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found a substitute in the bodies of his leading division for all the scientific expedients of the engineering art. His ideas on the principle and construction of military bridges are well explained by Joanna Baillie; they are somewhat rude and savage, it must be confessed, but they proved effectual; and, as Gibbon says, the death of the devoted vanguard was more serviceable than the life.' Some thousand carcasses, living and dead,

Of those who first shall glut the enemy's rage,
Push'd in, pell-mell, by those who press behind,
Will rear for us a bridge to mount the breach,
Where ablest engineers had work'd in vain.'

A work useful in itself comes with peculiar grace before the the subject and the duties of the author; and from an officer of Sir public when there is an especial propriety and connection between Howard Douglas's rank and character, selected as he is to superintend the Royal Military College, we receive, with peculiar satisfaction, a practical manual, founded upon scientific principles, for facilitating some of the most important operations of war.

An invaded country may be protected either by a line of artificial fortifications, or by the natural barriers of mountains and rivers. It is against the last obstacles that invaders are usually obliged to contend; and the generals whose names stand highest in military annals have gained their fame as frequently by surmounting the natural difficulties opposed to their progress by rivers, and the defensive lines which they cover, as by victory in the open field. In these cases the necessity of forcing a passage, or establishing communications by military bridges, is so obvious, that the first hostile invader upon record, whom we take to have been no less a person than Milton's Satan, immediately proceeded to secure the advantages which he had gained, by establishing a military bridge extending from the gates of his own fiery dominions, through Chaos, to our own terrestrial globe. Sin and Death formed on this occasion the corps of pontooners, and their formidable operations are thus recorded.

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Deep to the roots of hell the gathered beach

They fastened, and the mole immense brought on,
Over the foaming deep, high-arched, a bridge.
Of length prodigious, joining to the wall
Immoveable of this now fenceless world.'

The importance of Sir Howard Douglas's subject, in a military point of view, did not, indeed, require to be enhanced by quoting the example of the author of war and fighting' amongst us; but the case appears so strictly in point that we could not suppress it, especially as it seems to have escaped the gallant author's extensive researches.

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To treat more gravely what is certainly of grave importance, we may remark, that until the Chevalier Du Buat published his treatises on Les Principes d'Hydraulique, the theory of running water (without an accurate knowledge of which the success of the engineer must be a mere matter of chance) was very ill understood. And the erroneous principles previously adopted by Gulielmini and others being still unfortunately enforced in several popular works, are likely to mislead such military men as have not made this branch of natural philosophy their particular study. These errors are happily exposed, and the principles of Du Buat applied and explained in the work before us. Sir Howard Douglas has traced with great accuracy, from the joint operations of sinuosities in the course of a river, combined with the hydraulic impulse of the stream, the effects of running water in forming depositions, and in altering or modifying the bed in which it flows, as well as upon any obstacle opposed to the progress of the current.

The following note contains a perspicuous and accurate statement of Du Buat's fundamental theorem, with a commentary by Sir Howard Douglas.

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M. Du Buat (vol. i. p. 63) gives the following expression for the velocity of running water.

V=

297 (√r−0·1)

b-hyp. log. √b+1·6

-0 · 3 (√/r—0 · 1)

Where V denotes the velocity of the water in inches, per second of time. r = the mean radius, which is the area of the transverse section of the stream divided by its perimeter, both taken in inches.

b = the distance in which the fall or descent of the running water is 1 thus if the fall of a river is one foot per mile, or 1 inch in the distance of 5280 inches, then—is the fall, and 6 = 5280 inches. If g the velocity acquired by the perpendicular descent of a heavy body at the end of the first second of time; then, the motion of the water being supposed uniform, g xor will denote the accelerating force, relative to the slope (that force being as the velocity);

=

V2

1

6

1

and putting for the resistance, we have

m

V2 g

-=

whence VVmg

b' m

=

where m is some function of r to be determined. This is Du Buat's fundamental theorem. From many experiments with water running through different pipes, he finds the mean value of m to be 2437 (r−0·1) nearly, or m = 2437 r nearly, by neglecting 0 1: now g = 386 inches English

measure, whence mg = 386 × 245 · 7 r, and the equation V=Vmg 306·7 √r

46

becomes V=

No6

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 mg √mg_V, are all nearer those found by experiment in 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 (√r−0.1) ✔b-hyp.log.√b+1·6

01) are in the second column; and

-0·3 (√ r

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the velocities given by V=

297✔r
√6

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

adopt the expression

306 7√r
√6

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

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putting a = 306 · 7; then r =

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V2 b
a2

when V and b are given; and

when V and r are given.'--pp. 15—17.

In this note Sir Howard Douglas has proved the important fact, that in some cases the velocities computed from the expression 297√r are nearer those found by experiment than those resulting √b from the final expression V= 297 (r-01) -0·3V (r−0·1.)

√b-hyp. log.√b+1.6

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 corrections, 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 must 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 may also notice that the correction as given in Du Buat's fifth chapter, forb 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 Théorie des Eaux 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 in 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.

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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 1814; 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 flat batteaux and portable row-boats, which is illustrated by the fatal passage of the Limat by the French, in 1799, 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 when the powerful means of opposition which the river and its banks 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 and 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

communicate

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