Centre of
Gravity.

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

Gravity. 4037.6768 for that of double the plane 8 d IG, and its momentum 4037.6768X85-35= 344615-7149 51.12 the area of double the trapezium AR d8, and its momentum 51.12*8.47=

432.9804
the area of the foremost trapezium, and its momentum 79.16 x 158.61=

12555-5676
0.77
the area of the section of the post, and its momentum 0.77 x 0.29=

0.2233
0.77
the area of the section of the stem, and its momentum 0.77X169.76=

130.7152
4169.4968 Sum

357735.2074 Then 357735.2074

= 85.80, the distance of the fourth horizontal section from the aft side of the stern-post. 4169.4968

79.16

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

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

328

6

Hence the distance of the centre of gravity of double the plane 8ck G from its first ordinate is 2358 3

2358.25
328.04

X10

4=

X10.03=

72.10

Distance of this ordinate from the aft side of the post

13.50

85.60

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 AR c 8 from its ordinate AR
Distance of this ordinate from the aft side of post

7.42 0.58

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

8.00

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

4.22 153.78

158.00

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

0.29 169.76

The

Centre of
Gravity.

31.21

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

Gravity. 3290.2412 for the area of double the plane 8 ck G, and its momentum 3290.2412X85.6= 281644.6467 the area of double the trapezium AR c 8, and its momentum 31.21 X 8=

249.68 42.43 the area of the foremost trapezium, and its momentum 42.43 X 158=

6703.94 0.77 the area of the section of the post, and its momentum 0.77 x 0.29=

0.2233 0.77 the area of the section of the stem, and its momentum 0.77 x 169.76=

130.7152 3365.4212 Sum

288729.2052 Now 288729.20 52=85.79, the distance of the centre of gravity of the whole section from the aft side of the

3365-4212
stern.

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.
Ordinates. Double Ord. 1. Factors 1. Products. 2. Fact. 2. Products.
Feet. In. L. Feet. In. L.

Feet. In. L.

Feet. In. L.
of

4 0
2 5
4 5

2

1
7 3 6
(14 7

3
43 9

I

14 7
9
3 6
4

1

3 I2

I 21

I

24

2 6
13 3
26 6

1

26 6
13 9 9
27 7 6

193 4

I

27 7 6
13 7
27 2

8
217 4

1

27 2
I2 8
25 4

9
228

I

25 4 10 6 6

210 10

21
7
14 2

1

14
4 7 3 9
2 6

JIO 6

I

9
2 10 6
5 9

13
74 9

5 9
3 I
6 x (3 -4§ 4 3

of

I

2

I

I

4 10

4 10 17 8

8 10

IO

ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܪܕ

ܘ ܘ ܘ ܘ ܘ ܚ ܘ ܘ ܘ ܘ ܘ ܘ ܚܗ

Ноооооооооооооо

ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ 3

10

I

2

12

2

1

Hence the distance of the centre of gravity of double the plane 8 b v G from its first ordinate 8 6 is
1639_93

1639.77
X 10 4=
* 10,03 =

70.84
232 3

232.24 Distance of this ordinate from aft side of post

13.50

Hence the distance of the centre of gravity of the plane from the ast side of the post is
Distance of the centre of gravity of the trapezium AR 6 8 from its ordinate AR
Distance of this ordinate from the aft side of the post

6.88 0.38

7.46

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

2.92 153.78

156.70

0.29 169.76

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

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 b 8, and its momentum 21.52 X 7.46 =
15.04 the area of the foremost trapezium, and its momentum 15.04 X 156.7 =
0.77 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 =

196374.2366

160.5392 2356.7680

0.2233 130.7152

2366.4642 Sum

199022.4823

Now

Centre of
Gravity.

Centre of
Gravity.

Now 1990 22.4823

-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.

35 I 6

35.12

Hence the distance of the centre of gravity of double 352.2536, the area of double the plan

8 ah G, and its momentum this plane from its first ordipate is 205 4 6

X10 O 4

352.2536 x 72.15= 25415 9 2 205.37

17.1570, the area of double the rectanX 10.83=

58.65

gle A R a 8, and its moThe distance of this ordinate from aft side of

mentum 17.1570 X 7.03=

120.6137 post =

3.3250, the area of the foremost rect13.50

angle, and its momentum Hence the distance of the centre of gravity of

3.3250 X 155.03=

515.4747 this plane from the aft side of the post is 72.15

the area of the section of the

0.77, Distance of the centre of gravity of double the

post, and its momentum rectangle A R a 8 from its ordinate AR

0.77 X 0.29

0.2233 Distance of this ordinate from the aft side of

0.77, the area of the section of the

stem and its momentum
0.58
0.77 X 166.765

130.7152
Distance of the centre of gravity of this rect-
angle from the aft side of the post

374.2756

Sum 26182.1 242

7.03
Distance of the centre of gravity of the fore-
most rectangle from its ordinate 7'7ey

2618 2.1 242
1.25 Then

=69.95, the distance of the
Distance of this ordinate from the aft side of

374.2756
153.78 centre of gravity of the whole section from the aft side

6.45

the post

the post

of the post.

Distance of the centre of gravity of this rect-
angle from the aft side of the post

155.03

VII. Determination of the Centre of Gravity of the
Distance of the centre of gravity of the sec-

Eighth Plane.
tion of the post from its aft side

0.29
Distance of the centre of gravity of the sec-
tion of the stem from the aft side of the

This plane is equal in length to the seventh horizon-
post

169.76 tal plane, and its breadth is equal to that of the keel.

The distance between the seventh and eighth planes is Now, the areas of these several plans being calculat- three feet, but which is here taken equal to 2 feet 11 ed will be as follows.

inches.

Vol. XIX. Part I.

+

Qq

Distance

I

1

1

1

5974.16((348)—4) *• 19913,87

Centre of Distance between the aft side of the post and

Hor. Planes. Ist Fact. ist Products. 2d Faci. 2d Products.

Centre el
Gravity. the first ordinate

13.5 208.00 es

34.67 os 104.00 Gravity.
Fourteen intervals between the fifteen ordi.

374.27

374.27

374.27
nates, each interval being 10.03 feet 140.42 2366.46 2

4732.92

2366.46
Distance of the last ordinate from Ibe fore foot 2.2 3365-42

3 10096.26 3365.42

4169.50 4 16678.00 4169.50
Hence the length of the eighth plane is 156.12 4939.27

5 24696.35

4939.27
Which multiplied by the breadth

1.33 5592.27

33553.62

5592.27
The product is the ares of this plane
208.

of 2987.08
The distance of its centre of gravity from the
aft side of the post, being equal to half its

110079.96

23898.27
length, is

78.06

110079.96
The centres of gravity of these eight planes being

Now
23898.27

X 2.95=13.588, the height of the
found, the distance of the centre of gravity of the bot-

centre of gravity of the bottom of the ship above the
tom of the ship from the aft side of the post, and also

lower edge of the keel,
its altitude, may from thence be easily determined.

. We have now found the distance of the centre of gra-
From the principles already explained, the distance of vity of the bottom of the ship from the aft side of the
the centre of gravity of the bottom from the aft side of post, and its altitude above the tower edge of the keel.
the post, is equal to the sum of the momentums of an

Hence the ship being supposed in an upright position,
infinite number of horizontal planes, divided by the sum

this centre of gravity will necessarily be in the vertical
of these planes, or, which is the same, by the solidity longitudinal section which divides the ship into two equal
of the bottom. As, however, we have no more than

and similar parts; the position of this centre is therefore
eight planes, we must therefore conceive their momen-

determined.
tums as the ordinates of a curve, whose distances may

It now remains to find the height of the metacenter

70
be the same as that of the horizontal planes. Now the above the centre of gravity ; the expression for this alti-tion of the

Determina-
sum of these ordinates minus half the sum of the extreme

height of
ordinates being multiplied by their distance, gives thetude, as found in Chap. III. is **7"; which we shall

V
surface of the curve ; of which any ordinate whatever

center

now apply to determine the metacenter of the ship of above the
represents the momentum of the horizontal plane at the
came altitude as these ordinates ; and the whole surface

74 guns, whose centre of gravity we have already found. centre of

gravity.
will represent the sum of the momentums of all the ho.
rizontal planes.

Ord. of the Plane of Floatation. Cub.of Ordinates.

feet. Inches. Feet and dec, uf foot
Ilor. Planes Fac', Products. Momentums. Faet. Products.

14 9

14.7

3209.046
5974.16 012987.08 503037-73

251518.86

17
6
17.1

5000.211
5592.27 5592.27 473560.21

473560.31
18 9

18.7

6597.797
4939.27 4939.27 422084.77 I 422084.77

7762.392
4169.50 4169.50 357735.21 357735.21 20 7 6

20.6

8741.816
3365.42 3365.42 288729.20 288729.20 21

9
21.2

9595.703
2366.46 I 2366.46.1990 22.48 1990 22.48

21 6 3

21.5

9938.375
374.27
374.271 21682.1 2

21682.12

7 9
21.7

10289.109
208.00 of
104.00 16236.48 o'}

8118.24

ng 9
21.7

10289.109
21 7 6

21.7

10289. 109
23898.271

2022451.09

4
21.3

9663.597
6
20.9

9129.329
2022451.09
Now
=84.63, the distance of the centre 19 9

19.7

7703.734
of
23898.27

4
6
17.4

5268.024
gravity of the bottom of the ship from the aft side of

13 3

13.1

2248.091
The beight of the centre of gravity of the bottom 29.1 3

291.1

115719.442
above the lower edge of the keel may be determined by
the same principles. Thus,

Ordinate at 10.03 feet abaft the ordi-
To one-sixth of the lowermost horizontal section add

nate 8 g,=4, of which the cube is
the product of one-sixth of the uppermost section by 64, and 64

32.
three times the number of sections minus four the se- Ordinate at 10.03 feet afore the ordi-
cond section in ascending, twice the third, three times nate Goz6, cube of which is 216
the fourth, &c.; and to ball the sum of the extreme and 216 x

108.
planes add all the intermediate ones. Now the first of
these sums, multiplied by the distance between the planes Sum

115859.442
or sections, and divided by the second sum, gives the Distance between the ordinates

10.03
altitude of the centre of gravity of the bottom of the
ship above the lower edge of the keel as required. Product

1162070.20326

Product

1

1

19.8

I

I

I

I

32.

a

enbic feet: hence *sy'* =77517.26

Centre of Product
1162070.20326 In the valuable work to which we have just referred,

Appendix. Gtavity. Half the cube of the after

the following directions are given for cutting sails. most ordinate

" The width and depth being given, find the number Half the cube of the thick.

of cloths the width requires, allowing for seams, tabling ness of the stem

0.14

on the leeches, and slack cloth ; and, in the depth, al

low for tabling on the head and foot. For sails cut Sum

32.14

square on the head and foot, with gorés only on the Distance between the ordinates 3.0

leeches, as some topsails, &c. the cloths on the head,

between the leeches, are cut square to the depth ; and Product

96.42 the gores on the leeches are found by dividing the depth
Half the cube of the fore-

of the sail by the number of cloths gored, which gives
most ordinato
108.

the length of each gore. The gore is set down from a
Half the cube of the thick-

square with the opposite selvage; and the canvas being ness of the stem

.14

cut diagonally, the longest gored side of one cloth

makes the shortest side of the next; consequently, the Sum

108.14

first gore being known, the rest are cut by it. In the Distance between the ordinates 5.5

leeches of topsaily cat hollow, the upper gores are long

er than the lower ones ; and in sails cut with a roach Product

594.77 leech, the lower gores are longer than the upper ones.

This must be regulated by judgment, and care taken sys

1162761.393 26 that the whole of the gores do not exceed the depth of

the leech. Or, by drawing on paper the gored side of 23 y: x

2325522.78652 the sail, and delineating the breadth of every cloth by

a convenient scale of equal parts of an inch to a foot, sye a

775174.26217 the length of every gore may be found with precision. The solidity of the bottom is 25271 tons=70018.67

Sails, gored with a sweep on the bead or the foot, or

on both, have the depth of their gores marked on the :

=11.07 feet, the selvage, from the square of the given depth on each 70018.67

cloth, and are cut as above ; the longest selvage of one
altitude of the metacenter above the centre of gravity serving to measure the shortest selvage of the next, be-
of the bottom of the ship.

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 gorės that are irregular no strict rule
APPENDIX.

can be given; they can only be determined by the judge

ment of the sail-maker, or by a drawing. When a ship is built, she must be fitted with masts, “ In the royal navy, mizen topsails are cut with Elements yards, sails, ropes, and blocks, or in other words, she three quarters of a yard hollow in the foot; bat, in the and Pracmust be rigged before she can go to sea. To complete merchant service, top and topgallant sails are cut with this article, it may therefore be thought necessary to more or lesz hollow in the foot. Flying jibs are cut and Soatreat of the art of rigging vessels ; but tre have else- with a roach curve on the stay, and a thrie-inch gore minship, where (see Mast-Rigging, Rore-Making, and SAIL) in each cloth, shortening from the tack to the clue. vol. 1. p. 91. shown how the several parts of a ship's rigging are Lower studding-sails are cat with square leeches, and mades, and the art of putting them properly together, topmast and topgallant-mast studding sails with goring so as to make the ship best anstrer the purpose for which leeches. she is intended, depends upon a jast knowledge of the “ The length of reef and middle bands is governed by impulse and resistance of fluids, and of the theory and the width of the sail at their respective places; the leechpractice of seamanship. See Resistance of Fluids linings, buntline-cloths, top-linings, mast-cloths, and corand SEAMANSHIP). Nothing, therefore, of the subject ner-pieces, are cut agreeably to the depth of the sail; is left to us here, except we were to state in few words each cloth and every article should be properly marked the progressive method of rigging ships; but there is no with charcoal, to prevent confusion or mistake. Sails one undeviating mode which is porsued, as the nature of that have bonnets are cut out the whole depth of the the operation is such that all the parts of it may be ad- sail and bonnet included, alloiring enough for the tavancing at the same time. We shall therefore take our blings on the foot of the sail and head and foot of the leave of ships and ship-building with a few general ob- bonnet. The bonnet iz cut off after the sail is serred toservations on sail-making, and refer our readers for far- gether. If a drabler is required, it is allowed for in the ther information to the very elegant work on the Ele- cutting out the same as the bonnet. ments and Practice of Rigging and Scamanship in two When the cloth is thus properly cut, the different volumes onarto.

pieces are to be joined together in the form of a sail; Sails are made of canvas, of different textures, and are and for doing this properly we have the following diestended on or between the masts, to receive the wind rections in the work already quoted. “ Sails have a that forces the vessel through the water. They are double flat seam, and should be se wed with the best quadrilateral or triangular, as bas been else where de- English made twine of three threads, spun 360 failiomis scribed, and are cut out of the canvas cloth by cloth. to the pound, and have from one hundred and eight to The width is governed by the length of the yard, gaff, one hundred and sixteen stitches in every yard in length. boom, or stay; the depth by the height of the mast. The twine for large sails, in the royal navy, is based

tice of Rigging