of those experiments communicated in Mr. Fairbairn's work, and, also, of their importance. For, notwithstanding the imperfect manner in which they have been conducted, we consider their results, not only to science, but to the commerce of the world, as important. Were it only for establishing this fact experimentally, that by increasing the speed of a certain description of boats on a canal to nine or more miles an hour, the surge and wave, consequent on a slower motion, vanish, the experiments are highly important. It is, however, to be regretted that there is scarcely a circumstance mentioned, if we except this, that could aid in adding to, or perfecting the present state of science on this intricate subject. We see, also, from the mode of calculation adopted in exhibiting the results of the experiments, (pp. 61, 62) that their conformity or disagreement with theory has been tested by the single principle of the squares of the velocities, as if the essence of every other principle connected with this subject, had been concentrated in this.

We are not astonished, that a mere practical man, such as Mr. Fairbairn appears to be, should reason in this imperfect manner, nor are we astonished that he should quarrel with, and make every attempt to banish theory altogether, when the only light that appears to have beamed upon him from it, his squares of the velocities, proved to him an ignis fatuus. We are not surprised that this should be the case with Mr. Fairbairn, but we are both surprised and astonished to find in reading an article "On the Advantages of Rail-roads over Canals,' in Dr. Lardner's Cabinet Cyclopedia, vol. xvii. that this great luminary of science should have his vision so obscured, or his intellects so bewildered, as to suffer himself to be conducted by the same ignis fatuus. We shall quote his paragraph as we intend to offer a few observations on it afterwards.

"These considerations (he observes) place in a conspicuous point of view the advantages which transport, by steam-engines on a rail-road possesses over the means of carriage furnished by inland navigation. The moving power has in each case to overcome the inertia of the load; but the resistance on the road, instead of increasing as in the canal in a faster proportion than the velocity, does not increase at all. The friction of a carriage on a rail-road moving sixty miles an hour,* while the resistance on a river or canal, were such a motion possible, would be multipled 3600 times. In propelling a carriage on a level rail-road, the expenditure of power will not be in a greater ratio than

*Would not be increased, we suppose understood.

Here again we have by Dr. Lardner, the same square of the velocity as unscientifically applied, as by Mr. Fairbairn.

that of the increase of speed, and therefore, the cost will maintain a proportion with the useful effect; whereas in moving a boat on a canal or river, every increase of speed, or of useful effect, entails an enormously increased consumption of the moving principle. But we have here supposed that the same means may be resorted to for propelling boats on a canal and carriages on a rail-road. It does not, however, appear hitherto, that this is practicable. Impediments to the use of steam on canals have hitherto, except in rare instances, impeded its application on them; and we are forced to resort to animal power to propel the boats. We have here another immense disadvantage to encounter. The expenditure of animal strength takes place in a far greater proportion than the increase of speed. Thus if a horse of a certain strength, is hardly able to transport a given load ten miles a day for a continuance, two horses of the same strength will be altogether insufficient to transport the same load twenty miles a-day. To accomplish that, a much greater number of similar horses would be requisite. If a still greater speed be attempted, the number of horses necessary to accomplish it would be increased in a prodigiously rapid proportion. This will be evident if the extreme case be considered, viz. that there is a limit of speed which the horses under no circumstances can exceed. The astonishment which has been excited in the public mind by the extraordinary results recently exhibited, in propelling heavy carriages by steam-engines on rail-roads, will subside if these circumstances be duly considered. The moving power and the resistance are naturally compared with other moving powers and resistances to which our minds have been familiar. To the power of a steam engine there is, in fact, no practical limit; the size of the machine and the strength of the materials excepted. This is compared with agents to whose power nature has not only imposed a limit, but a narrow one. The strength of animals is circumscribed, and their power of speed still more so. Again the resistance arising from friction on a road may be diminished by art without any assignable limit, nor does it sustain the least increase, to whatever extent the speed of the motion may be augmented; on the contrary, the motion of a boat through a canal has to encounter a resistance by increase of speed, which soon attains an amount, which would defy even the force of steam itself, were it applicable, to overcome it with any useful effect."

If the object of Mr. Fairbairn and others, in their opposition to theory, was to falsify such doctrines, as most of those which are contained in the preceding paragraph of Dr. Lardner, their motive would be perfectly just; but this could hardly be the case, as works existed that could have informed them better. Such hasty publications as are generally, now got up for the trade, when treating of scientific principles, or practical subjects, do much more injury than is commonly supposed, when these prin

*This is false, as either theory or experiment would evidently shew.

VOL. VIII-No. 15.

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ciples are not accurately established, or clearly elucidated; for the authority of great names is too often a passport for these superficial works. If reviewed, they are generally reviewed in the Paul Clifford style, without perhaps examining the truth or falsehood of a single principle contained in them; they are thus puffed off the booksellers shelves, and it would be contrary to established etiquette, to dispute, after this ceremony, their title to utility and even to fame. It was not in this manner that Euclid produced his Elements of Geometry, or Newton his Principia; and hence these works have outlived and are destined to outlive the ravages of time, very unlike the ephemeral productions of our day. To this remark, we are glad to find, however, that there are some illustrious exceptions: we would instance the translation of the "Mécanique Celeste,” of Laplace, by Nathaniel Bowditch, L.L. D. This work, no less remarkable for the elegance and precision of its language, and the beauty of its typography, than for its profound and extensive notes and commentaries, would do credit to any age or to any country; and must enhance in a great degree, the value of the original; not only by the additional matter, but by removing, in a great measure, the difficulty attending the study of this immortal production.

We shall now endeavour in as clear, and, at the same time, as concise a manner as we can to point out some of those general laws and principles on which depend inquiries of the nature of those exhibited in experiments on the resistance of fluids.

Almost the whole of naval architecture, where there is any real difficulty to be encountered, depends upon hydrodynamics, and particularly on that portion of it which relates to the resistance of fluids, and their various actions on bodies. It is impossible that naval science can keep pace with the improvements and discoveries of the age, until with the practical skill so generally exhibited at present, be united a sufficient portion of theory, or correct science, to throw light on the difficulties that every moment present themselves.

If a non-compressible fluid act upon a plane opposed perpendicularly to the direction of its motion, the force with which it impels

*There are other works of Dr. Lardner of a different character from that of his Cabinet Cyclopedia, such as his " Treatise on Analytic Geomety," his " Elementary Treatise on the Differential and Integral Calculus," &c. and hence, we were the more surprised at the vague and obscured assertions of this eminent and profound philosopher, which we have pointed out. We are so inundated with these airy and fashionable works, and the taste and judgement so completely violated by theory, that a work of real merit, or profound research and science, will scarcely be read or consulted.

the plane or acts on it, will be as the square of the velocity of the fluid.

For the force on the plane must increase as the velocity increases, and also as the number of particles or the quantity of matter that strikes it in a given time: now with twice the velocity there is twice the force, with three times the velocity, three times the force, &c. and also with twice the velocity there is twice the quantity of matter, with three times the velocity, three times the quantity of matter, &c. acting on the plane at the same time; and as the force of a body in motion is as the quantity of matter multiplied by the velocity, it follows evidently that the force on the plane is equal to the product of these equal numbers, or their squares, or which is the same the squares of the velocities.

If the size of the planes vary, other circumstances remaining the same, the forces on the planes will be as their areas respectively; if the densities of the fluids only vary, the forces will evidently be as the respective densities; but when the size of the planes, densities, velocities, and other circumstances vary, then the force on the planes will be made up of all these varying actions, or as the product of their respective forces. These respective actions, or the combinations, according to circumstances, are usually represented by a variety of algebraical formula.

We must not suppose with most writers, we believe, indeed, with all who have written on the subject, that it is the actual velocity of the stream that is to be taken, but the velocity with which it actually strikes the plane; for after the particles of the fluid strike the plane, their action does not cease; they must necessarily diverge, and acting upon the particles behind them, must diminish their velocity. It is this diminished velocity that must be used when we suppose the plane at rest and the fluid in motion. But if we suppose the plane, or the body in motion and the fluid in which it moves at rest, then it is the velocity of the plane or body that is the actual velocity to be taken. This distinction is not made by any of the writers on this subject that we know, and hence theory will sometimes differ from experiment. If we suppose the fluid in motion, and the plane or body to be also in motion, either in a contrary or in the same direction. with that of the fluid, then the sum or difference of these velocities must be taken in estimating the actual force on the plane or body.

Suppose now that a vessel in the shape of a parallelopiped, or oblong rectangular box, be partly immersed in a stream of water, it is evident that besides the direct action of the stream on it, an additional action or resistance will be produced by the

friction on the sides and bottom, by the accumulation of water in front-thus exposing a larger surface to its action-and by the want of the full pressure behind, from the action of the current on both sides communicating a portion of their motion to that of the fluid behind the vessel, and thus diminishing its pressure; or even forming a hollow between the space where the currents on both sides meet, and the stern of the vessel. When all these circumstances are allowed for, then theory will agree with experiments. For want of attending to these circumstances, we scarcely ever find that any two sets of experiments agree among themselves, or with theory. When the form of the vessel at the stem is that of the above, the space, formed behind the vessel by the two currents, and the front is spoon-built, as Mr. Fairbairn would express it, or is of such a form as to diminish the rise of the wane in front, or produce none at considerable velocity, the resistance from the causes may be almost entirely done away with.

Thus far the law of the squares of the velocities will hold after making these necessary corrections, while the size of the planes or bodies exposed to the fluids, their position, densities of the fluids, and other circumstances remain the same, or do not vary. But we are not, however, to infer from this, or to take as granted, that if the velocities be considered as variable, other circumstances would not also necessarily vary with them, and modify the result of this general principle. To suppose the contrary, as Dr. Lardner, Messrs. Graham, Fairbairn and others have done, would be as absurd as to suppose that Euclid's axiom, "things equal to the same thing are equal to one another," would hold in every possible case, as well as that in which the comparison is made: or that because a man is an animal, and a goose also an animal, a man must, therefore, be a goose.

To shew clearly that a similar or false application of sound theory, was made in the instances alluded to, we shall have to establish a few more general principles.

Let AC, be a section of a plane C cutting the fluid A E F C in the direction of its motion E A, or B D, at right angles; we have shewn, D (that with some trifling allowances which we have pointed out) the action of the fluid on this plane will be as the squares of the velocities. Suppose now the plane to have the position A B, its inclina

f

F

B

e

b

a c

A

E