MENTS IN SHIPS AND OTHER FLOATING VESSELS
Year: 1855

page_text: MENTS IN SHIPS AND OTHER FLOATING VESSELS" to be as follows:-
My Invention consists in giving to ships and other floating vessels certain
forms, determinable by the under-mentioned principle or modifications of the
said forms so determined, for the purpose of enabling the ship or other vessel
to displace laterally the least quantity of water during her progress.
In determining the stability of a ship or vessel of a given tonnage or dis-
placement of water when loaded, I consider it as a prism, the length of which
is equal to that of the ship at the plane of floatation when loaded, and that
the thickness and density of the sides and decks, and the disposition and

page_text: weight of the masts, sails, stores, load, &c. are the same in both. I assume,
also, that when the wind is brisk, having an assigned pressure per square foot
of sail, that both shall equally carry the same assigned surface of sail, the
centre of effort of the wind being at a determined height, and that the angle
to which they shall be inclined shall also be assigned. I then assume such a
form for the transverse section of the prism as I think most likely to suit, and
by calculating the momenta of the weight of each detail above the keel, I can
approximate to the height of the general centre of gravity of the prism or ship
when loaded.
I then calculate in the usual manner the height of the centre of buoyancy,
both in its erect position, and when inclined at the above angle of inclination.
The position of these centres as well as that of the centre of gravity of the
prism being found, the relative stability can be ascertained in the usual manner.
-If it be deficient, I increase the ordinate and diminish the absciss at the plane
of floatation of the assumed transverse section of the prism, and vice versa, if
the stability be greatly in excess, until I obtain the required degree of stability,
and the required form of the transverse section of the prism.
The transverse section of the prism having thus been finally determined, I
then divide its total height or depth at equal distances by any convenient
number of horizontal sections parallel with the plane of floatation, and having
calculated the areas of the several horizontal sections of the prism, I divide
the ship by corresponding horizontal sections in a similar manner, and make
the areas of the respective sections of the prism determine the areas of the
corresponding sections of the ship, and make the latter in all cases equal to
the former, whatever may be the shape of the outline of the horizontal sections
of the ship.
The length of the horizontal sections of the ship is determined by such form
of the sheer plan as the ship-builder may consider to be most suitable for his
purposes, the vertical height or depth of which is to be divided by the hori-
zontal sections in the same manner as described for the prism, the height or
depth of both being the same. The calculated area of the several horizontal
sections being divided by the corresponding length on the sheer plan, the

page_text: quortent wit give the corresponding mean wrath of the horizontal sections of
the ship at corresponding heights or depths. Three halves of these mean
widths will give the corresponding extreme widths of all such horizontal
sections of the ship as are composed of two equal and similar segments of the
5 common parabola. But instead of the vertex of each parabolic segment being
in the opposite sides of the ship, as in the usual method of ship-building, I
place the vertex of each in the same point in the bow, and their other
extremity in the same plane at the stern; consequently the position of the
extreme widths of the several horizontal sections of the ship will not coincide
0 in the same vertical plane as in the midship section of a ship built upon the
usual principle, but will be ahead of their middle point and distant from it
according as the extreme widths increase in width.
I do not, however, confine myself to makeing the outline of the horizontal
sections common parabolic segments throughout the entire height or depth
of the ship, as in that case the extreme widths of the sections above any
assumed height may become inconveniently great, and above which height it
may be necessary either to continue the the extreme widths of the same width,
or even to lessen them in any convenient proportion; consequently the areas,
the lengths, and the extreme of the several horizontal sections above such
determined height being given, I either find such other variety of the parabola
than the common parabola, as shall be of the same area, length, and extreme
width, the outline of which shall form that of the corresponding horizontal
sections of the ship; or I introduce a parallelogram into the middle of the
horizontal section, which is terminated at each end by the segment of a common
parabola in such a manner that the area of the three together shall be equal
to that of the respective horizontal section, and the width of the parallel-
ogram shall be equal to the respective extreme width, whilst the sides of the
parallelogram shall be the mutual tangent of the two terminal segments
of the common parabola.
By this principle of construction, the lengths and areas of the several hori-
zontal sections may be equal to those of a ship of any ordinary construction,
whilst the extreme widths will be less than by adopting an assigned midship

page_text: section, as is usual, and consequently a less lateral displacement of the water
in the ship's progress would ensue, and consequently less power would be
required to propel a ship so constructed.
The sheer plan having been selected by the ship-builder's convenience, the
position thereon of the extreme widths being determined by all such horizontal
sections as have a common parabola for their outline, the vertex being in the
bow will describe on the sheer plan a curve advancing from near the middle of
the keel upwards towards the bow to the height where it has been determined
to narrow the extreme widths. From that point this curve should be continued
upwards, forwards, or towards the bow, if considerable room at the stern be
unimportant, but retrograde or towards the stern if it be essential to have a
roomy stern.
This curve is to regulate the position of such of the extreme widths as have
to be narrowed, and the abscisses to the ordinates of the parabolas or para-
boloids, forming the outline of the horizontal sections, are to be in or parallet
to the straight line joining the middle point of the length of the horizontal
sections with the extremities of the extreme widths.
The position at which the several transverse sections for forming the half
body plan may then be determined on the sheer plan, and thence laid down
upon the several horizontal sections of the ship, from which the ordinates may
be taken and the half body plan formed in the usual manner, thus giving the
necessary lines and dimensions for the ship's construction.
by the said Henry Emmanuel Scott in the Great Seal Patent Office on
the 22nd November 1835.
TO ALL TO WHOM THESE PRESENTS SHALL COME, I IlENRY
EMMANUEL SCOTT, of Brixton, in the County of Surrey, Civil Engineer, send
greeting.
WHEREAS Her most Excellent Majesty Queen Victoria, by Her Letters
Patent, bearing date the Twenty-second day of May, in the year of our Lord

page_text: One thousand eight hundred and fifty-five, in the nineteenth year of Her
reign, did, for Herself, Her heirs and successors, give and grant unto me, the
said Henry Emmanuel Scott, Her special licence that I, the said Henry
Emmanuel Scott, my executors, administrators, and assigns, or such others as
I, the said Henry Emmanuel Scott, my executors, administrators, and assigns,
should at any time agree with, and no others, from time to time and at all
times thereafter during the term therein expressed, should and lawfully might
make, use, exercise, and vend, within the United Kingdom of Great Britain
and Ireland, the Channel Islands, and Isle of Man, an Invention for "IN-
PROVEMENTS IN SHIPS AND OTHER FLOATING VESSELS," upon the condition (amongst
others) that I, the said Henry Emmanuel Scott, by an instrument in writing
under my hand and seal, should particularly describe and ascertain the nature
of the said Invention, and in what manner the same was to be performed, and
cause the same to be filed in the Great Seal Patent Office within six calendar
months next and immediately after the date of the said Letters Patent.
NOW KNOW YE, that I, the said Henry Emmanuel Scott, do hereby
declare the nature of my said Invention, and in what manner the same is to
be performed, to be particularly described and ascertained in and by the
following statement:-
My improvements consist, first, in making the horizontal sections of a ship
or vessel of two suitable segments of a common parabola, so that the vertex
of each shall be mutably in the same point at the bow, whilst their other
extremity shall be mutually in the same point at the stern, and their extreme
breadth together shall be equal to that of the ship or vessel at the correspond-
ing depth or height, the usual method being to place the vertex of the para-
bolic segments in the opposite sides of the ship; and this construction of these
sections may extend either throughout the entire height or depth of the ship,
or only to an assigned height above the keel, as may be suitable; secondly, in
arranging the extreme widths of the several horizontal sections of the ship in
such a manner that those above are in advance of or are ahead of those
beneath, instead of collecting them in one vertical transverse plane commonly
called the midship section."
In determining the stability of a ship or vessel proposed to be built of a

page_text: given tonnage, say 3,250 tons, or say 118,664 cube feet of displacement of
water when loaded, I consider it as a prism Us QV, Fig. 3, the length of
8
which is equal to S H, say 296 feet, that of the ship at the plane of float-
ation SH when loaded, and that the thickness and density of the sides, and
the disposition and weight of the masts, sails, stores, load, &c. are the same in
both. Then by calculating the momenta of the weight of each detail above
the keel d, Fig. 5, I can approximate to the height of the general centre of
gravity g of the ship or prism when loaded, say 4 feet above b C b, the plane
of floatation. I assume also that when the wind is brisk, having an assigned
pressure, say 3 pounds per square foot of sail, (distinguished algrebraically by
the letter W.) that both shall equally carry the same assigned surface of snil,
say 162,000 square feet, (distinguished algrebraically by the letter S,) the centre
of the effort of the wind P, Fig. 5, being at an assigued height P L, say 150
feet above the centre of buoyancy B, when the prism is assumed to be inclined
by the wind to an assigned angle, say 30, (distinguished algebraically by the
Greek letter,) from the erect position.
1
的
I then assume such a form for the transverse section of the prism y b d by,
Figs. 1 and 5, as I think most likely to suit, the area of immersion bdb of
which below the plane of floatation b C b must be equal to the quotient of the
above given amount of cubic feet of displacement, viz., 113,664 cube feet,
when divided by the above given length sQ of the prism, Fig. 8; that is,
the area of bd b must be equal, or 384 square feet. I then calculate
in the usual manner the height of the centre of buoyancy B. Fig. 5, of the
prism in its erect position, and B when inclined at the assigned maximum
angle of inclination 6. The stability at this angle of inclination can then be
ascertained in the usual manner.
1 1
113504
Thus, in the bent lever PB G, Fig. 5, we have at the end G of the arm G GB
the weight of the ship pressing downwards, and at the end P of the other
arm PB of this lever the lateral effect of the wind W in pounds, acting upon
the given surface of the sails S in square feet. Therefore, to counterbalance
this latter force, we must have the stability as represented by the momentum
of the product of the weight of the prism or ship in pounds, when multiplied by
the length of G B in feet, equal to the momentum of the lateral effect of the

page_text: wind W in pounds per square foot upon the given surface of the sails S in
square feet, when multiplied by the length of PB in feet. If the stability be
deficient to balance the other force, I increase the ordinate b C b, and diminish
the absciss Cd at the plane of floatation of the assumed transverse section
of the prism, and vice versa, if the stability be greatly in excess, until I obtain
the requisite degree of stability, and the required form for the transverse
section of the prism.
12
13
21 26
40
The transverse section of the prism y bd by, Figs. 1 and 5, having thus
been finally determined, I then divide its total height or depth d 40 at equal
distances by any convenient number of horizontal sections parallel with the
plane of floatation b Cb, and I distinguish algrebraically by the letter y the
several ordinates y 12 y, b Cb, y 24 y, &c. at these several heights or depths,
and the length sQ, Fig. 3, of the prism by the Italic letter 1, and I calculate
the areas of these several horizontal sections of the prism by multiplying the
respective ordinates y by the length 1 of the prism; thus ly represents algre-
braically the respective areas generally.
I then divide the ship by corresponding horizontal sections in a similar
manner, as shewn on Fig. 1 and 4, and distinguish their respective mean
widths by the letter b, their extreme widths by the letter B, and their corre-
sponding lengths by the letter 1. I then make the areas of the respective
horizontal sections of the prism determine the areas of the corresponding hori-
zontal sections of the ship, and make the latter in all cases equal in area to
the former. Thus algrebraically the areas 1b are equal to ly, and as the
lengths I have to be found by measurement at the corresponding height of the
sheer plan, Fig. 3, therefore the mean widths of the respective horizontal
sections of the ship are by, or are equal to the quotient of the areas of
the horizontal sections of the prism when divided by the corresponding length I
of the horizontal sections of the ship at the respective depths.
I then determine that the outline of the several horizontal sections of the
ship shall be of the form of two equal and similar segments of a common
parabola H BS, Figs. 2 and 7, the vertex of each being in the same point II
at the bow, and their other extremity at the same point in the stern. As the
several horizontal sections of the ship differ in width, so the position of their

page_text: extreme widths B or B D, Fig. 2, will not coincide in the same vertical plane
CF as in the "midship section" of a ship built upon the usual principle;
because, from the properties of the parabola in any segment HBS, Fig. 7,
made by a chord HS or 1, passing through the vertex H, a circle CBJ having
a radius AC equal to one-eighth of the above chord, and described from the
centre A at a distance of the above eighth of that chord from its middle point
C, will intersect the parabola at B, the position of the extreme width BD of
the parabolic segment. Consequently, the extreme widths B or BD of the
horizontal sections of the ship will be ahead of the middle point C of their
length in the proportion of the versed sine CD of the above circle, of which 1
the extreme semi-width BD or B is the sine, and A C, or one-eighth of the
length or HS, is the radius; therefore, in algebraic terms, the distance
CD={1-(*)}. Thus the length 1 and the extreme width B
of the horizontal section being given, I draw its outline as follows:-Draw
10 B 10 parallel with SH, Fig. 7, and at the distance of B or BD from it;
make CII equal to CS equal to 1; set off CA equal to 1 or HS, and
from the centre A and with the radius CA draw the circle CBJ intersecting
10 B 10 in the point B. From B drop the perpendicular BD, and join
C and B, and B and J; CB is parallel with the axis of the parabola passing
through the vertex at H, and BJ is parallel with II 5, the tangent of the para-
bola at the vertex H; then make II 10 and S 10 parallel with C B, making
B 10 equal to CH and CS, cach of which is to be subdivided into any given
number of equal parts, ten being the most convenient. Through these points
of subdivision 1, 2, 3, &c. draw 11, 22, 33, &c. parallel with C B, and then
make the offsets 1 a, 2a, 3a, &c. in the proportion of the squares of their
corresponding lengths or ordinates B1, B2, B3, &c. B 10. As there are ten
points of subdivision, so 1x is the one hundredth part of CB; 2r is
four hundredth part, of CB; 3 is nine hundredth parts of CB: 4 is six-
teen hundredth parts of CB, and so on, 10 II and 10 S being one hundred
hundredth parts of CB, being in fact equal to it. Join the several points
Br, x, a, a, &c. by an appropriate templet, when the required segment of the
parabola is described. By making Cg two-fifths of CB, g is the centre of
gravity of the segment II B S, and C I being made two-fifths of CD, I is the
1 2 3 4
1
3
1
3

page_text: The parabola may be described by other methods, but I consider the above the
most convenient.
The length of the horizontal sections of the ship is determined at the
respective depths by such form of the sheer plan, Fig. 3, as the ship-builder
may consider most suitable, the vertical height or depth OC 40 of which is to
be divided, as shewn on Fig. 3, by the horizontal sections in the same manner
as described for the prism, the height or depth of both being the same. The
suitability of the sheer plan is determined as follows:-On Fig. 5 let bp u be
the assigned extreme angle at which it may be deemed prudent to expose
the greatest surface of sail to a brisk wind when close-hauled. Then, what-
ever may be the propelling force of the wind in the direction of the ship's
course, it is exerted at the end L of the long lever B L, the length of which
varies with the angle of inclination 4, and the height at which the centre of the
effort of the wind P is fixed. The effect of this is to cause the ship to "luff""
or to run into the wind; the centre of resistance to being blown to leeward is
situated in the centre of gravity R of the immersed portion of the sheer plan,
Fig. 3. Therefore, to counteract this tendency to "luff," the centre of the
effort of the wind upon the sails must be so far advanced ahead of R that
RK, Fig. 8, when multiplied by the lateral effect of the wind, must balance
BL, Fig. 5, when multiplied by the longitudinal or propelling effect of the
wind, or R K = BLX the propelling effect of the wind; whence, from the point K
the position of the masts is to be calculated and determined, as well
as that of the extreme width of the horizontal section at the depth or
height D to which the ship's side is immersed when inclined by the wind.
to the assigned maximum angle of inclination . On Fig. 6 let he
the angle WOH of the direction of the wind with that of the keel
HS or ship's course; let the sails Zz be trimmed to half this angle, or
YO II is half of WOH, or equal to . Then, by the resolution of
forces, the propelling effect of the wind = S x W x ыinex cosine 9; the
lateral effect of the wind = S× W × sine X cosine X cosine 9 × PB,
Fig. 5; the deviating or "luffing" effect of the wind = S × W × sine 2 ×
cosine 4 × BL, Fig. 5; to counteract which we must have R K XS X W X
the lateral effect of the wind

page_text: COSITIO
отдо
RK
1
sine
BLX CORIDE
40
If the height be moderate of the centre of the effort of the wind above the
centre of buoyancy, it might be sufficient to make the form of the sheer plan a
rectangle like that of the prism; but when we assume a large surface of sail
to be set, the centre of the effort of the wind P, Fig. 5, must necessarily be
at a great height, and consequently when the angle of inclination is con-
siderable, the lever RK, Fig. 3, must be so long that the property before
described of the extreme widths of the superior and wider sections, being in
advance of the lower and narrower sections, must be further promoted by
causing the bow to project forwards. Thus I make the stern post SU,
Fig. 3, perpendicular to the keel, and I determine that, in ships propelled by
wind alone, all the after extremities of the horizontal sections of the ship shall
terminate at this vertical straight line sSU. I make the length SH at the
plane of flotation equal to sQ or of the prism. From Q. I set h back along
the line of the keel to a sufficient distance according to the above investigation,
so that at the depth D the length 1 of the horizontal section at that depth may
be sufficiently long to allow of its extreme width to be at the calculated hori-
zontal distance R K ahead of R, the centre of gravity of the immersed portion
of the sheer plan, Fig. 3. I then draw the straight line - H for the profile of the
bow below the plane of floatation. To avoid excessive projection of the upper-
most sections, the bow II II II may curve backwards above the plane of float-
ation, making h II N a tangent to the curve at I. Then sh, sh, SH, Ü II.
&c. will be the lengths of the several horizontal sections of the ship, of which
their middle middle points cc Cc, &c. will describe the centre line cc C
of the sheer plan Üsh II, Fig. 3.
25
12 24
12 13
12
24
24 40
But in a screw steamer the rudder must be fixed further aft than in a
sailing ship, so as to make room for the screw. Consequently, the upper
horizontal sections must project aft sufficiently to secure the upper end of the
rudder post. The curved line Sss, Fig. 3, suitably drawn, therefore represents
the after terminations of the horizontal sections of a screw steamer above the
2410
2441
h
24 40
plane of floatation; and the bow II must be advanced ahead of HI
as much as S* is carried aft of SÜ Ü, when SS sh H½ becomes the sheer
24 40

page_text: plan for the screw steamer, the centre line c C c being still the same as for the
sailing ship. The horizontal sections, Fig. 2, and the half body plan, Fig. 4,
have been drawn for the screw steamer only, but the mode of drawing them
for any other description of vessel is precisely the same; the lengths, however,
5 of the horizontal sections must be taken from the proper sheer plan determined
upon for the respective ship or vessel.
25
24
2421
21
The calculated area of the several horizontal sections being divided by the
corresponding length 1 or s h, &c. on the sheer plan, Fig. 3, the quotient will
give the corresponding mean widths bor b 24 b, &c., Fig. 1, of the several
horizontal sections of the ship. Three halves of these mean widths b or of
24 b, &c., Fig. 1, will give their corresponding extreme widths B or B 24 B,
Fig. 1. Thus, on Fig. 3, the length of the prisms Q or has been assumed
as being equal to 296 feet, and at the depth 24 feet above the keel, the ordi-
nate of the assumed transverse section of the prism is on Fig. 1, y 24 y, or y
equal to 47.6 feet. Then the area of the horizontal section is ly, or 296 × 47-6,
namely, 1,408.96 square feet. On the sheer plan, Fig. 3, the corresponding
length of the horizontal section of the ship is sh or 1, being 809 feet; conse-
quently, the corresponding mean width b of this section is b 24 b. being ¥,
1,40990
SUD
2626
24
26
21
ог or 45.6 feet. Three halves of 45-6 would give 68.4 feet for the
extreme width B or B24 Bon Fig. 1, to which the thickness of the keel is
to be added. In the same way the corresponding mean and extreme widths
any other horizontal section of the ship may be calculated.
of
On Fig. 2, I draw the straight line SE of an indefinite length, for the
chord of the several parabolic segments representing the outline of the several
semi-horizontal sections of the ship. At the required distance from it, I draw
a line parallel to it representing the semi-width of the keel. From C, the
middle of the length of the plane of floatation, which is 296 feet, the length of
the prism, as before mentioned, I sett off CS and CH, each 148 feet in length.
Having calculated and found the semi-extreme width B to be 28.75 feet, I
draw a straight line at this distanco parallel with SH. I then proceed to lay
down the position of the extreme width BD, and to draw the horizontal
section in the same manner before described in the explanation of the con-
struction of Fig. 7.

page_text: 12 19
19
12
At any other depth above the keel, say, 12 feet, I ascertain from the sheer
plan, Fig. 3, the horizontal distance 12 c of the middle point c of the length 1,
or s h of its horizontal section aft of C, the middle point at the plane of float-
ation, which I find to be 225 feet; I transfer this distance to Fig. 2, and set
it off in the proper direction from the point C, making the point c so set off
the middle point of the length of the corresponding horizontal section. From
this middle point c, I set off on each side c S and ch, equal to 146-5 feet, the
semi-length of the section as obtained by measurement of the sheer plan,
Fig. 3, at the respective depth. After calculating and finding the value of
the extreme semi-width, and laying down its position, I proceed to draw the
horizontal section in the manner before described.
13
15 19
In this manner I draw all the horizontal sections that may be necessary for
Fig. 2, the dotted lines representing those at and above the plane of floatation,
the inner three full lines representing those below that plane, all of which are
segments of a common parabola having their vertex situated in the bow at
H, n, &c.
I do not, however, confine myself to making the outline of the horizontal
sections common parabolic segments throughout the entire height or depth
of the ship, as it may often he inexpedient so to construct them above any
assigned height above the keel.
And it may be considered more suitable
above this assigned height either to continue the extreme width of the several
horizontal sections constantly of the same width, or even to lessen them or
enlarge them in any assumed convenient proportion, without altering the
respective areas calculated for the several horizontal sections. Consequently,
the areas, the lengths, and the extreme widths of the several horizontal sections
above such assigned height, say. at 12, Fig. 1, being given, I either find such
other variety of the parabola or paraboloid than the common parabola as
shall be of the same area and length, with such reduced extreme width
as may have been determined upon, the outline of which shall form that of the
horizontal sections of the ship; or I introduce a parallelogram into the middle
of the horizontal section, which is terminated at each end by the segment of a
parabola, in such a manner, that the area of the three together shall be equal
to that of the respective horizontal section of the prism, and the width of the

page_text: parallelogram shall be equal to the respective reduced extreme width, whilst
the sides of the parallelogram shall be the mutual tangent of the two terminal
parabolic segments.
m+1 m+1
21
21
21
m+1 m+1
m+1
21
m+1 m+1
Thus, on Fig. 1, above the depth 12 feet, let the extreme widths of tho
common parabolas BC B, B 24 B, &c. be reduced to those shewn on the narrower
Diagram, viz., CB, B 24 B, &c. The description of the construction of all the
respective horizontal sections being similar, it may be confined to that of one,
namely, at the depth of 24 feet, see Fig. 7. Having found the position of BD
for B, as before described, set off D 3 equal to $ 24, Fig. 1, and distinguish it
algebraically by the Greek letter ẞ. Join C and ẞ and draw 10 8 10 parallel
with HS, making 8 10 equal to CS and CH. Through the before-mentioned
points of subdivision 1, 2, 3, &c., along CS and CH draw 11, 22, 33, &c.,
parallel with CB. If necessary, other supplementary parallel lines may be
drawn from additional points of subdivision 7.5, 8.5, 9.5. Then, to find the
value of the several offsets 4 x, 5x, 6x, &c., it must be recollected, in every
variety of parabola or paraboloid there is this general proportion, viz., see Fig. 7:
ẞ1:8 10:1x: 10 H or 10 S; or 1:1:1x: Cẞ; or 5: 1 :: 5x: Cp. Con-
sequently, any offset, say, 9.5 x=Cẞx 95, because 89.5 is of 310, or the
offset 5 x, is equal to C 6 multiplied by 5 raised to the (m+1)th power, because
§ 5 is 1 of 8 10, and so on. This is invariably the rule, whatever may be
the value of m, which in the common parabola is 1, in the cubical parabola the
value of m is 2, and so on, each different variety of the parabola or paraboloid
having a different value for its exponent m+1. To find the value of m, there-
fore, of an unknown variety of the parabola or paraboloid, of which its length 1,
5 its extreme width 6, and its area ly, are given, the algebraic area of the para-
bolic segment becomes ly=lb=(1+B=1&B)=1+1 or 3B=b=18.
But both band B are known; thus, at the depth 24 feet, the mean semi-width b
is 22.8 feet, and ẞ on the Diagram, Fig. 1, measures 27.6 feet, when we have
mbx2b mẞ+3, from which we find that m=-, or is 8-75, and m+1
0 is 475; that is, the value of the exponent m+1 is equal to that of a fraction
of which the numerator is twice the mean semi-width of the section from
which the reduced extreme semi-width is deducted, and the denominater is the
difference of these semi-widths, and to the value of which fraction 1 is added.
ths
2b-8

page_text: 4'75
473
Consequently, in this section, Fig. 7, the offset 4x=C3 x 4, or is 444;
5x Cẞx 5, or is 1.281, &c. But to find the 4.75th power of these
decimal fractions, logarithms must be used. After finding the several points
xxx, &c., the paraboloid is to be completed by a templet. In the same way
the other paraboloidal sections are to be made, as shewn by the full lines
on Fig. 2, instead of the common parabolic segments, as shewn by the
dotted lines.
40
On Fig. 1, the extreme widths B and B have been so much reduced by fixing
the value of their exponent m at 15 and 10 respectively, that their bow is so
bluff as to allow of a battery of about six guns on the same deck to fire
directly ahead, the width at the bow being 52 feet. If it be required that at
the depth of 36 feet, the bow should have only the same bluffness as the Draw-
ing shews for the depth 28 feet, or that the value of m at the depth 36 feet
should be, say 7, and at the depth 28 feet, m should be, say 4; then, as
b= so 8=b. Now, at the depth 36 feet, b=26.04, therefore the
corresponding width = of 26.04, or is 293, and at the depth 28 feet,
b=24-26, therefore the corresponding width = of 24-26, or is 29.11. By
setting off these dimensions right and left at the respective depths on Fig. 1,
fill up the remainder of the Diagram 3 3 3, Fig. 1, by a templet, and
with the proper scale measure off the widths of 3 at the other depths, which
being found, and the value of their corresponding mean widths b, being also
already known, the respective value of the exponents m may be calculated as
before described.
we may
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Assuming the sheer plan to be selected by the ship-builder's convenience,
the position thereon of the extreme widths, being determined by all such s
horizontal sections as have a common parabola for their outline (the vertex
being in the bow), will describe on the sheer plan a curved line c D, Fig. 3,
advancing from about the middle of the keel, upwards towards the bow, to
such height where it has been determined to narrow the extreme widths, as
above described. Above this height the method of fixing the position of the S
remaining extreme widths may be modified from that which I have already
described in an endless manner, as the ship-builder may deem suitable. But
the advancing of the position of the extreme widths of the upper sections ahead

page_text: of those underneath is one of the distinguishing features of my Invention,
whatever may be the shape of the outline of those sections, the usual method
being that the several extreme widths shall all coincide in the same vertical
transverse plane or midship section. Moreover, it is evident that instead of
the horizontal sections being a horizontal plane, as shewn by the horizontal
straight lines in the sheer plan, Fig. 3, they may be modified by curving up-
wards similarly, as shewn by the upper lines on Fig. 8, but adopting the same
form of outline of the section as I have before described when the sections are
considered horizontal plane sections.
By the principle of construction before described, the lenghts and areas of the
several horizontal sections may be equal to those of a ship of any ordinary con-
struction, whilst the extreme widths will be less than by adopting an assigned
midship section, as is usual, and consequently a less lateral displacement of the
water during the ship's progress would ensue, and therefore less power would be
required to propel a ship so conconstructed, more especially as by my form for
the horizontal sections that displacement would be made in accordance with the
mathematical laws of gravitation.
The position at which the several transverse sections for forming the half
body plan, Fig. 4, may then be determined on the sheer plan, Fig. 3, as shewn
by the several vertical straight lines marked 1, 2, 3, &c., and thence laid down
upon the several horizontal sections of the ship, Fig. 2, from which the ordi-
nates may be taken, and the half body plan formed in the usual manner, thus
giving the necessary lines and dimensions for the ship's construction.
I have now ascertained and described the nature of my Invention, and in
what manner the same may be applied, and illustrated the same by the
-accompanying Drawings to the best of my ability.
In witness whereof, I, the said Henry Emmanuel Scott, have hereto set
my hand and seal, this Twenty-first day of November 1855.