approach to the feelings which an actual contemplation of them would inspire.

In a subsequent Number, we will introduce our readers to the second and concluding volume of this attractive publication.

[To be continued.]

ART. VI. An Essay on the Principles and Construction of Military Bridges, and the Passage of Rivers in Military Operations. By Col. Sir Howard Douglas, Bart. F.R.S. Inspector-General of the Royal Military College. 8vo. pp. 204. and 13 Plates. Egerton.

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N our last volume, p. 89., we made our report of a tract by Sir Howard Douglas, containing observations on Carnot's "Principles of Defence," &c. &c.; and we have now to call the attention of our readers to another work by the same author, the title of which is given above, and which had indeed a prior claim to our notice.

The crossing of a river is always so highly an important military movement, that on the due execution of it frequently depends the fate of armies and of nations: yet we are not aware of any work, except that which is now before us, exclusively undertaken with a view to develope and illustrate the various methods to be pursued, and the precautions necessary to be observed, in order to insure the success of such an operation. If an army could at all times be supplied with the requisite number of pontoons, there would be perhaps but little occasion to look beyond this mode of transfer: but, as it is well known that this is far from being the case, we must resort to the facilities that may be afforded by the small boats found on the rivers; and, if this resource should fail, other means must be adopted. These are sometimes found in rafts of timber, casks, air-tight cases, and even inflated skins. In certain instances, also, the carriages belonging to the army may be advantageously called in aid of this sort of operations; while in others trestles, piles, and trusses, may be used; and even rope-bridges, in particular situations, have been found extremely serviceable. A treatise, therefore, wholly devoted to these important objects, with all the requisite detail, directions, and precautions, clearly and scientifically pointed out and illustrated by actual example, cannot fail to prove interesting to the experienced engineer, and instructive to the military student.

It is obvious, nevertheless, that, besides the mere mechanical construction of such temporary bridges, other considerations

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necessarily present themselves to the mind of the officer intrusted with the direction of these works. The narrowest passage between two banks of a river is seldom the most desirable spot for executing a design of this description; because, where the opposite banks approximate nearest towards each other, the current is always the most rapid, and may frequently be such as to bid defiance to the most determined efforts. It is true that, in numerous instances, the situation of a military bridge is determined by circumstances over which we have little or no controul, and that we have generally to submit to hard necessity, without uselessly contemplating the conveniences or inconveniences of particular situations: but, in other cases, some choice is left to the engineer; and, if any advantages thus occur, it is of the highest importance to avail ourselves of them.

That our selection, however, may be judicious, it is requisite that we should be acquainted with the general theory of rivers, and with the natural indications of banks, shoals, eddies, &c.; for it is on a due appreciation of these circumstances that we ought to rest our final determination. The author of the work before us has therefore very properly, in our opinion, commenced his Essay with an introductory chapter, illustrative of the theory of rivers according to the principles of Du Buat: exposing, as he proceeds, the singularly erroneous doctrine of Guglielmini, who founded his whole theory on the hypothesis that the velocity of the stream at every point of its depth was that which is due to the altitude of the fluid above it; thus giving to the bottom of the stream the greatest quantity of motion, while the surface, according to the same principle, ought to be quiescent. Nothing could be more absurd than this assumption, except the way in which it was illustrated:

Suppose a vertical plane, perforated with an indefinite number of small holes, were placed across the section of a river, the velocities of the particles issuing through these holes would, he considered, be the same as the velocities of the particles of the river at the same depth; viz. those due to their respective distances below the surface of the stream.

From this it would follow, with many other deductions, not necessary to notice here, that the velocity at the bottom is greatest; that it is least of all at the surface; and that the velocity of the water increases as the square roots of the depths. These deductions, however, are not found to be the case; and if the principle were true, rivers would, ages ago, have produced destructive effects upon our soil. The mountain torrents would have left the elevated regions bare to their skeletons - the rich soil of our meadows would have been carried to the ocean and those effects

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effects which are now working by scarcely perceptible degrees would, ere this, have rendered uninhabitable a great part of what is, at present, dry land.'

It is very extraordinary that a theory so exceedingly erroneous should have been followed by such men as Varignon, s'Gravesande, Muschenbroek, Bélidor, and Buffon: yet such was actually the case; not one of these authors seeming to have been aware that the law indicated above depended solely on the circumstance of the several particles of the fluid at different depths being unsupported; whereas, in rivers, every particle having a counter pressure to sustain, the water can flow only with a velocity due to the slope of its surface. Such inaccurate doctrines, however, are unfortunately but too common in the theory of military works. A similar instance might be cited in the case of estimating the strength of timber and other materials, a subject intimately connected with the profession of a military engineer; yet in which, till lately, an entirely erroneous principle has been adopted: so false, indeed, that directions have been given, and followed, for placing timber in certain positions for the sake of strength, which were actually the weakest that could have been employed. Another example may likewise be adduced, viz. that of revetements, for the computation of which the most mistaken principles are still employed; although Col. Pasley has clearly demonstrated, by actual experiment, the fallacy of the conclusions hitherto drawn from investigation. He has not, however, (we believe,) pointed out the source of that error; which consists in resolving the force at the wrong point, and in rejecting, as unimportant, the adhesion of the materials. (See Barlow's Essay on the Strength of Timber, &c. noticed in our Number for May last.)

That these errors have so long passed current among our military engineers is much to be regretted: but it is equally a subject of congratulation that such men as Sir Howard Douglas and Colonel Pasley should be exerting themselves to dissipate them, and we may confidently predict that they will not exert themselves in vain. Nothing can be more absurd than the perpetual employment of French words and phrases in every part of our fortification-system, as if the French were the only engineers in the world; and as if the practice were so intimately united with that country, that no other language was capable of giving an explanation of its principles. It was a prevailing opinion, only a few years ago, that no troops or Generals were equal to those of France; and many persons are inclined to believe that we must still

look

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look to that country for engineers; an idea which the general adoption of their terms has a tendency to encourage. Colonel Pasley has done much towards eradicating this objectionable practice, in his work on "Military Instruction;" while the volume of Sir H. Douglas now before us, and that which we so lately noticed, (as already observed,) offer indisputable proofs that we have engineers among us as capable of disputing with France on the scientific principles of the military art in the time of peace, as in the practice of them in the open field and in fortresses during the period of war.

We must observe, however, that, in order to ensure complete success to our military science, it is necessary to pay particular attention to the education of our students in those institutions which are devoted to their instruction. All the principles of engineering ultimately reduce themselves to those of the mathematical sciences; and it is to little purpose that young men are taught to be good draftsmen, if they are deficient in mathematical knowlege. It is true that an officer has little concern with mathematical theories, otherwise than as they tend to some useful practical result: but who will say that the practical result can be well understood unless the theory has been first properly comprehended? An officer, who has a mere practical knowlege, may follow up the directions laid down by others, but he will never be able to judge of the accuracy of the principles on which they are founded: so that, if his author be right, all may be well, but, if wrong, so also will be his disciple. For the truth of this doctrine, we need look no farther than to the present and the preceding work by Sir H. Douglas, and to that of Colonel Pasley above mentioned. Had the former author not investigated for himself, he would never have been able, by means of the terminal velocity of balls, to have demonstrated the fallacy of Carnot's doctrine; nor would the latter have deduced, without the same aid, those useful practical conclusions on the subject of revetements at which he has arrived, from experiments conducted on a comparatively small scale.

We have been led almost involuntarily into the above train of observations by the nature of the work before us, by remarking the soundness of the principles on which the author proceeds, and by contemplating the ease and simplicity with which he obtains his conclusions: which we could not but contrast with the far-fetched and superficial theories of some of our neighbours, and the over-strained generality of their deductions;- with their problem of route, of Deblais et Ramblais, &c., and many other fanciful investigations of equal insignificance.

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Let

Let us now proceed to give a hasty sketch of the contents of the volume which has called forth these remarks. It has been already stated that the author, in his introductory chapter, undertakes to present a concise view of the theory of rivers; which he intersperses in different parts with observations of his own, made during his service in the Peninsula: thence drawing various practical deductions, highly useful to those who may be at any future time engaged in operations of the kind on which he treats. We select the following extract, as illustrative of the manner according to which the author makes his final deductions:

Ist, In small velocities, that at the surface exceeds that at the bottom in a very considerable ratio.

2dly, This ratio diminishes in proportion as the velocity of the current increases; and, in very great velocities, approaches nearly to equality.

3dly, Neither the magnitude of the bed, nor the slope of the river, changes this proportion, when the mean velocity remains the same: and,

4thly, When the velocity at the surface is constant, that at the bottom is constant also, whatever be the depth of water, or the magnitude of the section.

The mean velocity is an arithmetical mean between that at the surface and that at the bottom but it is very difficult to ascertain the latter by experiment, and the proportion between it and the former diminishes as the mean velocity increases. This variation M. Du Buat determined by experiment; from which he formed the following rule to find the bottom and mean velocities, when that at the surface is known.

Rule. Take unity from the square root of the superficial velocity, expressed in inches, and the square of the remainder is the velocity at bottom. Thus, if the superficial velocity in the middle of the current be 25 inches per second, √25—1= 4, and 42+25

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20 inches, the mean velocity.

This is a very important discovery: the velocity of the surface is easily measured, and it is the mean velocity that must be used in calculating the discharge, supply, force, and every other effect of running water.

Before I followed this investigation, satisfied that the foundation of Guglielmini's theory was erroneous, I made many experiments to determine the mean velocity of running water.

The following simple method was resorted to.

A straight rod of wood, of equal dimensions throughout, was prepared; the length nearly equal to the depth of water. One end of the rod was loaded with a piece of lead of the same circumference, so as to float perpendicularly in the current. It is evident that the progress of the rod must be exactly that of the

mean