Centre of

Gravity.

51.12 79.16

The areas of these several planes being calculated, will be as follow:

4037.6768 for that of double the plane 8 d1G, and its momentum 4037.6768×85.35=
the area of double the trapezium AR d8, and its momentum 51.128.47=
the area of the foremost trapezium, and its momentum 79.16 × 158.61=
the area of the section of the post, and its momentum 0.77 X 0.29=
the area of the section of the stem, and its momentum 0.77 X 169.76=

0.77
0.77

344615.7149
432.9804
12555-5676

0.2233

130.7152

357735.2074

Centre of
Gravity.

4169.4968

85.80, the distance of the fourth horizontal section from the aft side of the stern-post.

V. Determination of the Centre of Gravity of the Fifth Horizontal Section.

Distance of the centre of gravity of double the plane 8 c k G from its first ordinate 8 c.

14 10

12 10

96

9

8

I

123456789

3

27 86

Como o oo m96

30 6

32

32 10

32 6

31 6

29 8

25 8 6

19 5 6

12 3

3 30 66 0((3×15)—4) ×&

166 6 3 333 0 7

2358 3 0

Hence the distance of the centre of gravity of double the plane 8 c k G from its first ordinate is

Feet. In. L.

2. Products. Feet. In. L.

10

26323

9 O

16 6 O

4 6

27 8 6

30 6

I

32

282 9

233
159

O O O O 600

I

I

32 10 32 6

I

31 6

I

29 8

Distance of the centre of gravity of the plane from the aft side of the post

Distance of the centre of gravity of double the trapezium ARc 8 from its ordinate AR
Distance of this ordinate from the aft side of post

13.50

85.60

7.42

0.58

Distance of centre of gravity of trapezium from aft side of the post

Distance of the centre of gravity of the foremost trapezium from its ordinate G
Distance of this ordinate from the aft side of post

Distance of the centre of gravity of the foremost trapezium from the aft side of the post

Distance of the centre of gravity of the section of the post from the aft side of post
Distance of the centre of gravity of the section of the stem from the aft side of post

8.00

4.22 153.78

158.00

0.29 169.76

The

Centre of

Gravity.

C

The areas of these several planes being calculated, will be as follow:
3290.2412 for the area of double the plane 8 c k G, and its momentum 3290.2412x85.6=
31.21
the area of double the trapezium AR c 8, and its momentum 31.21 X8=
42.43
the area of the foremost trapezium, and its momentum 42.43 × 158=
the area of the section of the post, and its momentum 0.77 X 0.29=
0.77 the area of the section of the stem, and its momentum 0.77 X 169.76=

0.77

Centre of
Gravity.

281644.6467
249.68
6703.94

0.2233 130.7152

288729.2052

=85.79, the distance of the centre of gravity of the whole section from the aft side of the

VI. Determination of the Centre of Gravity of the Sixth Horizontal Section.
Distance of the centre of gravity of double the plane 8 bi G from its first ordinate 8 b.

Hence the distance of the centre of gravity of double the plane 8 bv G from its first ordinate 8 b is

1639 9 3

1639-77
X 10 O 4=
X 10.03 =
232 I 3
232.24
Distance of this ordinate from aft side of post

70.84

13.50

Hence the distance of the centre of gravity of the plane from the aft side of the post is

84.34

Distance of the centre of gravity of this trapezium from the aft side of the post
Distance of the centre of gravity of the section of the post from its aft side
Distance of the centre of gravity of the section of the stem from the aft side of the post

156.70

0.29

169.76

The areas of these planes will be found to be as follow:

2328.3642 for that of double the plane 8 b i G, and its momentum 2328.3642 + 84.34 =
21.52 for the area of double the trapezium AR 6 8, and its momentum 21.52 × 7.46 =
the area of the foremost trapezium, and its momentum 15.04 X 156.7 =
the area of the section of the post, and its momentum 0.77 X 0.29 =
the area of the section of the stem, and its momentum 0.77 x 169.76 =

15.04

0.77
0.77

2366.4642 Sum

Catre of

Gravity.

Now 199922.4823-84.1, the distance of the centre of gravity of the whole from the aft side of the post.
2366.4642

VII. Determination of the Centre of Gravity of the Seventh Horizontal Section.

Distance of the centre of gravity of double the plane 8 ah G from its first ordinate 8 a.

Centre of
Gravity.

The distance of its centre of gravity from the
aft side of the post, being equal to half its
length, is

78.06

The centres of gravity of these eight planes being found, the distance of the centre of gravity of the bottom of the ship from the aft side of the post, and also its altitude, may from thence be easily determined.

From the principles already explained, the distance of
the centre of gravity of the bottom from the aft side of
the post, is equal to the sum of the momentums of an
infinite number of horizontal planes, divided by the sum
of these planes, or, which is the same, by the solidity
of the bottom. As, however, we have no more than
eight planes, we must therefore conceive their momen-
tums as the ordinates of a curve, whose distances may
be the same as that of the horizontal planes. Now the
sum of these ordinates minus half the sum of the extreme

ordinates being multiplied by their distance, gives the
surface of the curve; of which any ordinate whatever
represents the momentum of the horizontal plane at the
came altitude as these ordinates; and the whole surface
will represent the sum of the momentums of all the ho-
vizontal planes.

Hor. Planes Fac', Products. Momentums.

110079.96
Now
×2.95=13.588, the height of the
23898.27
centre of gravity of the bottom of the ship above the
lower edge of the keel,

We have now found the distance of the centre of gra-
vity of the bottom of the ship from the aft side of the
post, and its altitude above the lower edge of the keel.
Hence the ship being supposed in an upright position,
this centre of gravity will necessarily be in the vertical
longitudinal section which divides the ship into two equal
and similar parts; the position of this centre is therefore
determined.

Fact. Products.

5592.27 I

5592.27 473560.21

I

473560.31

18 9

18.7

6591.797

422084-77

7762.392

8741.816

3365.42 I

3365-42 288729.20 I

288729.20

2366.46 I

2366.46 199022.48 I

199022.48

21

693

374.27 I

374.27 21682.12 I

21.7

10289.109

21.7

10289.109

9663.597

20 10 6

Now 2022451.09 84.63, the distance of the centre
23898.27

gravity of the bottom of the ship from the aft side of
the post.

The height of the centre of gravity of the bottom above the lower edge of the keel may be determined by the same principles. Thus,

Ordinate at 10.03 feet abaft the ordi-
nate 8 g, 4, of which the cube is
64, and 64 ×

Ordinate at 10.03 feet afore the ordi-
nate Go 6, cube of which is 216
and 216X

To one-sixth of the lowermost horizontal section add
the product of one-sixth of the uppermost section by
three times the number of sections minus four the se-
cond section in ascending, twice the third, three times
the fourth, &c.; and to half the sum of the extreme
planes add all the intermediate ones. Now the first of
these sums, multiplied by the distance between the planes
or sections, and divided by the second sum, gives the Distance between the ordinates
altitude of the centre of gravity of the bottom of the
ship above the lower edge of the keel as required.

Product

32.

108.

115859.442

10.03

1162070.20326
Product

32.

0.14

32.14

Distance between the ordinates 3.0

Product

96.42

1162070.20326 In the valuable work to which we have just referred,
the following directions are given for cutting sails.
"The width and depth being given, find the number
of cloths the width requires, allowing for seams, tabling
on the leeches, and slack cloth; and, in the depth, al-
low for tabling on the head and foot. For sails cut
square on the head and foot, with gores only on the
leeches, as some topsails, &c. the cloths on the head,
between the leeches, are cut square to the depth; and
the gores on the leeches are found by dividing the depth
of the sail by the number of cloths gored, which gives
the length of each gore. The gore is set down from a
square with the opposite selvage; and the canvas being
cut diagonally, the longest gored side of one cloth
makes the shortest side of the next; consequently, the
first gore being known, the rest are cut by it. In the
leeches of topsails cut hollow, the upper gores are long-
er than the lower ones; and in sails cut with a roach
594-77 leech, the lower gores are longer than the upper ones.
This must be regulated by judgment, and care taken
1162761.39326 that the whole of the gores do not exceed the depth of
the leech. Or, by drawing on paper the gored side of
2325522.78652 the sail, and delineating the breadth of every cloth by
a convenient scale of equal parts of an inch to a foot,
the length of every gore may be found with precision.
Sails, gored with a sweep on the head or the foot, or
on both, have the depth of their gores marked on the
selvage, from the square of the given depth on each
cloth, and are cut as above; the longest selvage of one
serving to measure the shortest selvage of the next, be-
ginning with the first gored cloth next the middle in
some sails, and the first cloth next to the mast leech in
others. For those gores that are irregular no strict rule
can be given; they can only be determined by the judge-
ment of the sail-maker, or by a drawing.

775174.26217 The solidity of the bottom is 2527 tons=70018.67 cubic feet: hence **_77517.26 sy 11.07 feet, the 70018.67 altitude of the metacenter above the centre of gravity of the bottom of the ship.

APPENDIX.

WHEN a ship is built, she must be fitted with masts, yards, sails, ropes, and blocks, or in other words, she must be rigged before she can go to sea. To complete this article, it may therefore be thought necessary to treat of the art of rigging vessels; but we have elsewhere (see MAST-Rigging, ROPE-MAKING, and SAIL) shown how the several parts of a ship's rigging are made; and the art of putting them properly together, so as to make the ship best answer the purpose for which she is intended, depends upon a just knowledge of the impulse and resistance of fluids, and of the theory and practice of seamanship. See RESISTANCE of Fluids and SEAMANSHIP). Nothing, therefore, of the subject is left to us here, except we were to state in few words the progressive method of rigging ships; but there is no one undeviating mode which is pursued, as the nature of the operation is such that all the parts of it may be advancing at the same time. We shall therefore take our leave of ships and ship-building with a few general observations on sail making, and refer our readers for farther information to the very elegant work on the Elements and Practice of Rigging and Seamanship in two volumes quarto.

Sails are made of canvas, of different textures, and are extended on or between the masts, to receive the wind that forces the vessel through the water. They are quadrilateral or triangular, as has been elsewhere described, and are cut out of the canvas cloth by cloth. The width is governed by the length of the yard, gaff, boom, or stay; the depth by the height of the mast.

Appendix.

Rigging

"In the royal navy, mizen topsails are cut with Elements three quarters of a yard hollow in the foot; but, in the and Prac tice of merchant service, top and topgallant sails are cut with' more or less hollow in the foot. Flying jibs are cut and Scawith a roach curve on the stay, and a three-inch gore manship, in each cloth, shortening from the tack to the clue. vol. i. p. 91. Lower studding-sails are cut with square leeches, and topmast and topgallant-mast studding sails with goring

leeches.

Sails

"The length of reef and middle bands is governed by
the width of the sail at their respective places; the leech-
linings, buntline-cloths, top-linings, mast-cloths, and cor-
ner-pieces, are cut agreeably to the depth of the sail;
each cloth and every article should be properly marked
with charcoal, to prevent confusion or mistake.
that have bonnets are cut out the whole depth of the
sail and bonnet included, allowing enough for the ta-
blings on the foot of the sail and head and foot of the
bonnet. The bonnet is cut off after the sail is sewed to-
gether. If a drabler is required, it is allowed for in the
cutting out the same as the bonnet.

When the cloth is thus properly cut, the different
pieces are to be joined together in the form of a sail;
and for doing this properly we have the following di-
rections in the work already quoted. "Sails have a
double flat seam, and should be sewed with the best
English made twine of three threads, spun 360 fathoms
to the pound, and have from one hundred and eight to
one hundred and sixteen stitches in every yard in length.
The twine for large sails, in the royal navy, is waxed