Charnock says the "sailing of a vessel depends on a myriad of circumstances."No table founded on actual performance of different vessels can be minutely accurate; and this of Mr. Seaward, except in the second instance, (which differing so materially from the three following must have been misquoted,) gives practical confirmation of the received theory. The results of the experiments of Colonel Beaufoy, although, they will doubtless be familiar to your scientific readers, may with propriety be submitted here for inspection, and the accompanying extract from his table will show how nearly practical experiment and theoretical deduction coincide. "The scale on which these experiments were conducted, the extreme accuracy observed, the ample means possessed by, and the extraordinary devotedness to the science, and the perseverance of the experimentalists are certain guarantees that the results may be depended upon."

The law in hydrostatics governing the theory of resistance, is that, "if any body move through a fluid at rest—or the fluid move through the body at rest, the force or resistance of the fluid against the body will be as the square of the velocity and the density of the fluid." And what can be more plain than the demonstration? "For the force or resistance is as the quantity of matter or particles struck, and the velocity with which they are struck. But the quantity or number of particles struck in any time are as the velocity and density of the fluid-therefore, the resistance, or force of the fluid is as the density and square of the velocity." Founded on this law of quadruple resistance, that of octuple power is the necessary consequence, for in a current of 10 miles an hour, double the number of particles must impinge and pass the vessel, as in one of 5. The velocity and density of the fluid are both doubled, the square of which gives the octuple ratio.

To this law and its consequences Mr. Booth demurs, and for the purpose of testing it, he caused a trough 26 feet long. 3 feet wide, and 2 feet deep to be constructed, which was supplied with 18 inches depth of water.

As many of your readers may not have access to the book, I must trespass on your space by giving his experiments.

No. 1. A weight of 2 lbs. falling 7 feet 6 inches drew the boat 7 feet 6 inches in 6

seconds, (the cord attached to the boat, and the cord attached to the weight, passing round pulleys of the same diameter.")

"No. 2. Other things being the same, I increased the weight, till it fell 7 feet inches in 3 seconds, the weight being then 8 lbs."

This, as Mr. Booth says, accords with the "quadruple ratio, or of double speed requiring octuple power.”

But Experiment No. 3 gives vastly different results. This was so arranged, that the weight or power should always move through the same space in the same time; the cord attached to the boat was passed round a pulley twice the diameter of the pulley round which the cord attached to the weight was passed: the boat would, consequently, move through the water 15 feet, while the weight, as before, moved 7 feet 6 inches.

"By repeated trials," Mr. Booth says, "I found that 5 pounds sufficed to draw the boat 15 feet in 6 seconds, the said weight falling 7 feet 6 inches in the same time;" "thus by changing the mode of applying the power, 5 pounds become as effective as 16." "That is, 24 times the power, moving through the same space in the same time, was required to draw the boat double the space in the same time, or twice the distance at twice the speed."

Experiment No. 4 confirms the "quadruple ratio." No. 5 and 6 accord with No. 3. And with these six experiments, (he says he made others of a similar kind, with which he will not trouble the reader,) he sets up the doctrine, that all received opinions founded on theory and practice

are erroneous.

On the new theory, 5 lbs. are as effective as 16 on the exploded one. According to it, a boat placed in a tide-way of 5 miles an hour, with a power on board of 30 horses, which exerted would just enable her to stem the current and hold her own, would be driven against this tide of 5 miles another 5 miles, by the addition of 45 horses; 45 is, therefore, to effect the same speed in a current of 10 miles that 30 has done in one of 5!

Now, let us imagine, for the sake of illustration, that a 30-horse engine, by increasing the effective force of the steam, may be converted at pleasure into a 60, 120, and 240-horse power. Making the same number of revolutions, double the quantity of steam must be expended in the 60 that is required for the 30; and at double speed, 10 miles an hour instead of 5, four times, making it an engine of 120 horses. But there is yet another

difficulty to be encountered. At 10 miles, there must be double resistance from "twice the number of impinging particles;" the power must therefore be again doubled, resulting in the "quadruple ratio."

Mr. Booth's experiments 1, 2, and 4, confirm the received law; but 3, 5, and 6 present an extraordinary anomaly, for, according to these, twice the distance and twice the speed are acquired by a little more than twice the power; and 5 lbs., by changing the mode of applying the power, become as effective as 16, under the old system, which his other experiments confirm. This astounding result Mr. Booth infers to be in consequence of the loss occasioned by the more rapid falling of his weight, or motive power, in the one case than in the other; and by changing its speed from 15 feet in 6 seconds to 7 feet 6 inches in

the same space of time, he gains in the ratio of 16 to 5. Now, it is perfectly true, as Mr. Booth says, "if you increase the velocity of descent, you diminish the effectiveness of weight as a power, and, carried to the point indicated by the law of gravitation as affecting falling bodies, a weight has no power at all." But what is this law? "A heavy body falling freely will pass through a space of 1,208 feet the first second, and then attain an increased velocity, in the inverse ratio of the square root of the height from which it falls: in 4 seconds it will have acquired 16; in 9 seconds, 24; in 16, 32; and in 25, the rate of 40 feet in a second. The highest velocity in the experiments 1, 2, and 3 is 15 feet in 6 seconds, the lowest 71, making 74 feet the difference, or one foot and a quarter per second to be deducted for loss by the increased velocity of descent, from the average speed of a body falling six seconds. This is hardly sufficient to account for a gain of upwards of 300 per cent! Would a body, falling through a given space at the rate of one foot and a quarter in a second, raise a greater weight double that distance, the cord attached to it passing over a pulley of double size, than it would passing through double space in the same time, both pulleys being alike? Or would the difference be more than the smallest fraction, even although the falling body should be feathers, and the one raised lead?

There must have been some screw

loose-some mistake in a figure in the experiments. They are so contradictory in themselves, and so utterly at variance with theory, established with mathematical certainty, and practice, as proved by close observation, and the most elaborate experiments, that I must be excused for taking with distrust assertions in direct opposition to my own assent to a Q. E.D., and the authority of such men as Colonel Beaufoy and Mr. Seaward-indeed, of all "engineers and men of science in the present day." The resistance to a body passing through the water is resolved by writers on naval architecture into three distinct causes head pressure, lateral friction, and stern pressure. The first of these, caused by the water impinging the bow of the vessel, must necessarily be in the ratio of the number of particles impinging, and their velocity, and, of course, must be quadruple at double speed. It constitutes by far the greater portion of the whole resistance. Lateral friction is caused by the water passing in contact with the sides and bottom of the vessel, and will be in direct proportion to the number of particles so passing. By an inspection of the diagram, it will be found that it constitutes but a small proportion of the resistance; the forms presenting the greatest surface for its action, from having a better entrance, are those that move most easily through the water. Stern pressure being the tendency to a vacuum caused by the passage of a body through a fluid, with the fine lines adopted for the after bodies of steamers, and at their slow speed must offer but little obstruction. A cannon-ball, on first leaving the piece from which it is discharged, is much retarded by it, its motion being so rapid, that the air cannot rush in with sufficient speed to fill up the vacuum; but at 10, or even 16 miles an hour, the water readily flows in-its ratio, no doubt, will be double at double speed.

Suppose, by way of approximation, we divide these resisting powers in the following different proportions-head presure, increasing according to the squares of velocity, and friction and stern pressure in direct proportion, following Cql. Beaufoy's table of actual resistance at different velocities. [See Table next page.] At slow speed, it will be seen that friction and stern-pressure have a much greater relative effect than at high, on

the velocity being increased to the practical desideratum of 12 miles an hour,

TABLE.

1 mile. 2 miles. 3 miles. 4 miles. 5 miles. 6 miles. 8 miles. 10 miles. 12 miles.

for friction and stern pressure 557 x 2 = 1114

*Thus, 75 per cent. of 0.2229 for head pressure = 1672 x 4 = 6688

25

do.

0.7802 &c. &c.

head-pressure increasing four-fold, while the other causes of retardation are only doubled; the division of nine parts for the

one, and the remaining tenth for the other two, approximates very nearly to the practical results, which it would otherwise be difficult to reconcile. It would thus appear, that "the force or resistance (from head-pressure) is as the quantity of particles struck, and the velocity with which they are struck," and that friction and stern-pressure are fixed quantities, increasing in a direct ratio.

Having disposed of the "Theory," I may be allowed a few remarks on the "Practice" as involved in the "improved method of applying mechanical power to steam navigation."

To drive a boat at any given speed, say from 10 to 12 miles an hour, the calculation in ordinary steamers, is to allow a loss of one-third of the power applied. Let us suppose, however, that Mr. Booth's propeller possesses such advantages as to lose only one-fourth—to give 10 miles speed to the boat, it must therefore go through a space of 66,000 feet in an hour, or 183 feet in a second, which, whether given in short, quick strokes, or long, slow ones, must require about 90 percussions in a minute, 90 × 12 × 60=67500. But he says, the piston of his engine moving at the rate of 24 miles an hour, will give 314 miles speed to his propeller. Take, however, 30 miles speed as the average, and it is obvious that there must be a loss of more than half from the want of resistance; for unless the irregularities are such as to make a tremendous jerking motion, 15 miles is as much as can be expected at any one moment of time; and that subsiding to 8.30 times in a minute, will not be over-pleasant. The piston of an engine of 4 feet stroke moving 24 miles an hour, would give 33 revolutions in a minute; 33 x by 124, the length of the stroke of the propeller, would give less than 5 miles an hour, whereas 12 would be required; the residue must therefore be made by the "concentration of power." Few engineers will agree with the writer in his principles of concentration. Does he suppose that the power absorbed and concentrated in a fly-wheel is any greater when given out at a single impulse, than if divided into ten? Or in other words, that any more power can in any possible way be obtained from the recipient than is communicated to it? If this can be effected, we need look no further for perpetual motion. If his 200

horse engine can be made to give out more than 200 horse power "by a slow succession of rapid strokes," or in any other manner, the effect must be greater than the cause, and perpetual motion the inevitable result. The writer does not appear to take into consideration the resistance and friction that will be opposed to the returning frame-work and open propelling-plate; 10 miles an hour is the speed at which the vessel is supposed to go; say 880 feet in a minute; the stroke must be repeated 33 times x by 12 = 412, or 1292 feet speed for the returning propeller: this, too, supposing each concentrated stroke of 12 feet to drive the boat 261, in which I apprehend he will be greatly disappointed: 1292 feet, however, in a minute, on the octuple ratio, which he must pardon me for still believing in, would be no inconsiderable drawback even from an open valve-plate.

It is unnecessary to dwell upon the practical difficulties that would be opposed to such an application of power. What material could possibly be made to stand the shock of the concentration of a 500 horse power into a single impulse of 5000? The best iron, and the most perfect workmanship, are already in requisition for the cranks and shafts of engines as now constructed, to meet an uniform resistance. What reasonable belief can there exist that the quality of the material can be so improved, or the quantity so increased, and, necessarily, the skill to forge such masses so much advanced, as to meet so great a demand for additional strength, as the conversion of an uniform motion of 500 into one of impulses of 5000 would require? The tremendous friction on a cam-wheel, giving out this power in the space of 1 foot 3 inches 38 times in a minute, must be apparent to all; but how Mr. Booth arrives at the conclusion that he has not half the resistance to overcome, unless he intends to monopolize the discovery that the power of 5 is equal to 16, I am at a loss to understand. That his "engine will not be of half the usual height," and his "coals of not half the quantity," will be the necessary result of 5 × 0=16.

Your obedient servant,

O. B. F. P.S. I have written the above before I saw your Number of 16th July. If you think it worth insertion it is at your ser

vice. I should like to call the attention of your scientific readers to the table of head-pressure, friction, &c. If the principle be correct, the exact proportions may easily be found. I have not the book at hand for references, but I think "Charnock on Naval Architecture" will give the requisite information. O. B. F.

THE IRON STEAMER QUEEN." Sir,-As your valuable publication is almost the only means through which any works of art, either of merit or otherwise, can be brought fairly before the scientific world, I beg the favour of your inserting the following statement of the dimensions and performance of a new iron steamer recently started upon the Thames.

The vessel I refer to is named the Queen; and, so far as a judgment may be formed of her capabilities from a careful inspection of her, inside and out, and the few trials of speed that have yet been made with her, (more than one of which I have had the pleasure of witnessing,) I am of opinion that she will fully merit the high name her owners have selected for her. A more beautiful specimen of a light river steamer, whether as regards design or workmanship, I have never before seen.

The vessel was designed by, and built under, the immediate superintendence of Mr. Edward Pasco, (a gentleman well known on the river, and of considerable promise as a shipwright;) and the engines, manufactured by the eminent engineering firm of Messrs. George and Sir John Rennie, of Blackfriars. She is 160 feet long, between perpendiculars; of 16 feet 6 inches beam; 8 feet 9 inches deep; and draws about 4 feet 3 inches water. In her engines there is nothing new, but they are constructed on certain known and well-approved principles, which have produced a most efficient result; and I feel confident this will be at once admitted, by all competent judges, when I state their performance. On Saturday, (the 6th instant,) her owners were honoured by the Lords Commissioners of the Admiralty using her as the mode of transit from Deptford to Woolwich Dock-yards, when their Lordships were pleased to express, in no measured terms, the high gratification they felt on