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Du Buat Has considered the effects of tenacity, friction, &c. in obtaining his final expression; but it may be remarked, that the velocities

computed with ^li!!£=zv, are all nearer those found by experiment in

*Jb the River de Hayne, than those resulting from the other equation. Thus, in the following table, the velocities found by experiment are in the first column; those computed from V= 297(^_0.1) 0.3 w,._

jb—hyp. lug.*/b+ 1-6

0" 1) are in the second column; and

297 s/r the velocities given by V= ——r- are

v" in the third: (see p. 63, vol. i.) If we

,, • 306-7v'r_ adopt the expression -7— =

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then any two of the quantities V, r, b, will readily give the third; thus

V* b putting a = 306 - 7; then r = -—- when V and b are given; and

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In this note Sir Howard Douglas has proved the important fact, that in some cases the velocities computed from the expression

^A are nearer those found by experiment than those resulting 297(^_0-1)

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from the final expression V=

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*Jb hyp. log. */b+1 o" But it ought to be noticed that a general rejection of the corrections for tenacity and friction, merely because the velocities computed from the pure expression agree.more nearly with those found by experiment in one particular river, may lead to inaccuracy. It would have been more satisfactory to explain the nature of the correction1;, and to compare the results yielded by the whole expression with those found by actual experiment in various rivers, leaving the practical engineer to decide every case upon its own peculiar circumstances. That this is the more accurate view of the subject must be obvious, when it is considered that the corrections niust necessarily vary according to the character of particular rivers. The correction for tenacity, for example, occasions a more sensible diminution of r, the mean radius, (the area of the transverse section divided by its perimeter,) in small than in large rivers. And we inay also notice that the correction as given in Du Buat's fifth chapter, for y/ b the square root of the slope, ought to have been illustrated and explained. An extension of this useful and, so far as theory goes, fundamental department of the work would also be desirable, and ought to exhibit a collation of the doctrines of the

last last edition of Du Buat's work, with Prony's ' Theorie des Eavx Courantes.'

In general, however, this correct and clear statement of an important theorem is likely to be of practical advantage to the civil as well as the military engineer; and Sir Howard Douglas remarks that in exploring rivers ill unknown countries it will also aid the traveller to ascertain the declivity of the stream, and the elevation of the country through which it flows, by merely measuring the velocity.and width, and taking its several depths. These observations repeated from time to time, and carefully noted, may afford a mode of levelling which will supply the occasional want of experiments by the barometer.

The discussion of these principles in hydraulics occupies the first section in the work before us. Having laid down general rules for ascertaining the nature and force of the element to be surmounted, Sir Howard Douglas gives in separate sections an account of the various expedients which ' war's vast art' affords for surmounting them. Pontoons of course occupy the first section, and accurate tables are given calculating the weight borne for every inch of immersion, and thus at once ensuring to the engineer the information necessary for his profession. Directions for constructing the pontoons, and for laying them where they are to be used, are also given, with many valuable practical hints against the means of destruction to which the enemy may have recourse.

The next section respects bridges of boats, and contains a description of that which was constructed by the Duke of Wellington for repairing the bridge at Alcantara, and that for passing the Adour in IB 14; of both which operations excellent plans are given. An account of the splendid movement by which the left wing of the British army, under the present Lord Hopetoun, crossed that river, is, to us at least, one of the most interesting of the historical illustrations by which Sir Howard has judiciously enlivened his work, and we willingly select it as an example of his style of narrative. It had been designed to make a lodgement on the opposite bank by men transported over, during the night, upon rafts formed of pontoons: but morning broke before a raft could be formed, and thus this memorable movement was destined to take place in open day-light.

* A few men were first pushed over in the row-boats attached to the pontoon train, and drove away the enemy's piquets;—rafts of pontoons were immediately constructed, but not being found to answer, owing to the great strength of the current, boats and pontoons used as row-boats, when the tide was slack, were employed to reinforce, as fast as possible, the small force sent over in the first instance. During all this time demonstrations of an intention to pass the river opposite to the enemy's

posts posts in front of his intrenched camp, were made; and his inactivity

can only be attributed to the success of this feint, which at first completely deceived him as to the real design; and it was not until towards the evening, when 5 or 600 men were got over, that he made any attempt to molest the enterprize. He then brought down some battalions; but a discharge of rockets from the infantry already lodged on the right bank, threw the enemy's troops into disorder, and they soon retired.

'The vessels could not get over the bar until the evening of the same day; when by the able management and determination of the navy, but with the loss of several boats and vessels, a sufficient number to make a bridge were brought in, and it was completed on the second day following. In the meantime all the troops were crossed in boats—and the horses of the cavalry were swum over at their sterns, or transported upon a flying bridge made of pontoons.'—pp. 122, 123.

The author proceeds to treat of the passage of rivers by means of Hat batteaux and portable row-boats, which is illustrated by the fatal passage of the Limat by the French, in 179!), which first gave a turn to the campaigns hitherto so favourably maintained by the Russians, as the Russian general Korzakow was in consequence driven from Zurich, and the right of Suwarrow's army completely turned, just when that general was on the point of prosecuting his Italian victories by carrying the war across the Alps.

The fourth section is occupied by an account of flying bridges, that is, such as consist of a raft, boat, or other floating body, so suspended in the current of a river as to receive the action of the stream obliquely, and be thus forced from the one side to the other. As this species of transportation is particularly useful in desultory and daring enterprizes, it leads to a series of excellent remarks on the attempt to force the passage of rivers by open and unmasked force, which the author, after presenting us with a variety of instances from history, assures us has hardly ever succeeded wheu the powerful means of opposition which the river and its bank* afford to the enemy have been actively and boldly employed to defeat the attempt. We extract the plan which he recommends to the defenders, as more intelligible aud interesting than his mathematical and mechanical demonstrations; having great sympathy with that class of gentle readers who, far from being able to preserve their equilibrium on Sir Howard's military bridges, experience, perhaps, some difficulty in passing the pons asinorum.

'The first consideration in defending the passage of a river, is, to take every possible measure to procure intelligence of the enemy's movements. Light row-boats, concealed on shore near the banks of the river, in the day time, should be used during the night, to row guard—to descend quietly with the current, close to the enemy's bank— to glide near to such places as are favourable for collecting boats; and

communicatf

communicate any appearance of movement. Should a surprize be in contemplation, the preparations may generally be discovered by a proper degree of bold vigilance, or at least an actual movement of boats seen, and its direction ascertained, which should instantly be communicated by signal. The different divisions of the army should be held ready to move with the greatest rapidity, and their disposition such, as to be able to oppose the first attempts to land, with a powerful force, and use the most vigorous, devoted exertions to prevent a lodgment from being made; for, if that be once firmly obtained, we are authorized from a review of such events, in stating, that the measures the assailants will have taken to support their advance, will reinforce it more rapidly, than the defendants can possibly support theirs; for, all the force and means of the former may have been withdrawn during the night, from points whence serious demonstrations were made the preceding evening, and opposite to which the defendants must keep in strength till the movement is unmasked/—pp. 119, 120.

The adventurous attempt to achieve a passage by undisguised force has, notwithstanding the hazard, been attempted by the best generals, remembering perhaps the maxim, 'in rebus bellicis maxime dominatur fortuna;' and taking the chance of the terror and confusion of spirit which a desperate effort often strikes into a less skilful general, or troops of an inferior character. But of such enterprizes, even when successful, Sir Howard Douglas seems to Speak as instances rather of fortunate audacity, than of warlike skill; and recommends that the passage of no considerable river should be attempted without some feint or stratagem, by false attack or demonstration, to diminish the chance of resistance, and to prevent the enemy from concentrating his forces at the real point where the passage is meditated.

In the fifth section is stated the mode of constructing bridges of various kinds, where it has been found impracticable to transport pontoons or batteaux, or to find boats. In such cases, the engineer lays his bridge upon rafts of timber, or upon empty casks, or upon cases rendered air-tight, or even upon inflated skins. In the last case, Sir Howard observes, with a composure which may disturb a pequin, that ' the buoys should be small and numerous, to multiply the. chances against injury by shot-holes, for a single musket-ball penetrating a buoy instantly deprives it of its principle of buoyancy.' To this section tables are added, containing the solid contents of timber of various lengths and mean girth; so that upon reference to the specific gravity of the timber used to construct a raft, the quantity required to support a given weight may readily be determined. In like manner the weight of water displaced by casks of various sizes is also given, and thus the work affords every facility to the engineer, who, on a pressing emergency, gency, is required to estimate with correctness the means required for given purposes. •

The sixth section treats of temporary bridges, formed by employing the carriages of an army, or composed of ropes; with directions for constructing both, and practical observations on their advantage and inconvenience. The reader might now think the engineer's invention was completely exhausted—but another section contains instructions for constructing bridges by means of tressels, of piles, of trusses, and.other mechanical devices: so that the mind of the military pupil is completely stored with ingenious resources, by which in time of need and under various contingencies, he may form means of passage out of almost any thing that falls in his way.—This section, which, like the others, is illustrated by historical sketches drawn from ancient as well as modern history, is not the least interesting or likely to be the least useful. The direct information which it contains, and the hints and openings which it gives for the exercise of mechanical invention in the student himself, are equally important;—and it is scarcely necessary to add that operations carried on by such extraordinary resources of genius, are frequently successful, because an enemy often rests an undue and confident security upon the deficiency of the usual means.

The various resources by which Sir Howard Douglas 'with art pontifical' proposes to turn to the purpose of the military engineer implements constructed for very different ends, remind us of an anecdote of the greatest general of the age, which used sometimes to afford amusement to those around his person. At entering a large town in Spain, it was not unusual for him to inquire particularly about the height of the cathedral or finest church of the place. These questions, which were of course considered as marks of interest taken by El Lord in their splendid ecclesiastical structures, were answered with great complacency by the authorities civil and religious. 'Then if it is so high, you must have long ladders for cleaning it occasionally?' This question, though its scope could not be so easily comprehended, was also answered usually m the affirmative. In which case the ladders marched on with the English waggons to assist at the next storm. «

Such are the contents of this valuable manual for the young engineer. The style is plain and manly, as it should be, without any affectation of misplaced ornament; and the military illustrations are those of a soldier who has himself witnessed much in his own profession, without neglecting to avail himself of the experience of others. Some inaccuracies of the press and of the pen should be corrected in a subsequent edition—as, p. 16, theory for theorem;

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