THE THEORY OF NAVAL ARCHITECTURE.
No. II.

IN constructing a ship, the drawing is made to
give the form either at the outside of the
planking, or at the outside of the frame-timbers.
If it be made to the outside of the timbers, before
any exact calculations can be made respecting the
ship's displacement, or any other of her qualities, it
will be necessary to obtain the form at the outside
of the planking-that is, in technical phraseology,
to put on the planking, in order that we may
operate upon the form corresponding to the
actual surface of the ship when she is afloat. The
method for putting on the planking will be given
hereafter; for the present, in the investigations
which we are about to make, we shall presume that
our drawings give the form at the outer surface
of the ship.

But before proceeding with these investigations it is necessary to explain that the drawings of a ship made to the outside of the frames-called the BUILDING DRAUGHTS-have for their planes of projection, 1. a vertical longitudinal plane passing through the middle of the ship, dividing it into two symmetrical portions; this corresponds with the SHEER PLAN: 2. A plane perpendicular to this, passing through the upper edge of the rabbet of the keel, corresponding with the HALF-BREADTH PLAN: 3. A plane through the broadest part of the ship perpendicular to each of the other planes, corresponding with the BODY PLAN. The drawings giving the form at the outside of the planking, denominated the CONSTRUCTION DRAUGHTS, have the same sheer plan as the "building draught," but the Load water section, or a plane parallel to it, becomes the half-breadth plan, and a plane perpendicular to each of these through the broadest part of the ship, becomes the body plan of the " construction draught."

A.

FIC.5.

axes.

an ellipsoid, for instance, of which 4 B, AD, and
AC are the semi-axes, and equal to a, c, and b
respectively; and take these as the co-ordinate
Then the surface of the ellipsoid is such
that all sections of it made by planes perpendicular
Let a number of such
to the axes are ellipses.
planes, which are also parallel to the co-ordinate
planes, CDA, DBA, be drawn, at distances
dr and by respectively apart, dividing the solid
into a very large number of bars, each having for a
base the very small area of 8.r.dy, in the plane CBA,
Let PP' Q'Q,
Corresponding to the sheer plan.
be one of these bars, and the distance from P to
the plane CBA be equal to z., its distance
from CDA=r, and from DBA =y, then z.dx, dy
is the content of this bar very nearly, and the sum
of all these bars will give the contents of the
solid when the area dr.dy is exceedingly small.
This sum is represented in the language of the
integral calculus by the symbol

SS z. da.dy

Now z depends for its value upon its position, or
FIG. 4.

Let, then, fig. 4 represent the construction
sheer draught of a ship, A B being the line of
the load water section, and let the equidistant
transverse sections, perpendicular to the sheer
plan and load water section, be turned round
their lines of intersection with the sheer plan.
Now, what we have to do in finding the "dis-
placement" of the ship is, to find the contents of and the content of the solid is represented by

upon the corresponding values of x and y, and by
giving x and y any values in the equation to the
surface the corresponding value of z is obtained.
The equation to the surface of the solid we have
taken as an example is

the solid the transverse sections of which are re-
presented by the shaded parts of the figure.

If ships were similar to each other, on knowing the displacement of one, that of any other could readily be found; it would be to the given displacement as the cube of one of its principal dimensions is to the cube of the like dimension of the first ship. Or if the submerged parts of ships were of any regular form, such as a hemisphere, a semi-spheroid, &c., the cubic contents could be obtained from the principal dimensions by the rules of mensuration. The content of a hemisphere of which the diameter is a, is a3,* or, fl. b. d. if 1, 6, and d, represent the length, breadth, and depth respectively of a ship of that

form;

But these rules are obtained by the aid of the Integral Calculus, and as the manner of obtaining such rules will, we think, throw much light on the more general question which we have to do with, we will now endeavour to describe the process, and render ourselves intelligible to those who are without a knowledge of the calculus.

Let A B CD, fig. 5, represent any regular solid, (pi) is the ratio of the circumference of a circle to its diameter. Its numerical value is 3.1416 nearly.

dx. dy.

When the first integration is performed one of
the quantities x or y remains constant (z suppose)
and the other (y say) will be variable, consequently
the integral taken is that of z.dy. The result,
when the limits have been taken, is represented by

S

be 4 a2

π bc
4. a2

(a-x) dr.

The quantity
(a2 — x2), is nothing more than
the area of the section of the solid made by the
plane in which P lies, and which is parallel to
ACD at a distance x from it, and by giving any
values between zero and AB we may obtain the
areas of the sections of the solid, at any distances

from CDA.

Let these be obtained at the distances, zero, AS, AS,,&c., and through these points let dotted lines AR,,S,R,, S3 R3, &c., be drawn perpendicu lar to AB on the other side of it in the plane ABD, and the numerical values of the sections set off upon these; and in the same manner as lines are taken to represent forces in mechanics, let AR1, SR, &c., just set off, represent the areas of the sections of the solid through the same point: then, if Y be the general value of the ordinate at the

the area of any part RR, SS, numerically the same as the contents of the solid intercepted by planes parallel to CDA through the same points SS It is clear therefore that in order to obtain the content of a regular solid by the integral calculus, it is necessary in the first place to obtain the general value of the complete area of the sections parallel to one of the co-ordinate planes, as CDA, and in the second place to do what amounts to finding a curvilinear area, the ordinates to the bounding curve of which represent the areas of the corresponding sections.

If the moment of the solid about one of the coordinate planes CDA be required, we see that the moment of the whole would be equal to the sum of the moments of all the bars z.dx.dy, or to the sum of all the quantities z.x.dx.dy, which is

represented by the symbol Sz z.x dxdy.

As before, z will be constant, and the first process gives the same quantity as that obtained in the first operation, multiplied by x;

represented by the ordinates to a curve, and the area of the superficies included between the coordinate axes and the curve will represent the whole moment of the solid about the plane CDA.

We have above attempted to prove that each step in the process of integration is identical with that of finding a curvilinear area; aud that if we represent areas, moments, &c., by ordinates we are really doing the same as the integrator when, step by step, he proceeds until he completes the process of his integration, and obtains rules for measuring cubic contents, the accuracy of which is never doubted. And, as a consequence, the questions of finding the cubic contents of a solid, its moment about any plane, &c., are all reduced to that of finding a curvilinear area.

The reason why such prominence has been given doubt the accuracy of a result which has been to the above proof is this: many persons seem to obtained by representing an area by a line; and the following instance in the mensuration of a square balk of timber, fig. 6, is taken as a case of FIG6

Definition. A curvilinear area is the area of a plan figure bounded by a curve and one or more straight lines

FIC.2.

FIG 4

FIC.3

by coarse sieves or wire netting. These trays are mounted in the same frame as the sieve B, and vibrate with it. The seed is thus shaken over the end of the tray V, and falls on the tray W, and thence through the openings n o, on to the sieves N O. shown in Fig. 5. If too much of the seed should pass through the opening n, a hole v may be made in the tray F, so as to equalise the quantity falling on each sieve. Instead of the crank motion, the vibrating sieves and trays may receive a jogging motion, by being moved in one direction by a cam or tappet, and allowed to return and strike against a stop by their own weight or by springs. Fig. 7 is a transverse vertical section of a machine for cleaning carrot seed, constructed according to Mr. Scott's invention. Fig. 8 is a side view partly in section. A is a feed hopper, in which is a revolving drum B, carrying four brushes a a, which run in contact, or in close proximity, to a semi-cylindrical sieve or grating C, with meshes or openings large enough to allow of the passage of the seeds. and dirt, and any small seeds which are shaken through the The seed falls into a case D, which consists of wire gauze siave B. The main shaft carries another pulley, round which supported by a coarse wire netting, which is itself supported passes a band which drives a pulley on the spindle of a by bars or frames, jointed together at d d. These frames blowing fan, or winnower F. The air from the fan Fis are supported at the top by two blocks EE, adjusted by conducted up a spout or trunk G, with an adjustable screws, and at the bottom by a lever or wedge (not shown), opening, and is directed upon the seed falling from the by adjusting which, and the blocks EE, the distance of sieve B. I is an aperture for the escape of the air and the wire gauze case from the drum F is regulated. Fis chaff, or light particles. J is a box or pocket. K is a sieve a drum covered with wire card similar to that employed which may be fixed, or made capable of adjustment to for carding cotton, &c. By the revolution of the drum F, various angles. L is a tray or box under the sieve K, the seeds are forcibly rubbed at the parts where the wire which directs the matters passing through this sieve into ganze approaches closest to the drum, and they are rolled the space M. N and O, are two inclined sieves with a space about in the recesses opposite the joints d, and are again Punder them to receive anything which passes through detached and reduced to powder or dust, and pass with the carried on and rubbed about until the horns or tails are them, and with two boxes, QR, to receive all that passes off the top of the sieves. S is a sort of cap or saddle to seeds through the wire gauze, falling on the vibrating sieve prevent any seeds from falling between the top of the H. This sieve is suspended by links h h, and is driven sieves N 0. These sieves may be fixed, or may be capable backwards and forwards by a connecting rod, and crank of adjustment to various angles. The sieves NOK and, on the spindle g, which carries a pully f, driven by a B are constructed with longitudinal bars, as shown in Figs. band from a palley e, on the shaft of the drum F. Another 2, 3, and 4; i ii are longitudinal bars, having a bead along pulley e on the same shaft, drives a pulicy & on the spindle the top edge, and made thinner beneath, so that anything of the brush drum B. The shaft G may carry a fly wheel passing through the top may escape freely at the bottom. I, and may be driven by hand winches JK, or otherwise. The mode of making these bars may be varied. They are The horns and tails being reduced to dust, pass through kept at the proper distance apart by small pieces of metal, the vibrating sieve H into the space beneath, while the kk, and are held together by a rod passing through them, clean carrot seed is shaken out at the end of the sieve and or otherwise. They may be made adjustable. The falls on an inclined sieve, which is jointed to the sieve Hat pieces k k are angular at top, and kept a little below the upper end, and rests upon a roller or bar at the lower the bead, so as not to obstruct the passage of the end. M is a rubber, formed of a flat piece of wood, covered seeds, like the cross wires of an ordinary sieve. More- with leather or plush, and bevilled or curved at its upper over the bars i are so strong and stiff that few transverse end. This rubber lies on the sieve L, being confined by a supports are required. The bars are so close that good lodge at each side of the sieve, and a bar or stop N on the grass seed cannot pass through. The action of this machine frame of the machine. As the sieve L moves backwards is as follows:-The seed to be cleaned is thrown into the and forwards, the seeds pass under the rubber M, which hopper 4, and allowed to fall on the sieve B, which is rubs off and through the sieve any slight portions of the kept in rapid vibration by the winch. The dust, small horns which may remain on the seeds, these finally passing particles of dirt, round seeds smaller than grass seed, and off in a clean state from the lower end of the sieve. This some of the immature and useless grass seed pass through machine, like the others, admits of several modifications, the sieve B into the box E. The tailed or horned seeds of some of which are described in the patentee's specificaweeds, although smaller or thinner than grass seed, lie tion. The machines described above particularly refer upon the sieve, very few of them passing through. They to the dressing of grass and carrot seed, but they may be ere carried forward with the grass seed by the vibration of used for clover and many other seeds, the width of the the sieve, and fall over the end into the blast of air from spaces in the sieves and wire gauze being varied according the fan. The lighter downy portions are thus blown out at to the size or nature of the seeds operated upon. the opening I; while the heavier fall into the box J, and the still heavier fall on to the sieve K. The good grass seed and the heavier horned or tailed seeds of weeds fall upon the sieves N O. The seeds are so shaken and separated by falling from the vibrating sieve through the blast of air, that for the most part each seed falls separately through the air. The grass seeds slide down the sieves into the boxes QR. The horned or tailed seeds, on the contrary, fall like little darts or arrows, frequently acquiring a revolving or spiral motion, and pass between the longitudinal bars into the space P. A similar effect takes place with the lighter seeds which fall on the sieve K, and a portion of rather lighter grass seed runs off the lower end of this sieve. If any grass seed should be found in the box J, it will be of inferior quality. The heaviest clean grass seed is received in the box R, and the next heaviest in the box Q, and a rather lighter seed runs off the sieve K. Instead of the three sieves KN 0, more may be employed, to separate the grass seed into a greater number of qualities.

The above machine admits of several modifications:-Thus a plain vibrating table, or tray, may be used in lieu of the vibrating sieve B, or a revolving fan may be employed for scattering the seed, and throwing it on the sieves and 0. The winnowing fan may also be dispensed with. Fig. 5 is a longitudinal section of a machine in which the seed is thrown into the air by centrifugal force. 4 is the hopper, with its slide a. B is the vibrating sieve, driven by a connecting rod c, and crank d, which is driven by a band passing round a pulley on the crank shaft, and another pulley on the main shaft, which may be turned by hand or otherwise. E is a box, which receives the dust and dirt, and any small seeds which are shaken through the seive B. The crank shaft carries another pulley, round which passes a band which drives a pulley on the spindle of a centrifugal beater or fan, placed in a case or spout, v. Nand O are the two inclined sieves, with longitudinal bars as before, and P is the space between them; and Q and R are the boxes for the reception of the clean seed. S is the saddle piece on the sieves N O. The seed descends from

the hopper 4, on to the vibrating sieve B, and drops from the end of this sieve into the case U, and is then thrown out of the spout by the rapid revolution of the centrifugal beater. It falls on the sieves N O, and the grass seed slides off the sieve at Q and R, while the horned or tailed ends of weeds pass through the sieves into the space P. The arms or blades of the beater may be of different lengths, or placed at different angles, so as to throw the seeds to different distances. A revolving disc may also be used to Fig. 6 is a section of another arrangement of apparatus which may be substituted for the centrifugal beater, and the upper part of the apparatus shown in Fig. 5. 4 is the hopper, with its slide a. B is a vibrating sieve, driven by a connecting rod c, and crank d. Vis a table, or tray, and If is another table, or tray, with two openings n o, covered

project the seed on to the sieves.

It is not our intention, either here or in future cases, to urge agriculturalists to the use of newlyinvented apparatuses. Our business is mainly to describe them, and thus afford the reader the means of judging for himself. We may, however, state that there seems to be no room for doubting either the utility of the machines described above, or the urgent necessity for them which exists. In reference to the grass-seed separator, the patentee, in his prospectus, speaking of Italian rye-grass, says:

Very few samples of the seed of these valuable plants are eradication from the land-expensive weeds known to the free from admixture with that of the most noxious and-in its farmer, viz., couch' or 'twitch grass, and the great difficulty and expense attendant on even its partial removal is well known to all in the agricultural seed trade. It is to the presence of the seeds of this pest that the observation now becoming so general amongst farmers is attributable

We proposed adding a remark or two on the importance of the purification of carrot seed, and of the fitness of the above machines for effecting it; but our space is gone, and we must, therefore, refer inquirers to the patentee for further information.

THE UNITED STATES' NAVY. THE Secretary of the United States' Navy says that since his last annual report it became necessary to charter a number of vessels. As these vessels would be useful, he recommends their purchase. The sum required for six would be 244,000 dols., of which 94,800 dols. must be paid for the use of them for a period of six months, and a porpormade. The five steam sloops-of-war authorised tionate sum for a longer time if no purchase be by the Act of 1857 will soon be completed. The seven screw sloops-of-war, under the Act of 1858, are in a state of great forwardness. All experience evidences a necessity for an increase of the navy. Twenty effective vessels of smaller class can be build and keep at sea four or five vessels of a built and kept at sea for what it would cost to larger class. Let Congress increase the number of heavy-armed vessels of light draught until we can frequently display our flag at every point where American interests may need protection. The addition of at least ten more vessels of that description is not only a necessary measure, but will be found to be as efficient as any that can be desired, requiring so small an expenditure of the public money. In the construction of the steam-ships authorised by Acts of Congress, it has been the aim of the Department to combine speed and power with strength in the highest practical degree for vessels of their class. Accordingly models have been selected with particular reference to their adaptation to the greatest attainable speed, and contractors for the engines and machinery under the Act of last session have been required to guarantee the result of their plans, by stipulating the number of revolutions to be performed in a given space of time. In placing an estimate upon the value of high speed, the importance of it has not been too highly appreciated. Of two war vessels-the equals of each other in every other respect- the one which has the greatest speed has a decisive advantage over the other, and in a contest is most sure to win. The time has gone by when steam can be regarded in any other light than as the principal motive power on the water for warlike purposes. It is impossible any longer to regard the unsteady and uncertain power of the wind as anything more than an auxiliary power, subordinate to that of steam. In the construction of a war vessel everything connected with it has ultimate reference to a single point, the use of the gun; by which alone, as the means or instrument of power, important results are to be accomplished. To place it in the presence of the enemy, or beyond his reach in the shortest possible time, and to use it with the

that, when they have sown rye-grass with clover, they greatest possible effect, is the great object to

find, on ploughing for the succeeding wheat crop, that the
land is replete with a luxuriant braird of healthy twitch,'
although in the preceding fallow it had been thoroughly
cleaned. The detection of the seeds of couch-grass amongst
those of rye-grass, in such quantity as to produce the effect
above referred to, is, by a mere superficial inspection, by
hear intelligent farmers allege that to sow rye-grass and to
no means easy; and hence it is now no uncommon thing to
nothing could be more erroneous than this conclusion, by
sow couch is synonymous. It is needless to say that
which two of the most valuable grasses in cultivation are
confounded with one of the most objectionable and expen-
sive weeds.

It will be the fault of farmers themselves if,
after the production of Mr. Scott's machines, they
continue to propagate " twitch," for while it may
not be expedient in all cases to have a machine for
their own separate use (although we see that the
patentee has contrived one of somewhat smaller
capacity, which is within the reach of almost every
occupier of land), they have only to bargain with
the local seedsman, and insist on the condition
that their rye-grass shall be entirely free from
"twitch," "couch," "hair," or "spear" grass
seed.
The seedsman cannot now urge in excuse
the impossibility of extracting these noxious seeds.

be sought for in the construction of a navy or the maintenance of its auxiliary establishments. It is to attain this object that the skill of the departments of ordnance, of construction, and of engineering is taxed to the utmost. They will not rest satisfied until they have given to the service the fastest war ship which skill and science can produce.

RIFLE SHOT.-There are cases in which the expanding principle of lead, or other elastic matter, is not required in rifle shot. For instance, it is not required for breech-loading rifles, neither is it required when shot have projections on them to fit accurately into the grooves of a rifle when loading at the muzzle, nor with the rifle shot of the late gallant and intelligent officer, General John Jacob. It is not required in shot adapted to the two-groove elliptic bore rifle, and for this latter the shot may be made of a mixture of lead and tin, which is desirable for shooting lions, tigers, and other strong wild animals, or wherever great penetration is required.-J. NORTON.

MR. SCOTT RUSSELL'S PATENT THREE-
CYLINDER ENGINES.

THE three-cylinder oscillating engines lately fitted
by Mr. J. Scott Russell in the exquisite light
draught yacht built by him for El Hami Pasha,
deservedly excited much attention. The extreme
smoothness of their working, evidenced by the
almost entire absence of tremor in the vessel
when under steam, was most remarkable, and Mr.
Russell has found that a much better result, in so
far as indicated horse-power is concerned, is ob-
tained from the three-cylinder engine than from
any two-cylinder engine he has ever had in use.
The form of engine, although patented some years
since by Mr. Russell, has not, we believe, been
extensively applied until lately. Now, however,
it is to be introduced into a light draught
steamer building on the Danube; in another
built for navigating the shallow rivers of India
(a vessel now lying in the Thames at Mill-
wall), and in other vessels, as well as in the
Turkish yacht before-mentioned. Several new
engines of the same construction are also in
course of manufacture at Mr. Scott Russell's
works. As an example of this form of construc-
tion, we have, however, selected for illustration,
not a marine engine, but a fixed engine, which has
been erected to drive a portion of the machinery
at those works. Fig. 1 of the annexed engra
vings is a front elevation of it; fig. 2 is
a side view partly in section. The engine
is in this case supported by a cast-iron frame,
A; but for marine purposes the frame is some-
times forged in a single piece, and sometimes
formed of plate and angle-iron, suitably arranged
and riveted, forming a very light but strong
combination. The three oscillating cylinders are
supported in the positions shown, the piston-rod
of all three coming to the same crank-pin. All

The

MACHINE.

the cylinders are jacketed, being cast with an TINDALL'S PATENT STREET-SWEEPING
external cylinder or casing for the purpose; the
escaping steam keeps the inner cylinder hot. All
the cylinders condense through pipes, B, into one
condenser, C, placed below the engine.
cylinders are each cast with long necks, D, which
act as guides, and improve the steadiness of the
engine. The valves are worked by a single
eccentric, on the main shaft, E, by means of rods,
F. The valve-spindles pass through long stuffing-
boxes, G, in the hollow trunnions, H, which are
also the steam induction-pipes, leading from the
steam-pipe, K, proceeding from the boiler. The
outer extremities of the valve spindles are sup-
ported by brackets, I, projecting from the frame,
4. The arrangement and action of the air-pump,
feed-pump, &c., will be understood upon inspection
of the engravings. The power is taken from the
engine by means of a large bevil wheel (not shown)
on the extremity, E', of the main-shaft, E. We may
remark that the third cylinder is sometimes placed
below and the two side-cylinders above the shaft.
Mr. Russell has been materially aided in bringing
this form of engine to its present perfection by
Mr. Dickson, the able and experienced manager of
the engineering department of the works at Mill-
wall.

OBSERVATORY IN ALGERIA.-An Astronomical Observatory has recently been established near Algiers by the French Government. Besides making astronomical observations, for which the climate is particularly favourable, it is intended to register the meteorology of the district. The observatory will be under the superintendence of Professor Simon, of the Government Lyceum at Algiers; and M. Bulard, who has been furnished with a powerful telescope, will have the charge of the astronomical observations.

IN the present age, when men are more than ever bending their powers to the development of something better and more ingenious than their predecessors in almost every mechanical department, it is remarkable that no efficient machine has been introduced to supersede the old and degrading system of hand street-cleansing. Attempts have, it is true, been made to accomplish so desirable a result; but, from the expensive, heavy, and inefficient performances of the machinery used, they have proved abortive, and instead of conferring any positive advantage, have rather been retrograde, and consequently abandoned. The simple fact that such attempts have been made, and the machines experimented with officially, is sufficient evidence, however, that our municipal bodies and street contractors are not insensible to the disadvantages of hand street-cleansing, or opposed to its abolition. There is, perhaps, hardly any occupation which could be named which is more unsuitable for manual labour, or which renders the use of machinery more desirable than that of street cleansing. To cleanse all the streets in a town is indispensable. To neglect any is a serious omission, fraught with results far more pernicious to the moral and sanitary wellbeing of its occupants than is, perhaps, often contemplated. But such neglect of necessity forms part of the present partial and inefficient mode of operation. It is not our present intention to enter minutely into the details of the inconveniences and annoyances of the present plan. Of these, most people who are under the daily necessity of traversing our streets have sufficiently disagreeable proof and reminiscences. Our object is rather to direct attention to the accompanying engraving of a newly-invented machine, just patented by