XA

M.C.

G.Z..
G.M.
B.M.

.

L.M.C.

៥

G

m

Mid-section area.

Height of transverse metacentre above base.
Stability lever.

Height of transverse metacentre above centre of gravity.
Height of transverse metacentre above centre of buoy
ancy.

Longitudinal metacentre above base.

Centre of gravity below L. W.L.

Centre of gravity above L. W.L.
Prismatic coefficient.

I.H.P. Indicated horse power.

E.H.P..

N.P.

.

Effective horse power.
Nominal horse power.

B.P.. Length of ship between perpendiculars.
W.L. Length of ship on load water line.

Length of ship over all.

Placed before dimensions indicates that these are the

.

registered or tonnage dimensions.

Moment of inertia of load water plane.

Metacentre and moment.

Moment to alter trim one inch at load line.

On drawings locates the intersection of projected water line with the elevation.

Centre of gravity, or moment about centre.

Centre of gravity of water line.

Centre of gravity of mid-section area.

Centre of gravity of sail plan, or centre of effort.
Ordinates or stations.

Common interval or abscissa between ordinates.
Area of wetted surface.

Resistance.

G, or U, Half-girth of midship section (Lloyd's).
Draught of water moulded (mean).

7.

Per inch; also tons per inch of immersion at L. W.L.

Square foot.

Square inch.
Cubic foot.

Algebraical Signs.

Positive. Semicircle.

Minus, subtraction. Nega- Quadrant.

+Plus, addition.

Compression.

:: Multiplied by. Ratio. Is to. f Functions.

: So is. As (ratio). Divided by.g Gravity.

Perpendicular to.

Parallel to.

Not parallel.

... Because.

... Therefore.

Angle.

L Right angle.

Δ Triangle.

Parallelogram.

Square.

O Circumference.

Circle.

k Coefficient.
n Any number.

a An angle.

S Variation.

A Finite difference.

THE

NAVAL CONSTRUCTOR

CHAPTER I.

DISPLACEMENT (D).

THE displacement of any floating body whether it be a ship, a arrel, a log of lumber or, as in the case of the great Philosopher vho first discovered its law, the human person, is simply the mount of water forced or squeezed aside by the body immersed. The Archimedian law on which it is based may be stated as: — All floating bodies on being immersed in a liquid push aside a volume of the liquid equal in weight to the weight of the body immersed. From which it will be evident that the depth to which the body will be immersed in the fluid will depend entirely on the density of the same, as for example in mercury the immersion would be very ittle indeed compared with salt water, and slightly less in saft vater than in fresh. It is from this principle that we are enabled o arrive at the exact weight of a ship, because it is obvious that we can determine the number of cubic feet, or volume as it is alled, in the immersed body of a ship, then, knowing as we do hat there are 35 cubic feet of salt water in one ton, this volume Livided by 35 will equal the weight or displacement in tons of the essel. If the vessel were of box form, this would be a simple nough matter, being merely the length by breadth by draught ivided by 35, but as the immersed body is of curvilinear form, he problem resolves itself into one requiring the application of ne of a number of ingenious methods of calculation, the principal nes in use being (1) The Trapezoidal Rule, (2) Simpson's Rules, nd (3) Tibyscheff's method.

Simpson's First Rule.

The lculation of a curvilinear area by this rule is usually defined s s dividing the base into a suitable even number of equal parts, acting perpendicular ordinates from the base to the curve, and aft measuring off the lengths of these ordinates, to the sum

of the end ones, add four times the odd and twice the even ordinates. The total sum multiplied by one third the common interval between these ordinates, will produce the area. It should, however, be stated that the number of equal parts need not neces sarily be even, and as it is sometimes desirable to calculate the area to an odd ordinate by taking the sum of the first ordinate and adding to it four times the odd ones, and twice the last as well as the even ordinates into one third the common interval, the area may be calculated accurately. In the foregoing definition it should be noted that the first ordinate is numbered "0," and that the number of intervals multiplied by 3 should equal the sum of the multipliers.

And if half ordinates be inserted between yo and y1 and between yз and y4 we should then have :

Area(+2+1}
· ( 1⁄2 Y 。 + 2 y z + 1 1⁄2 Y 1+4 Y2+11⁄2 Y3+2 Y 31 + 1⁄2 Y4).

3

2

Should, however, we desire to calculate the area embraced within the limits of yз only, omitting the half ordinate then :

(Yo+4y1+2 Y2 + 2 Ys).

So that it is immaterial what subdivision of parts we may use as long as the multiplier is given the relative value to the space it represents as exemplified in the subjoined table. It will be obvious that we may also give multiplier only half its value, as

Yo+ 2 Y1 + 1 Y2 + 2 Ys + 1⁄2 Y4,