Abbildungen der Seite
PDF
EPUB

BIDDER'S TABLES.-ADDITIONAL FORMULE, &C.

Sir, I find from No. 1195, p. 7, of your valuable journal, that Mr. Creedy has furnished us with an improved edition of Bidder's Tables. This edition I have not yet seen, but it appears from your account of them, that he has extended them beyond depths of 50 feet. This, every one in the habit of using Bidder's original table, will hail with satisfaction, especially as they will have found, with me, that Mr. Bidder's rule for obtaining the contents from his table for heights exceeding 50, is, in numberless cases, a failure. He tells us to enter the table with one half, or one third, or one fourth, &c., of the measures,' and coolly leaves us to shift for ourselves, whenever heights occur which have no common measure, and which, of course,

66

[ocr errors]

we cannot, by division, bring within the range of his table. We must, in these cases, either perform the calculation in detail, according to the formulæ, or find out for ourselves a shorter method. The following contrivances have suggested themselves to me in using the table, and may, perhaps, not be uninteresting to. some of your numerous readers.

First for the slopes. Let A and B be the given heights. Now, it is manifest, that whatever be the magnitudes of A and B, we can find a number "n" which, being subtracted from both, will reduce each to, or below 50. Let the numbers which remain after this subtraction be doubled by a and b, (corresponding to a and b in Mr. Bidder's formulæ,) then we have at once the following equation:

22 { (A + B)2 - AB } = 22 { (a + b + 2n)2 − (a + n) (b + n) }

27

[blocks in formation]

132 (a+b+54,) and so on. Whence we have the following rule: If the heights fall between 50 and 77, subtract 27 from each, and enter the table with the remainders; note the contents, then add together these said remainders and the number 27; multiply this sum by 66, and add it to the above content. The result gives the content required; for example

Let the heights be 62 and 55.

Take 27 from each, and we have 35 and 28.

Entering the tables with these, we ob2436

tain

[ocr errors]

Add (35+28+27) 66=90 × 66=5940

Content required=8376

If the heights fall between 77 and 104, subtract 54 from each; proceed as before, and add 132 (a+b+54.)

Ex. gr. Suppose the heights are 77 and 93.

is.

Less 54 they are 23 and 39.

The corresponding content to which

[ocr errors][merged small]

Add (23+39 +54) 132-116 x 132=15312

Content required..17713

Second. For the "middle section." The rule for this is very simple. We enter the tables with the same numbers as for the slopes, take out the content, and add thereto 66 or 132, according as the numbers with which we enter the tables are less by 27 or 54 than the original

[blocks in formation]

BIDDER'S TABLES. ADDITIONAL FORMULÆ, etc.

These formulæ enable us, with very little trouble, to obtain the quantities up to heights of 104 feet. The method of application is obvious, should heights exceeding 104 present themselves; but as these depths are not at all usual in practice, we need not at present notice them further. It may, however, be observed that whenever the heights exceed 54 feet, the expression founded on the subtraction of 54 may be employed, and that it is not intended to be understood from what has been before stated, that this formulæ must not be used till we have reached a height of 77 feet. All that is intended is, that the subtraction of 27, where practicable, will generally

149

produce a simpler calculation than the subtraction of 54.

Another case, however, remains to be noticed.* It is quite common for one height to be above 50 and the other below it. In this case, if the heights exceed 27, we can, of course, subtract 27 from each, and the formulæ already given will obtain; but, if the lesser height be below 27, we cannot, of course, subtract 27 from it, and must therefore proceed as follows:

Let A and b denote the heights, A being, as before, above 50, and "b" below it. Subtract "n" from A, the remainder being, as before, denoted by a, and enter the tables with a and b. We shall find here that

227 { (A + b)2 — Ab } = 22 { (a2 + ab + b2) + n(2a + b + n) }

1

[blocks in formation]

mence at 24 and 0, and procced consecutively. The remainder of the operation is denoted by 44a+22b+594, of which the last term is a constant; the remaining two are, of course, variables; but a very slight examination of the matter will suffice to show that we can readily obtain a system of values for each, that 44 has a certain value which it retains throughout each vertical column, that this is also the case with 226 as far as the horizontal rows are concerned, and that, when they do vary, they increase the one by 44, the other by 22. An example or two will show clearly the truth of these observations.

Starting then with 51 and 0 (in which case 226=0.)

66

Slopes. Middle.†

4699 106.3

[blocks in formation]

Enter with 26 and 34.

[blocks in formation]
[blocks in formation]
[blocks in formation]
[blocks in formation]

* There is, it is true, another case still untouched by the preceding formulæ. It occurs whenever the heights 51, 52, or 53 are brought into combination with heights exceeding 77 feet. It is, therefore, after all, only a partial case. The rule, however, in this instance, would be to subtract 54 from the greater and 27 from the lesser, and then enter the tables. Then if the greater height =a+54, and the lesser=b+27, the quantity to be added to that taken from the tables will be found to be 22 (5 a+4 b+189.) The proof of this is the same as for the other formulæ. It is therefore unnecessary to occupy any space with it.

The content of the middle is given merely for illustration, it being obvious that so long as the sum of the two heights is less than 100, we can take the quantity from the table at once. These examples agree with 50 and 1, 50 and 2, and 50 and 3.

[blocks in formation]

Mr. Editor,-I have now to address you in proof of my second proposition in favour of the screw, viz., as it affects the steamers of the Royal Navy in the most important point of their efficiency as ships of war, and to show that its adoption will clear the batteries of both upper and main decks of all obstruction to the use of the guns, and permit of an increase to, and a more effective use of, the whole armament.

This proposition is divided into two parts-that which affects bona fide steamers, and that which affects the ships having auxiliary steam power. I proceed to view the case of the first of these two classes; but before doing so, will

first glance at the position in which, as regards armament, we find ourselves placed at present with respect to our paddle steamers,-a position which may be characterized as most felt by those who have most to do with and to study the subject,-to be neither permanent nor satisfactory. Its want of permanence is evidenced by the constant changes which are made even in the armament of the same ship, sometimes during the period of the same commission, sometimes in the interval between two commissions; and it is also evidenced by the differences in size, weight, number, position, and mode of working the various guns of each individual ship; it being apparently the rule that, on more or less, or on all of these points, each ship should supply a case distinct from its neighbour, and none supply a guide for any material number of the rest.

To this, which is a state of things in itself very undesirable, is to be added the general unsatisfatory fact that our paddle steamers are, for their size, armed, at the best, with a very small proportion of artillery, of a nature calculated for limited offensive operations only, and that in case of fatal accident to any of their machinery, they would be liable to fall a prey, though ships of great size and value, to an enemy very far their inferior in both.

To the chance of such, fatal accident when in action, the exposure of so large a portion of important machinery, external and internal, unquestionably and seriously exposes them; and though we fall back, and attempt to console ourselves with the reflections that steamers are not intended for close action-that their most important offices will consist in enabling ships better adapted for it to bear its brunt,-that in general they will be but auxiliaries to a fleet; but from the size and range of their guns, many most important military operations may still be performed by them. Yet a feeling something like anxiety will arise with the further considerations that an active enemy may sometimes surprise a steamer under the guns of a far more powerful broadside than her own;-that the emergencies of warfare may require her to be placed where the ability to maintain a close fight would secure her safety; and regret will be added to anxiety when we see ships so many in number, and varying in size

THE SCREW AND PADDLE-WHEEL.

from the 1100 tons of Cyclops and Gorgon to the 1650 tons of Retribution, so little prepared to maintain a broadside

action for even a limited time,-so vulnerable even if accidentally forced to engage in one, and unable as they all are to carry a single gun on their main decks, deprived of the means of performing that important service in the ascent of rivers or narrow harbours which, in other respects, they are so well adapted to do, and which, with the addition of a covered battery, they would be enabled to effect.

Now much of the want of fixed system and plan in the details of armament of these ships appears directly to hinge on the want of fixed plan and system in their construction. It is very difficult to find any two alike in tonnage, form, or dimensions; and this variation in these respects involves in most cases a corresponding variation in steam power. This again of weights in engines and in fuel, and these again in ability to bear with weight of armament. Nor in these days of novelty and transition is the important question itself, of the most efficient and best adapted size, weight, and character of gun for these ships a settled one. These causes, therefore, must bear their respective share of blame for all the variations and changes in armament which our various paddle steamers, at various times, are seen to undergo; yet do these changes give evidence also of some more remote and recondite difficulty which we are struggling to get over, in which I conceive the weight and uneasiness of the paddle-wheels to have no inconsiderable share, while they alone I believe to be responsible for the actual deficiency in armament which we see and lament,-this deficiency being directly traceable to the crying sin, the great overweight, and great upper weight necessarily attendant on all paddle propulsion.

In the case of each man-of-war steamer the naval constructor has, no doubt, a problem of much practical difficulty to solve; speed is a most essential element of her efficiency, and this involves the power and weight of her engines; endurance is the next element considered, and that as a necessary corollary. Three, four, five days' coals only?-it is very true with great speed,--but it won't do, and then follows weight of fuel; power and weight of armament then come in their turn, to be accommodated to the greatest practicable extent;

151

and a very limited extent is practically found to be left for it, for a very fine form has to sustain the weight of all. The day of trial with her stores in, has been with most of our steamers the day of discovery that in their case the problem has not been solved the ship is largely below her draught, the paddles gorged, and all her power of no avail-she won't go-and to enable her to do so something must; the engines can't, that's clear-and what's the use of them without the fuel? especially as we dare not add heavier masting; -and thus the unfortunate third term in the equation becomes the victim; is eliminated; the armament is reduced to the greatest practicable amount; and so many lessons of this nature have now been learnt that the idea of a main-deck armament seems to be given up, and we see ships of the size of the Birkenhead of 1400 tons without an attempt even at a port on that deck; and those scarcely less large, such as Centaur and Gladiator, eschewing the weight even of the eye and breeching bolts to the ports which on that deck they have.

I am not here bringing into question the principles of construction of any individual, or desiring in any way to attach blame to any. The difficulty of reconciling powerful armament with great speed and necessary endurance, will be found no small one, I believe, by whomsoever may undertake to get over it; and the trials to do so which are now being made in Odin and Sidon will, I trust, prove successful. I have noticed the difficulty in order to point it out as directly occasioned by the great weights, and their unfavourable disposition in all paddle-steamers; and I have noticed it in order to point to its solution in the much smaller weights, and their very favourable position in all those fitted for

the screw.

I do not think it would be well to alter any ship designed for the paddle into one to be driven by the screw, or vice versa. But when I know the Sidon to be contending for a main-deck armament against 184 tons of dead weight which she would not have but as a paddle-steamer; and the Odin against 119 tons, which the same principle has alone entailed on her, I hope more than expect their success; and I turn in proof of my proposition and point to the clear upper and main-deck batteries of the Dauntless, and I point to the 177 tons saved in her

weight as compared with her sister Avenger, to justify the conviction that here no reduction will be found requisite. I point again to the saving effected from the adoption of the screw also in Conflict and Desperate to claim in its favour the merit of arming their maindecks. I point to the 79 tons saved in the hull and engines in Encounter, as compared with Medea, as the means of giving to her a far superior artillery power. I point to the Rifleman with an armament such as only is carried by paddle ships of double her size; and I reply to the charge of the small and inefficient armament of the Rattler that the 71 tons of extra weight of paddle engine with which she is now burthened, is one, of which, if she were relieved, that would amply supply additional armament with which to relieve her from the unmerited reproach.

It is true again, that, as yet, these ships referred to are not launched, or but one of them; but past experience justifies us fully in looking on the great saving of weights which has been effected in them, as practically enabling us to solve the problem which hitherto has given so much trouble and disappointment; and past experience further justifies the statement that so low in the screw ships will be the disposition of the weights of engines, that increase of guns, and increase of masts will be necessary even, in order to adjust such a balance as may give the easiest motion to the ship; a consideration of no small moment as regards the practical efficiency of any

armament.

But not only does the screw hold out to us these advantages as regards increase of armament and ease of ship to meet it ; it has removed out of our way very great and serious obstructions, by which, in all paddle steamers the efficiency of such limited armament as their other weights admits of, is much impaired. There is not in these, or in any other ship so ill-adapted a position wherein to fix a heavy gun, as the very extremities; yet this position, forward and aft, is the one, and almost necessarily so, in which the very heavy guns carried by these ships is now fixed. It is very injurious to a ship's speed so to place such great weights, because an amount of buoyancy must there be given in order to her supporting them, which interferes largely with the fineness of her form in these parts. Its ef

fect in a sea way is to produce the greatest practical amount of uneasiness, and distress. In action it leaves a large space, in which the foremost gun cannot support the after, or the after the foremost one; because, from the form of the ship in these parts, the smallest range aft from the foremost gun can be thence procured; and the smallest range forward from the after one; and besides these serious disadvantages, it involves a difference in the length of gun slide in every different ship, owing to the difference of their breadths in these parts; nay, even in the same ship, owing to her unequal breadth, at the fore and after extremities. Yet is this position forced on us, at least in ordinary-sized paddle steamers; the midships of the ship is occupied by the paddle boxes; the space immediately before and abaft these by houses for various purposes; then comes the rigging of the fore and main masts; and the extremities of the ship, with all their disadvantages, remain as the only unobstructed positions, from which, to the best advantage under such circumstances a paddle steamer's large revolving guns can be used.

The adoption of the screw, however, by the removal of all obstruction opens to us a far more extensive and efficient lateral range, of which it is to be hoped that due advantage will be taken; and though there yet seems some strange predilection for keeping the weights of guns in the extremities, and it is to be lamented, that the Rifleman is not to be relieved of them, and the efficiency of her guns themselves, as well as herself, largely improved by the change; yet even in her it is open for us to do so, and in general, positions, even far removed from the extremities, will be found to give a much encreased range both forward and aft; to enable guns to support each other, which at present cannot do so; to be less affected by unavoidable motion than the extremities necessarily must be ; and the working of the guns, from which will tend largely to promote both the ease and improved form of the ship.

That second portion of the proposition which regards our auxiliary steam ships, calls for less remark. The adoption of the screw in them is too evidently advantageous to call perhaps for any-and if any were required, it would, as a point of comparison be limited to this; viz. that the paddle could scarcely, with reason, be pro

« ZurückWeiter »