ASCERTAINING THE SAFETY-AS TO STABILITY—OF A VESSEL, FOR ANY DRAUGHT OF WATER AND STOWAGE
Year: 1884

page_text: PROVISIONAL SPECIFICATION.
PABLO PEREZ SEOANE Y CHICо, Royal Spanish Navy, Naval Architect, living
in this city of London, 25 Bedford Place, Russell Square W.C. do hereby declare
the nature of my invention for ASCERTAINING THE SAFETY-AS TO STABILITY—OF
A VESSEL, FOR ANY DRAUGHT OF WATER AND STOWAGE, to be as follows:-
It accomplishes the object of presenting in view at one and the same time all
the elements of statical stability in the position they keep in the vessel, affording
means for measuring them, thus fulfilling the purposes of the ordinary diagrams
without the contusion-like arising from more or less forcible conventional arrange-
ments for a doterminate graphic representation, and providing means-consistent
with the exigencies and ready management of merchant vessels-for locating the
centre of gravity, in any circumstances, as well as for representing the water line
at any
inclination; and all this for any draught of water and stowage, within the
usual limits, and within a range of inclination from the upright position to 90.
A plate of any suitable material, or board overlaid with slate or any other
material able to be easily drawn upon, and let the drawing be rubbed off, is cut
out in the shape of the midship section, M, of the vessel, for which the apparatus
is to serve, in a convenient reduced scale with the vessel; parallel to the vertical
middle line, L of the section M, on both sides and at oqual distances from it, two
grooves are cut in the plate, in which grooves the ends of a bar B perpendicular
to Lare to slide; another bar perpendicularly fixed to B at B's middle
point, directed towards the top edge of the plate and guided by an eye fixed on
the plate at the top end of L, steadies the right sliding of B; the T piece thus
formed keeps itself parallel and close on to the plate.
The middle point of B is to represent the vessel's centre of gravity: a set screw
in the eye-guide fixes the T piece in its due positions and sot-screws at the ends
of B correct side-ways the position of B's middle point. To the T piece and at
its cross point, another bar C, able to swing 90° from L, around the said cross
point, is connected: at its upper end it has fixed to it a quadrant,-whose centre
is the cross point-to tell its angle, C's angle, with L; at its lower part and able
to slide perpendicular to and along it, there is another bar D.
The whole just described (bars B, C, D and quadrant at C's top end) is to keep
itself parallel and close to the plate.
On the plate are indelibly drawn or otherwise marked in their correspondent
positions, several curves of centre of buoyancy, say the two extreme ones and two
intermediate; these curves are divided or graduated, showing the degrees of
inclination corresponding to their points when coming to be centres of buoyancy;
they need be drawn only on one side of L, say the right one, and to the extension
of 10° on the left side; these portions of curves on L's lelf side, are to be used in
locating the centre of gravity and it is assumed that 10° is the maximum heel to

page_text: be reckoned in that operation to be explained in the complete specification; the
quadrant at the upper end of C extends from C's end towards the right and so
does the bar D from C's lower part; L is divided, from the middle keels on top,
upwards, into fect and inches, if conveniently allowed by the ratio of the scale
adopted, and so are C from the cross point downwards, and D from C. After
bringing the T piece cross point to coincide with the vessel's centre of gravity-on
the section M-and swung the bar C-its upper part to the left-and D brought to
be tangent to one of the curves on the plate, the distance read on D will be the
righting-lever, and the quadrant, as well as the graduation on the curve, at the
point of contact, will tell the inclination; the dynamical stability between any two
inclinations will be given by the difference between the two lengths read on C,
one at each heel, multiplied into the displacement.
For locating the centre of gravity a little instrument is used, which may be
conceived by imagining a short straight line P; from its centre, on one side only,
and perpendicularly fixed to it, another straight line Q; perpendicular to Q, and
able to slide along it, being always in the plan of P Q, another third one R; at one
end of R, perpendicularly fixed to it, in the same plan with the other three and
only on the side of R different to that on which Qis, a small fourth one S; and
by materializing these four lines into four flat bars; the bars Rand S are graduated
into feet and inches, in the same scale as the drawing on the plate, from the point
of concurrence with each other. Drawing on the plate, at the most, two normals
to the corresponding curve or curves, corresponding the normals-to two different
inclinations and conveniently using the little instrument, accordingly with some
most elementary principles of geometry and statics, the centre of gravity can be
located as it will be amply explained in the complete specification; a recess cut in
the plate perpendicularly to L and conveniently lower than the lowest curve
guides the handling of the little instrument.
For displacements not being those of the curves drawn on the plate, a process of
interpolation is used, both for the righting couples and the dynamical stability and
for-locating the centre of gravity, to be explained in the complete specification, and
which requires nothing different to that already said but, the drawing on the plate
of one, or, at the most, two straight lines.
For the representation of the water line, the four half curves of flotation
corresponding to the four half curves of centres of buoyancy, are marked on the
plate in their relative position; at their left and under side, and conveniently near
them a circular small hole-is cut in the plate and a quadrant marked on the plate,
from the parallel to L at the hole, towards the left above the hole; the following
instrument is to be used for representing the water line: a straight bar U with a
pivot towards its middle point; connected to U and able to slide perpendicular to and
along it at its right side, another bar V, connected itself with another .bar X always
parallel to V, by two cross bars. parallel between themselves, and joint-connected
with V and X so that V, X and the two cross bars form always a parallelogram
of constant sides; these cross bars have their portions between V and X divided.
in the same number of equal parts, say 10: by settling the pivot in the hole and
bringing V and X to be tangent to two contiguous curves of flotation, another
bar Y set on the cross bars at the same number say 4, will' accurately enough
represent the water line for the displacement corresponding to the lower of the
two curves of flotation plus 3-the difference between that displacement and the one
corresponding to the other curve and for the inclination marked on the quadrant.
The sliding parts are fitted with set-screws and micrometer screws may be added
if the greatest correctness is wanted.

page_text: I, PABLO PEREZ SEOANE Y CHICO, Royal Spanish Navy, Naval Architect, late
of 25 Bedford Place, Russell Square, now of 4 Vernon Chambers, Southampton
Row, London W.C. do hereby declare the nature of my invention for "APPARATUS
FOR ASCERTAINING THE SAFETY AS TO STABILITY-OF A VESSEL FOR ANY
DRAUGHT OF WATER AND STOWAGE," and in what manner the same is to be
performed, to be particularly described and ascertained in and by the following
statement:-
My invention has reference to apparatus for ascertaining the safety-as to
stability and line of flotation-of a vessel, for any draught of water and stowage..
This apparatus is designed to show at a glance all the elements of statical
stability in the positions that obtain in the vessel and to afford means for
measuring them. It thus fulfils the purposes of the diagrams ordinarily used and
obviates risks of confusion such as are liable to arise with the less appropriate and
somewhat forced (though conventional) methods heretofore generally adopted to
illustrate stability.
The use of my invention affords a determinate graphic representation and
provides means whereof those in charge of merchant vessels may readily avail
themselves for ascertaining the location of the centre of gravity under any given
conditions of stowage and draught, as well as for representing the water line due
to any given inclination with a given draught of water-and this within a range
of inclination from the upright position to 90°.
And in order that the nature of my invention and the manner of carrying it
into practical effect may be clearly understood, I proceed to explain the same by
reference to the accompanying sheet of illustrative drawings, whereof Fig 1
represents in plan a device that I will for clearness call a drawing board, and
which is specially fashioned and fitted for the use on it of special instruments to
be hereinafter described. Fig 2 represents a section in line X. X. of Fig 1. i. are.
two metal slides grooved at 2. m on their outer sides. g is a thin layer of any
suitable material, such as slate, that can be indelibly marked (for instance by
engraving) with a drawing or lines and can have drawn upon it a second drawing
or lines that may be rubbed out without interfering with the permanent or indelible
drawing or lines.
U Fig 1 is a bush or thimble set flush in the slating and filling board g¹ Fig 2.
M. Fig 1 is an arc of a circle a little over a quadrant. Its centre is 0 the centre,
of the bush U, and it is divided in degrees from 0° to 90° as is shewn in
Fig 1. Y Fig 1 is a detail view shewing the section of the arc M and bush U
through a a. The top face of the are M is on a level with the upper surfaces of
the slides i. k. The curve A' A. A A' is the midship section of the particular
ship for which the apparatus being described. is to serve; A¹ B. B. A¹ is the deck
taken as limiting the buoyant closed body at its top. The scale of the midships
section must be sufficiently large to allow of the necessary measurements being
•

page_text: taken with sufficient accuracy, at the same time it must not be so great as to make
the drawing board.and instruments connected with it inconveniently large. For
example, a board 20" x 18" is of sufficient size. to enable the user to appreciate
dimensions representing 400 foot tons in the case of a vessel of 8000 tons displace-
ment. Or to appreciate 25 foot tons in the case of a vessel of 1000 tons
displacement. This is in the assumption that a length of " is readily appreciable
on a drawing by one whose eyesight is rather worse than the average and that
about an inch margin is left at each side of A¹ A. A A'.
In the case of a vessel of 8000 tons displacement and (say) 60 feet beam the
drawing of the midship section A A A A¹ should be made to a scale of about 5
of the full size so as to get the said appreciation of 400 foot tons; to get the same
minuteness-not absolutely, but in the corresponding ratio-in the case of a vessel
1000 tons displacement, the scale of the drawing should be doubled and thus it
would be about and generally this scale should vary inversely as the beam the
proportion of being adopted for a vessel of 60 feet boam.
TV
This rule is based upon the assumption implicitly made, that all vessels are
similarly in the geometrical sense of tho word-proportioned and of the same
materials similarly distributed; this assumption is far from being correct, but it
may be taken as being so for the purposes of selecting a scale for the diagrams.
a. b. c. d are four curves of centres of buoyancy, a. d corresponding to the
maximum and minimum practical displacements, and b. c to two intermediate equi-
distant ones; theso curves are extended at one side of the central line L so as to
contain the centres of buoyancy for all inclinations on that side, from the upright
position or 0° inclination up to 90°, and at the other side of L only up to 10°
These curves are marked from 0° at their intersection with L, to 10° on the left
side of L, and 90° on the right side, in such a way that where a given point is the
centro of buoyancy, the mark at that point gives the number of degrees of
inclination of the ship. Upon the four straight lines a, b c d there are
marked, and with the same numbers, the points where they intersect with the
normals to a. b. c. d. respectively. These points are marked from 0° to 30° on the
left side of L, and from 0° to 10° on the right side of L. a. b. c¹. d' are the four
curves tangent to all the flotations between 0° and 90° of inclination on the one
sido of Leach of them corresponding to the displacement of the one of the four
curves a. b. c. d named with the same letter.
The intersections of the 4 curves a¹. 61 c. d' with L are referred to at the
edge e Fig 1, and there are marked the numbers of tons of the corresponding
displacements.
In the case assumed in Fig 1 they are 2,500, 3000, 3500, and 4,000 tons. The
line L is divided into fect and inches to the scale adopted from K, the top of the
keelson, upwards. The edge of the drawing-board between the lower ends of the
two slides i. is lined with a brass anglo set flush on the slate and on the bottom
side face of the drawing board, as is seen in section through line 8. a in the detail
view at S (Fig 1).
Fig 8 represents a stayed T square fitted with a smaller square d. f. g capable of
sliding along c; the two squares may be fastened together by the set-screw α which
inay be supplemented by a micrometer screw; both bars f. g, f. d of the small square
are marked out on their inner edges, from o in feet and inches in the scale adopted.
Several sections annexed to Fig 3 completely illustrate the construction of the
instrument. The bar a. b as shewn is thicker than the bar c so that the instrument
can be slidden along the bottom edge of the drawing board in the usual way.
Fig 4, represents another instrument which may be described as follows:-
a. b and c are 3 straight bars whereof a and b are equally shaped and are perpen-
dicular to c The distance a¹. b is equal to a¹¹ 61 (Fig 1.) the whole constituting
an open frame of unvariable form stayed by the quadrant q whose centre is 0 and
which is marked in degrees from 0° at m to 90° at n; The bar d is attached by
means of a hollow boss in such a way that it may be swung round 0. A piece of
some transparent substance such as mica, or horn is fitted in the hollow buss with

page_text: the centre marked in it. The bar d is prolonged into a pointer i which moves over
the quadrant q. The adjustments of the bar d to the angle required is effected by
means of the screw P which works in a swivelling nut on the pointer. Connected
with d, by means of the connecting piece a, there is another barf always kept
perpendicular to d and capable of being made to slide both along d and endwise
running through a; these two bars d. f may be steadied together by the set-
screws 8. which may be supplemented by micrometer screws if great accuracy is
required. The part of the bar d opposite the pointer i is divided as shewn into feet
and inches in the adopted scale it being assumed that zero is at the point y, tho
distance 0 y being equal to a 6 on the connecting piece a; is similarly divided as
shown from zero at the point f¹ the distance of point f¹ from the nearer end of the
barbeing not any particular length but only conveniently long as will be readily
understood when the use of this instrument is described; several sections annexed to
Fig 4 completely shew the construction of the instrument.
Fig 5 represents another instrument which may be described as follows :——
:
A is a straight bar along which another bar B, at right angles to it, can slide; a
third bar C is connected with B by two small identical bars, b. c; d. f; so that
the four bars B, C, b. c; d. f, form a jointed parallelogram whose vertices are the
four centres o, o o, o of the 4 joints; the two bars b. c; d. fare grooved at.
their top face as is shown in sections m. n; in these grooves two small and equal
blocks.whose section is shewn at n, can be run the whole length of the small
bars b. c; d. f, these two blocks by means of the pivots u (section n) which are
screwed in them, are connected by another bar h in which the distance a y is equal
to o, o¹¹ and o¹, ol so that the two small blocks t, t' must be always at the same
distance from the centres o, o¹¹ or o¹, o¹ll respectively; the pivots u being screwed
in the blocks serve also as aet-screws to the block; the distances from the ends b, c,
d,f of the two small grooved bars to the centres o o', 011 0111 respectively are equal
to the half of the common length of the two blocks tt; the distance v, z in bar b, c
and v¹, s' in the bar d, fare divided and marked on the top faces into ten equal
parts; the lengths . w; ², w being equal to the common length of the two blocks..
The bar B can be fixed to A by means of a set screw F when required. The
straight arm K is defined, as to its position in the instrument, by the conditions that
angle a (Fig 5) is equal to angle a (Fig 1) and distance a. al (Fig 5) perpendicular:
to arm K and equal to 0 (Fig 1). K¹ is a set screw to work on the inner edge
of quadrant M (Fig 1) when the instrument is used.
The sectional views annexed to the several figures clearly indicate the details of
construction of the several portions of the apparatus shown in the drawings.
The use of the instrument illustrated in Fig 3 is to locate on the slate (Fig 1)
the new position taken by the centre of gravity of the vessel, after any alteration
in the stowage or quantity of cargo or weights of any kind has been made. Let
us suppose a vessel whose midship section is A (Fig 6) L the middle line P the
displacement and C the curve of centres of bouyancy for the said displacement P;
let us suppose that the alteration made in the stowage, has been the change of
position of a known weight p from a to b; and that dis-the centre of gravity of
the vessel when p is taken off altogether. The three points a. b d and the two
resultant centres of gravity g. g', ( being the resultant centre of gravity when p
was at a and g¹ when p is at b,) will form the figure a, b, g¹, d, g, a in which is on '
the line a. d, and g' on the line b. dg. g' being parallel to a. b; if we draw a. n.
and g. m parallel to L, and b, n; g. m perpendicular to them we have:

page_text: always on the liner until q comes to be on the lines then this point of intersection
will be the centre of gravity g¹ looked for.
Lot us suppose now a vessel whose midship soction is B (Fig 7), L its middle
line, C the curve of centres of buoyancy for the displacement P with a given cargo,
and Cher curve of centres of buoyancy when her cargo is added to by a known
weight p; supposing g to be the position of the centre of gravity before p has been
added, a the position of the centre of gravity of the additional weight p and g¹ the
resultant centre of gravity after p is added at a, we have it that g¹ will be on the
straight line a. g and that drawing a. t perpendicular to L and g'. 9 parallel to
the linor wbich is the normal to C at the centre of buoyancy before adding
the weight p we may write :-
8
P
==;
;; therefore q.t=
a.g
P + P
•
a.t.
Now in the case of Fig 6 it is plain that by (1st) drawing on the slate the lines r
and & which can be easily done if the two inclinations have been ascertained, one
when the weight p was at a and the other when it was at b-by using the figured
marks on the corresponding curve and straight line of curves a, b, c, d and
lines a, b, c, d (Fig 1)-it being assumed that P exactly corresponds to one of
the curves a, b, c, d drawn on the slate; (2nd) by bearing in mind, or by marking
on the small bar g (Fig 3) the mark bearing the number .a. n which number is
known, and on bar d the mark with the number b. n, and 3rd conveniently
moving the instrument (Fig.3) on the slate (Fig 1), keeping the underside faces of
Cd f g (Fig 8) close on to the slate and the shoulder projected in a¹ b' (Fig 3),
coinciding with the face projected in a¹. 6¹ (Fig 1) and conveniently running the
small square d, f. g (Fig 3) along c (Fig 3) we may easily and promptly come to
the coincidence of the points marked one on g and the other on d (Fig 3)
respectively with two points one in each of the two normals to the curve of
centres of buoyancy O before drawn; these two points thus found will be the
centres of gravity before and aftor the weight p has been moved from a to b.
As for the case referred to in Fig 7 we may, by marking or reckoning on d
(Fig 3) the point bearing the number xat, which is known—since we may
P + p
draw (supposing that P and P + p are two displacements corresponding to two
of the curves a. b. c. d) on the slate, reckon on L the height Kb above the keelson
top face, of the added weight p then measure bt (Fig 8) by the arm & of the small
square d. f. g (Fig 3), add to this measurement the known distance a, b of the
weight p (added at a), from L which represents the vessel's diametral plan, and
multiply the result by + easily and promptly have 0 (Fig 3) somewhere on
the line taking the place in Fig 1 of the liner Fig 7, and the point on d bearing
the number
xat, Fig 7, on the line on the slate, taking the place of line s
in Fig 7. The last point thus found will be the new centre of gravity after having
added the weight p at a.
-
P
It will be seen from the preceding description that it is necessary to draw on the
slate (Fig 1) the two straight lines 7. 8. (Figs 6 and 7); this may be readily done
when the displacement P in the first case and P and P + p in the second, coincide
with one in the first case and two in the second, of the four displacements dealt
with in the drawing on the slate; when it is not so, the corresponding straight
lines are easily drawn from the following considerations, 1st That the different

page_text: pu
ונק
-
normals to different curves of centres of buoyancy at points being centres of
buoyancy for the same inclination, are all parallel amongst themselves; 2nd that the'
elements or portions of the curve in which are located the centres of buoyancy for
different displacements and the same inclination, between any two curves of centres
of buoyancy for the same displacement, within the limits of practical draughts may
be considered practically as straight lines and 3rd that within the said limits of
practical draughts we may assume that increments of displaceinent keep ratio with
the rising of the centre of buoyancy. Thus the operations required for drawing on
the slate a normal corresponding to an observed inclination and to a displace-
ment P greater than P and smaller than P, P¹ and P¹ being displacements
corresponding to two adjacent curves in the group a. b. c. d drawn on the slate
(Fig 1) are: To lay on the slate a rule or scale divided into equal small parts,
so that its marked edge passes through the two points marked on the two
curves of centres of buoyancy corresponding to the displacements P' and Pill
with the number of degrees of inclination we are dealing with; keeping the
rule or scale in this position, to mark on the slate the centre of buoyancy for
Pl
the said inclination and displacement P¹¹, which requires a division
pupi
a reading on the rule, of the distance between the two points on the curves.
of centres of buoyancy corresponding to P¹ and P, & multiplication of this
reading by the taking on the rule or scale of the last result from the
point on Pupwards, and the marking on the slate of the point coinciding with
it; the whole of these operations being done while the rule is kept still. Theso
arithmetical operations are so simple that they may be done mentally: After
having marked on the slate the centre of buoyancy, there only remains to draw by
the ordinary means of rule and square a parallel line to the direction of normals, to
the curves a, b, c, d, at points marked with the number of degrees of inclination in
the case, which direction is shewn on the slate on any couple of corresponding
curves out of the group a, b, c, d, and straight line out of the group a¹¹, b, c, d¹¹
Now the practicability of the application of this method to merchant vessels lies
in the fact that it neither interferes with the haste in which, in most cases, the
operation of loading need be effected, nor gives the crews of such vessels any extra
work; and it requires only that the person who directs the loading, shall have the
load so distributed that at some stage near the end of the loading, an appreciablo
inclination of the vessel shall obtain, and be measured and that the space still
empty at this stage and remaining to be filled up with the rest of the cargo be
such that the distances of its centre of volume to the keels on top and to the
diametral plan of the vessel may be approximately guessed. (It is assumed that
the portion of cargo left for this last stage of the loading is homogenous in its
nature).
In many cases and through the experience of the person directing the loading,
the second inclination will almost coincide with the upright position or vertical
line L, in which cases half the work on the slate will be saved viz; that relating to
the second normal, but if not so, and a slight alteration in the stowage is required,
this it may safely be assumed can be made in every case without changing the
height above the keelson of the total centre of gravity for the second inclination by
conveniently moving part of the cargo without greatly changing the heights above
the keelson of the centres of gravity of the weights moved; so that the centre of
gravity found for the second inclination may give the definitive one by referring it
to L by means of a perpendicular thereto.
This method for locating the centre of gravity has, besides its practicability and -
readiness, the essential difference with reference to the common one, of not being
influenced by the error arising from taking the metacentric height as constant with
the displacement for any finite though small inclinations; as a consequence of this,
the greater the first inclination, the better for the accuracy of the result with the
method herein explained.

page_text: The changes in the height of the centre of gravity due to the consumption, of
coal during the voyage of the vessel can be ascertained by a geometrical proportion,
since in these changes the centre of gravity remains in the diametral plane of the
vessel.
The use of the instrument illustrated in Fig 4 is for measuring for any practicable
draught and inclination, the righting couple and the dynamical stability between
any two inclinations. The instrument placed flat on the slate or board the
points h. k (Fig 4) being placed in the grooves 7 m (Fig. 2) and the bar C (Fig 4)
passed through the guider (Fig 2).
The instrument, when the centre 0 (Fig 4) is brought to coincide with the
centre of gravity marked on L, is set by the screw a (Fig 2) and screws 2. el
(Fig 4). When this has been done, if the displacement of the vessel corresponds to
one of the four curves a. b. c. d (Fig 1), and it be required to know the righting
couple for any given inclination, the bar d (Fig 4) must be turned round 0 until
the index i marks on quadrant q the inclination given.
Keeping d in this position the bar f must be moved both along the bar d and
perpendicularly to it until fis tangent to the corresponding curve of centres of
buoyancy at its zero point. The point of tangency on the curve, must be, the one
.marked with the number of degrees of the given inclination, pointed by the
index; then the reading on the bar fat 6 multiplied by the displacement will
give the righting couple. The dynamical stability between any two inclinations
will be obtained by multiplying by the displacement, the difference between two
readings on the bar d, each of them to be obtained by successively placing the bar d
at each of the two given inclinations and making bar f tangent to the curve of.
centres of buoyancy and reading on bar d the number at a; the first result is a
statical couple in foot-tons and the second is dynamical work also in foot-tons. If
it bo now supposed that the displacement P" of the vessel comes between the
displacements P1, P₁ll corresponding to two adjacent curves of centres of buoyancy P¹
being <P; then, if we want to know the righting couple for an inclination & it
will be necessary keeping 0 (Fig 4) always on the centre of gravity previously
marked on the slate and the index i pointing to the proper angle on quadrant q
to find the length of the levers of the righting couples which would refer to the same
position of centre of gravity and to the same angle of inclination but to displace-
ments P' and P. Then multiply the first by
the second by
these two products and multiply the result by P, this comes out readily from the
geometrical properties of the curves of centres of buoyancy, herein before referred to
and from the value, in a trapezoid (Fig 8) of c parallel to the bases B b, in functions
of the said bases B, b and H h The same geometrical properties of the curves of
centres of buoyancy, enable us to find out the dynamical stability for the displace-
ment P¹¹ between two given inclinations 8. 81. by finding the difference between
two quantities; one to be found by placing the bar d (Fig 4) at the inclination
with L, reading on d the numbers pointed on it at a by the bar f, made successively
tangent to the two curves of centres of buoyancy corresponding to P¹ and P¹,
finding their difference; multiplying it by
and adding the result to the
reading at the point a corresponding to P¹¹; the other quantity to be found by
doing the same with bar d at the angle Ŏ' with L; and finally multiplying the
difference thus found, by P".
Pl
- ו11כן
-
pl
Pil
ווין
-
1
pi po
sum
The instrument illustrated in Fig 5 is intended to shew the line of flotation at
any inclination and for any draught within the practical limits assumed in the
drawing on the slate. Its use requires first the withdrawing from the slate of the
instrument illustrated in Fig 4; after which, and if it happens that the displace-
ment of the vessel corresponds to one of the four curves considered in the drawing,
then by settling the pivot p (Fig 5) into the bush U (Fig 1) swinging A (Fig 5)
round pivot p until the edge a¹ a coincides with the mark or quadrant M (Fig 1)
bearing the number of degrees of inclination of the flotation wanted, and making h

page_text: (Pill-P)
(Fig 5) tangent, by conveniently running B along A,-to the corresponding curve
in the group a' b, c, d (Fig 1) the position of h will shew the line of floatation.
When the vessel's displacement is not one of the four to which the curves a. b. c. d
and a, b, c d correspond, it is necessary to begin by setting the two blocks t, t'
(Fig 5) in the bars b. c d. f so that the ends of the blocks nearer, respectively to o
and oli (Fig 5) coincide with the marks on the tops of bars b. cd.f bearing the
number 10
(PPI) as before P¹ being the actual displacement and P¹ p™ two
adjacent displacements amongst the four assumed in the drawing between which P¹¹
stands and P being > P¹; After this, placing the pivot p in the bush, and bar A
Fig 5 as before, at the angle required and placing-by conveniently running B
along A and making use of the articulations or joints at o, o¹, ol, o¹¹-the inner
edges of B and C tangent, each of them, to each of the curves corresponding
to P and P¹ then the edge of h which if continuous would pass through the
centres of the pivots a y screwed in the blocks t, t, will mark or show correctly
enough the line of floatation required. For the case when P11 is very near to Pl
and in order that the attainment of the tangency of the inner edge of C to the line
of flotation corresponding to P' may be seen, the bar h is to be lifted above the
screws 2. y. turned over and then let down again on to the top faces of the blocks,
the heads of the screws y passing therethrough as before. By this operation the
edge of h which previously was the nearer to B now becomes the further edge, but
it still remains passing through or in a line with the centres of the blocks, and the
width of the bar h does not cover the inner edge of C.
If a competent person in charge of a vessel bo provided with apparatus of the
kind hereinbefore described, the midship section and graduated scales boing
specially adapted for his vessel, he will be in a position to determine the
conditions of safety of his vessel-as to stability-in any case, likely to arise
in practice.
As to the indispensable datum-momentum of inertia to the centre of gravity in
every case, it is to be found by the direct process, after the centre of gravity
as well as the storage is known, the facility afforded by the whole arrangement
herein described being that of stating at K (Fig 1) the momentum of inertia
referring to the line projected on to K (Fig 1) of the vessel ready for sea
(without any cargo or coal) which in the case assumed with reference to Fig 1 is
25,000 foot-tons.
Having now particularly described and ascertained the nature of my said
invention, and in what manner the same is to be performed, I declare that what
I claim is
1. The apparatus substantially as herein before described with reference to Figs 1
and 2 of the drawings for the purposes specified.
2. The apparatus substantially as described with reference to and illustrated
in Fig 3 of the drawings for the purpose specified.
3. The apparatus substantially as described with reference to and illustrated
in Fig 4 of the drawings for the purposes specified.
4. The apparatus substantially as described with reference to and illustrated
in Fig 5 of the drawings for the purpose specified.
5. The use in conjunction with apparatus substantially such as described with
reference to Figs 1 and 2, and in the manner hereinabove explained, of an instru-
ment substantially such as described with reference to and illustrated in Fig 3, for
locating on the drawing of a vessel's midship section the centre of gravity of such
vessel.
6. The use in conjunction with apparatus substantially such as described with
reference to Figs 1 and 2, and in the manner bereinabove explained, of an instru-
ment substantially such as described with reference to and illustrated in Fig 4
of the drawings, for measuring the righting couples and dynamical stability of
a vessel.

page_text: 7. The use in conjunction with apparatus substantially such as described with
.reference to Figs 1 and 2, and in the manner hereinabove explained, of an instru-
ment substantially such described with reference to and illustrated in Fig 5, for
showing on the drawing of a vessel's midship section the line of flotation of such
vessel.