dublin. At Wexford he married, in October 1809, Maria Charteris, an actress from the Edinburgh Theatre. In 1810 he wrote _Leo_, in which Edmund Kean acted with great success; another play, _Brian Boroihme_, written for the Belfast Theatre in the next year, also drew crowded houses, but his earnings were so small that he was obliged to become assistant to his father at the Belfast Academical Institution. In 1817 he removed from Belfast to Glasgow, where, besides conducting a flourishing school, he continued to write for the stage. His first important success was _Caius Gracchus_, produced at Belfast in 1815; and his _Virginius_, written for Edmund Kean, was first performed in 1820 at Covent Garden. In _William Tell_ (1825) Macready found one of his favourite parts. His best-known play, _The Hunchback_, was produced at Covent Garden in 1832; _The Wife_ was brought out at the same theatre in 1833; and _The Love Chase_ in 1837. In his later years he forsook the stage for the pulpit, and as a Baptist preacher attracted large audiences at Exeter Hall and elsewhere. He published two polemical works--the _Rock of Rome_ and the _Idol Demolished by its own Priests_--in both of which he combated the special doctrines of the Roman Catholic Church. Knowles was for some years in the receipt of an annual pension of £200, bestowed by Sir Robert Peel. He died at Torquay on the 30th of November 1862.

A full list of the works of Knowles and of the various notices of him
will be found in the _Life_ (1872), privately printed by his son,
Richard Brinsley Knowles (1820-1882), who was well known as a
journalist.

KNOW NOTHING (or AMERICAN) PARTY, in United States history, a political party of great importance in the decade before 1860. Its principle was political proscription of naturalized citizens and of Roman Catholics. Distrust of alien immigrants, because of presumptive attachment to European institutions, has always been more or less widely diffused, and race antagonisms have been recurrently of political moment; while anti-Catholic sentiment went back to colonial sectarianism. These were the elements of the political "nativism"--i.e. hostility to foreign influence in politics--of 1830-1860. In these years Irish immigration became increasingly preponderant; and that of Catholics was even more so. The geographical segregation and the clannishness of foreign voters in the cities gave them a power that Whigs and Democrats alike (the latter more successfully) strove to control, to the great aggravation of naturalization and election frauds. "No one can deny that ignorant foreign suffrage had grown to be an evil of immense proportions" (J. F. Rhodes). In labour disputes, political feuds and social clannishness, the alien elements--especially the Irish and German--displayed their power, and at times gave offence by their hostile criticism of American institutions.[1] In immigration centres like Boston, Philadelphia and New York, the Catholic Church, very largely foreign in membership and proclaiming a foreign allegiance of disputed extent, was really "the symbol and strength of foreign influence" (Scisco); many regarded it as a transplanted foreign institution, un-American in organization and ideas.[2] Thus it became involved in politics. The decade 1830-1840 was marked by anti-Catholic (anti-Irish) riots in various cities and by party organization of nativists in many places in local elections. Thus arose the American-Republican (later the Native-American) Party, whose national career begun practically in 1845, and which in Louisiana in 1841 first received a state organization. New York City in 1844 and Boston in 1845 were carried by the nativists, but their success was due to Whig support, which was not continued,[3] and the national organization was by 1847--in which year it endorsed the Whig nominee for the presidency--practically dead. Though some Whig leaders had strong nativist leanings, and though the party secured a few representatives in Congress, it accomplished little at this time in national politics. In the early 'fifties nativism was revivified by an unparalleled inflow of aliens. Catholics, moreover, had combated the Native-Americans defiantly. In 1852 both Whigs and Democrats were forced to defend their presidential nominees against charges of anti-Catholic sentiment. In 1853-1854 there was a wide-spread "anti-popery" propaganda and riots against Catholics in various cities. Meanwhile the Know Nothing Party had sprung from nativist secret societies, whose relations remain obscure.[4] Its organization was secret; and hence its name--for a member, when interrogated, always answered that he knew nothing about it. Selecting candidates secretly from among those nominated by the other parties, and giving them no public endorsement, the Know Nothings, as soon as they gained the balance of power, could shatter at will Whig and Democratic calculations. Their power was evident by 1852--from which time, accordingly, "Know Nothingism" is most properly dated. The charges they brought against naturalization abuses were only too well founded; and those against election frauds not less so--though, unfortunately, the Know Nothings themselves followed scandalous election methods in some cities. The proposed proscription of the foreign-born knew no exceptions: many wished never to concede to them all the rights of natives, nor to their children unless educated in the public schools. As for Catholics, the real animus of Know Nothingism was against _political_ Romanism; therefore, secondarily, against papal allegiance and episcopal church administration (in place of administration by lay trustees, as was earlier common practice in the United States); and, primarily, against public aid to Catholic schools, and the alleged greed (i.e. the power and success) of the Irish in politics. The times were propitious for the success of an aggressive third party; for the Whigs were broken by the death of Clay and Webster and the crushing defeat of 1852, and both the Whig and Democratic parties were disintegrating on the slavery issue. But the Know Nothings lacked aggression. In entering national politics the party abandoned its mysteries, without making compensatory gains; when it was compelled to publish a platform of principles, factions arose in its ranks; moreover, to draw recruits the faster from Whigs and Democrats, it "straddled" the slavery question, and this, although a temporary success, ultimately meant ruin. In 1854, however, Know Nothing gains were remarkable.[5] Thereafter the organization spread like wildfire in the South, in which section there were almost no aliens, and the Whig dissolution was far advanced. The Virginia election of May 1855 proved conclusively, however, that Know Nothingism was no stronger against the Democrats than was the Whig party it had absorbed; it was the same organization under a new name. In the North it was even clearer that slavery must be faced. Know Nothing evasion probably helped the South,[6] but neither Republicans nor Democrats would endure the evasion; Douglas and Seward, and later (1855-1856) their parties, denounced it. In the North-West the Know Nothings were swept into the anti-slavery movement in 1854 without retaining their organization. In the state campaigns of 1855 professions were measured to the latitude. The national platform of 1856 (adopted by a secret grand council), besides including anti-alien and anti-Catholic planks, offered sops to the North, the South and the "doughfaces" on the slavery issue. Millard Fillmore was nominated for the presidency. The anti-slavery delegates of eight Northern states bolted the convention, and eight months later the Republican wave swept the Know Nothings out of the North.[7] The national field being thus lost, the state councils became supreme, and local opportunism fostered variation and weakness. By 1859 the party was confined almost entirely to the border states. The Constitutional Union--the "Do Nothing"--Party of 1860 was mainly composed of Know Nothing remnants.[8] The year 1860 practically marked, also, the disappearance of the party as a local power.[9]

Except in city politics nativism had no vitality; in state and national politics it really had no excuse. Race antipathies gave it local cohesive power in the North; various causes, already mentioned, advanced it in the South; and as a device to win offices it was of wide-spread attraction. Its only real contribution to government was the proof that nativism is not Americanism. Public opinion has never accepted its estimate of the alien nor of Catholic citizens. Some of its anti-Church principles, however--as the non-support of denominational schools--have been generally accepted; others--as the refusal to exclude the (Protestant) Bible from public schools--have been generally rejected; others--as the taxation of all Church property--remain disputed.

See L. D. Scisco, _Political Nativism in New York State_ (doctoral
thesis, Columbia University, New York, 1901); L. F. Schmeckebier,
_Know Nothing Party in Maryland_ (Johns Hopkins University, Baltimore,
1899); G. H. Haynes, "A Know Nothing Legislature" (Mass., 1855), in
_American Historical Assoc. Report_, pt. 1 (1896); J. B. McMaster,
_With the Fathers_, including "The Riotous Career of the Know
Nothings" (New York, 1896); H. F. Desmond, _The Know Nothing Party_
(Washington, 1905).

FOOTNOTES:

[1] E.g. for some extraordinary "reform" programmes among German
immigrants see Schmeckebier (as below), pp. 48-50.

[2] "The actual offence of the Catholic Church was its non-conformity
to American methods of church administration and popular education"
(Scisco).

[3] The Whigs bargained aid in New York city for "American" support
in the state, and charged that the latter was not given. Millard
Fillmore attributed the Whig loss of the state (see LIBERTY PARTY) to
the disaffection of Catholic Whigs angered by the alliance with the
nativists.

[4] The Order of United Americans and the Order of the Star Spangled
Banner, established in New York respectively in 1845 and 1850, were
the most important sources of its membership.

[5] This year "American Party" became the official name. Its strength
in Congress was almost thirty-fold that of 1852. It elected
governors, legislatures, or both, in four New England states, and in
Maryland, Kentucky and California; minor officers elsewhere; and
almost won six Southern states.

[6] For it delayed anti-slavery organization in the North, and
presumably discouraged immigration, which was a source of strength to
the North rather than to the South.