170

Cape, has been built for an armed steamer. The other five belong to private persons, and are employed on different stations as passenger boats. The Jernbarden, an iron vessel of 62 tons, was brought over in pieces from Scotland, and plies in the Miösen lake, 50 miles inland.

ceived

RUSSIA.-No return has been refrom Petersburgh or Riga. Return from Liebau, nil. The Consul, at Odessa, reports 25 steamers, 12 of which are of from 400 to 510 tons, and 5 belonging to the admiralty of 824 tons each. The whole were built in London, with the exception of six, which were built at Odessa and Nicolayof.

PRUSSIA. Two of small tonnage, "only fit for passengers and for tuging."

HAMBURGH.-Three of from 520 to 560 tons; and four smaller vessels. One built in London, two in Glasgow, the rest at Hamburgh, Bremer, and Bremerhaven.

LUBECK.-Four of 820, 750, 414, and 70 tons. All but the last, London built.

BREMEN.-Seven of from 82 to 289 Three home built; two London; one Dublin; one French.

tons.

SPAIN.-Cadiz owns 6; one of which is of 600 tons; another of 500; the rest from 40 to 210. The first two are seagoing steamers, employed in the conveyance of passengers and goods from Cadiz to Marseilles. Engineers, all English.

Corunna has, or rather had, one of 162 tons. "This steamer," says the Consul, Mr. Baker, "is the only one within my consulship, and is now laid up and for sale, in consequence of not meeting with any success. She was purchased with the view of running between Corunna and Ferrol, but did not defray her expenses. This is to be attributed to the Spanish character, as persons prefer going to Ferrol in a sail-boat for sixpence, to paying eighteen-pence by the steamer, although they could by the latter conveyance be certain of a two hours' passage; while in the sailing vessels they are often seven and eight hours out."

The Balearic Islands boast of one steamer, the Majorquin, of 400 tons, which trades between Palma and Majorca and Barcelona,

·

and "is allowed a yearly gratification by the Spanish Government to take in the mails." English engineers.

PORTUGAL.-Lisbon has one steamer, of 420 tons, armed with four long 12-pounders; another of 370 tons, and six of lesser dimensions. Native engineers chiefly.

Oporto owns 2, of 302 and 300 tons.

AUSTRIA. There is an Austrian Lloyd's Steam Navigation Company, which owns 14 vessels of a very respectable description. Two are of 550 tons, and seven of from 300 to 470 tons; and all except three are armed with from 8 to 12-pounders each. The engineers of five are English; the rest foreign.

The Government has two vessels at Venice, the Marie Ann, of 643 tons, which carries eight brass 12-pounders, and four 1lb. swivel guns; and the Vulcano, of 687 tons, which carries two 16-inch chambers guns, and four 12-pounders.

SARDINIA. In the Government mail service there is one vessel employed, of 550 tons, carrying one gun of 80 lbs., four of 30 lbs., and two of 12 lbs. ; and two others, of 300 tons, carrying four 12-pounders each. Besides these there are six steamers, of from 200 to 450 tons, belonging to Genoa. At Cagliari there are three steamers, of 600, 320, and 300 tons. The whole of these vessels are worked by English engineers.

A steamer, of upwards of 600 tons, is stated to be at present building in Genoa, to be called the Malfalano. "Engines, British manufacture."

TUSCANY.-TO Leghorn belong the Leopoldo Secundo of 354 tons, and Maria Antonietta of 375. They were originally the property of a company in Tuscany, the principal shareholders in which were English, but they are now owned by a French Company, at Marseilles, although they still continue to navigate under Tuscan colours. There is a third vessel at the same port, the Lombardo, of 540 tons, but she is laid up at present pending the result of a law-suit respecting her. She is intended to run between Genoa and Spain. There is a fourth vessel called the Toscano, formerly the Napoleon, but of 87 tons only. Engineers all English.

66

English.

Engineers all

(To be continued.)

ANSWER TO

IVER M'IVER'S" QUERIES ON CARDAN'S RULE.

When the second term of an equation of the 3rd order is taken away, it may be generally represented by the equation x23±px±q=o. When pa is positive, the equation is solveable by Cardan's formula. Again, also: The equation x3+px=r can only have one real root, and that root must be affirmative and two impossible or imaginary roots; because in all the higher equations impossible roots must enter in pairs, all having their origin in quadratics. Now suppose the three roots of the equation 3 —p x= ±g are all possible; then, from the theory of equations, when q is negative, the equation will have two positive roots, and one negative; and the negative root will be equal to the sum of the two positive; but when q is positive, the equation has two negative roots, and one positive, the positive root being then equal to the sum of the two negatives. Supposing the three roots to be + a + b and (a + b), then z-a=o, x-b=0, x-(a+b)=o; hence, b) × (x + (a + b) =o; or, (x − a) × (x x3- (a2+ab+b2)x = − (a2 b + a b2); then

171

this equation will fall under the irreducible case of Cardan's rule. 1st. Suppose a=b, then the equation assumes the

form a3 3a2 x=-2a3; here

or (a2)3 being equal to (243);

(947)3:

or as,

shows that the equation just falls between the limits of the reducible and irreducible cases of Cardan's rule. But if a is unequal to b, the equation will belong to the irreducible case. Suppose a is less than b, and let m a=b, then m is greater than unity; hence, by substitution, the equation becomes

x3 — a2 (1+m+m2) x = − a3 (m + m2). Now if we can demonstrate that 2 (1 +m+ m2)

is greater than

1 + m + m2

3

3

(m

2

a3 + m2)2; or that -)*is greater than

3

1 +

30 + 22)2

v2 3

2

=

Hence (1 + v + 2)2 is greater than

1 + 3 v + 34 v2 + 1} v3

x = Z

27

Now,

and

formula. The converse of the proposi-
tion may be demonstrated in a similar
manner. But if "Iver" will attend to
Cardan's notation, he will find that Car-
dan has made an arbitrary assumption.
Thus, given 3 px = ±q, assume
v and z v =
Now this last
supposition may be possible, or it may
be impossible; and when impossible,
Cardan's formula gives a false value of
the unknown quantity. But, Mr. Edi-
tor, on this subject I may have something
more to state. Until then, I remain, &c.
GEORGE SCOTT.

5, Winchester-row, New-road,
February 11, 1845.

water.

Description of Engraving.

A, the air-pump and its valves as usual. B, the atmospheric cylinder through which all the condensing water passes on its way to the condenser, and by means of which atmospheric pressure is given to the beam.

C, the valve by which the water enters the atmospheric cylinder.

D, the valve through which the water enters the condenser; these two valves are moved by the eccentric rod.

E, a small valve, opening only outwards, to clear the cylinder of any water that may be forced past the piston.

Mode of Working.

On the first movement to the top, the cylinder is cleared of air or water and below the piston it is filled with water. As soon as the piston reaches the top, the valve to the cold-water cistern C is closed, and so the atmosphere is cut off, and the valve to the condenser D is opened, consequently the water in the cylinder falls into the condenser. The piston is brought down without any resistance, for it moves in a vacuum in consequence of the water by gravitation making its way into the condenser, and as the cylinder is air-tight, there is a vacuum above the piston as perfect as can be formed. Now, when the valve to the condenser closes, which it does on the arrival of the piston at the bottom, and the valve to the water opens, the piston is immediately subject to the pressure of the atmosphere against the vacuum above it. This we may estimate at the power of 144 lbs. per square inch of the piston. The power of the additional cylinder being the pressure of the atmosphere on a surface and for a space equal to the bulk of the condensing water, and the resistance to the discharge of the same quantity of water by the air-pump

173

A LOOKER ON." being the pressure of the atmosphere, less the pressure of the vapour below the bucket of the air pump, there will be a power gained, which may be estimated as equal to the load of the air-pump and the friction in working, and where the vacuum in the condenser is not good it will be beyond these. Suppose the area of the air-pump 300 square inches, the stroke 3 feet, one foot against the atmosphere, the vacuum in the condenser 12 lbs., and the revolutions 25 per minute, the load, including the weight of water, will be equal to 101,250 lbs., raised 1 foot per minute, while the power of the atmospheric cylinder, 100 square inches will be 105,000 lbs. per minute.

The atmospheric cylinder may be placed on the rod of the air-pump, the boiler pump, or the cold-water pump, or it may be attached to the beam in any position by a piston rod, and it may yield atmospheric pressure each single stroke or each alternate stroke.

66

THE CRANK-REPLY TO A LOOKER ON." Sir,-Your correspondent, "A Looker On," has undoubtedly put the question at issue in the true point of view, and narrowed the discussion very properly to the only question in dispute. If the second question he has put (see p. 54) can be answered in the affirmative, then I do agree with him, that the mathematicians have not fairly met the question. Nor have the advocates for a loss of power until now made the proper objection. In my opinion the friction connected with the machinery excepted, does not extend outside the engine-house, and the error your correspondent has made, if he supposes it does, is this, that he does not sufficiently distinguish the impulse communicated to the crank by the piston-rod, from the impulse given out by the crank by its action on the machinery outside the engine-house.

This distinction is sufficiently manifest, if we consider the case of a crank on the axle of a water-wheel. In this case your correspondent will not contend that, by such an arrangement of working the machinery from that crank, there would be any loss of power caused thereby, however inconvenient such a mode of arrangement would be. Now as your correspondent admits (leaving out of view the friction within the walls of the

174

side the engine-house cannot be the friction excepted. With respect to the first query, the friction must be so small it would not be worth enquiring into. No doubt it would cause a loss of power in the crank.

I am, &c.,

X. Y. Z.

There are two considerable deficiencies in this construction, first, that the hand cannot be turned even so much as a quarter of a circle from its horizontal towards a perpendicular grasp; secondly, that there is no movement equivalent to the usual bending of the wrist, which gives so great a variety of positions to the natural hand; indeed, it is not obvious, at first sight, how any other than an horizontal grasp can be given by this instrument, the movement of the pin M being horizontal, and parallel to itself. When, however, the hand is turned up to effect a perpendicular grasp, the action of this pin is oblique to the eye N, which then slides along it, and thus communicates its movement to the hand, full as forcibly as when it is in the horizontal position.

To obviate these defects, let the wrist A, fig. 3, be constructed with a hollow ball and socket movement, or other equivalent contrivance, having a range of about the eighth part of a circle; and let this be held fast at any required point by a spring catch as before, falling into a hole in the stationary portion, which

must be drilled like a sieve, to suit every position. To the inner or moveable portion the hand is fixed; and the movements of the fingers and thumb are communicated from the eye N, through a small rod B, turning on a hinge, and from thence, through a connecting-rod carrying universal joints at both ends, to a cylindrical rod, C. This rod slides freely in the tube D, and can permit one of these universal joints, E, to turn freely in a groove round it. The motion of the thumb piece F, which here as in nature is slower than that of the fingers, is derived from the centre pin of the joint G, passing through a slit or elongated eye in a rod hinged at the bottom, and on its prolongation above, carrying an eye, forming the joint H, from whence the steel tendon, I, gives the second movement to the fingers as before. The bent finger-piece is also coupled with the end of the rod C by a short connecting piece, L. In some cases the rod B, which elongates the movement, may be dispensed with, and the universal joint E be connected directly with the joint M.

It is evident, from this construction,