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338

USE OF THE SLIDING RULE.

of a most excellent workman and done, having no other end in view but agreeable companion.

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Description of the Drawing.

A, the frame in which the different, beds or wire-supports are screwed. Length, 9 inches; breadth, 14 inch; to be held in a vice, B, placed in the centre of the frame. In this the wires are secured while cut. 2 of C, one placed at each end, which turns in an angular direction to keep the wires in a straight line while they are cut, having screws and washers, viz. FF. Eis the support in which the saw or cutter works, and is open at the top; the saw, K, is made to move in the back by means of the screws in it, to suit any sized wire, and is always forced down till the back comes in contact with the top of the support E. The first cut the wire receives, E is placed in the holes P, Q, R, S, according to the length of the figure of trellis required, and D in the slit X. In D and E are two centres, which give the diagonal of figure; and according to the figure required, so are these centres placed. After these supports are properly placed, namely, in the proper angle after the first ends of wires are cut, they are reversed, and the spear, G, is pushed into the slit, to keep the wires straight, and the screw, Y, is forced against the wires to keep them together. in this manner we cut the. wires the first time. The second time the support, E, is placed on the other side, in the slit, X, between B and D, and the one-half of the former distance taken. M is a slip of steel, which is placed in D, which fills the first cut, and two small pins are put in at the ends to keep it there, and above is placed the spear, H, to keep them fast. In this manner trellis-work is cut.

[L is a view of E and D, as seen in the direction DE.-J. YULE.]

USE OF THE SLIDING RULE. SIR, I trust that I need not make any apology for the liberty I am taking with some of the Problems of the Slide Rule, by G. A. S., and, as I make no doubt of his being a man of good sense as well as a man of science, he will not find fault with what I have

the good of my fellow-mechanics. The guage-points he makes use of must either be wrong, or he must have miscalled the numbers on the rule-a mistake very easily made, but which, if not corrected, would tend to puzzle or lead others into error.

I shall begin with his 9th Problem, Example 1st., page 227: his answer to this question is 23 solid feet. Now, I make use of Routledge's improved engineer's rule, and the answer upon this is 264 feet. The true answer by 16,432 figures, thus: × 14=26,24 feet. 144 Example 2nd.-The answer is 45 feet very nearly; by Routledge's rule it is 192 464 feet, and, by figures, × 18,5 144

-46,36 feet.

Problem 10th, Example 1st, is so very plain that it would hardly be possible to make an error, as it can easily be done by the head, without either figures or rule. But Example 2nd is of a very different description, and G. A.S.'s method of doing it, I am afraid, will rather tend to puzzle than instruct the young mechanic. Instead of taking twice the length, and 1-5th of the circumference, it is much better to take the proper length, and, after the mean circumference is found, it is very easy to find the diameter, which is the only true way to come at the solid content. Routledge's rule gives for answer to this question 312 feet full. By figures, first, 15 x 12 = 180 = circum180 =57,209 3,1416 diameter; then 57,2092 x ,7854 2570,97-area of the section in square 2570,97 inches, and × 17,5=312,42 feet,

ference in inches, and

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144

the true answer.

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CALCULATION OF INTEREST-BUNTEM'S SYPHON, ETC,

bear a proper proportion to each other, This is done by drawing the slide out of the rule and reversing it, or putting it in again the wrong way; the line C will then be next A. Set 282 on C, 78,6 on A, and against 231 on C is 95,96 on A; thus each divisor has its proper number of gallons which are contained in the same vessel.

This last example will prove the correctness of the measurement of any vessel, the contents of which are to be taken both in ale and wine gallons. I shall here conclude for the present.

I am, Sir,
Yours respectfully,

A MAN IN THE MOORS.

In the Moors,

On the 6th of August, 1825.

CALCULATION OF INTEREST.

SIR,-In my communication in your Magazine of the 18th of June (page 167, vol. iv.), which contained a new Method of Calculating Interest at Four per Cent., I mentioned that I would send a short method of the same nature at Five per Cent.

Every one knows (and the reason why, I presume) that, if any sum be divided by 7300, the result will be the interest at Five per Cent. Now, instead of this long division by 7300, we shall find that, if any sum, the interest of which is required for one day at Five per Cent., be divided by 3, 30, and 300, the quotients added to the sum, and the 10,000th part of this result subtracted, the answer will be given in decimals, inserting the decimal point four figures from the right hand,

It is evident that there is but one actual division here, which is by 3, the others being merely a repetition differently placed.

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I could send methods to you, ad infinitum, to produce the same result; but it is impossible, I may safely say, for a shorter one to be devised. I am, Sir, Your obedient servant,

21st June, 1825.

G. U. A.

P.S. In my last I omitted to put, (6 at Four per Cent." after the words, "required for one day."

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SAFETY FROM CARRIAGES FALLING.

SIR,-In Number 90, page 88, of your Magazine, there is a plan to prevent Two-wheel Carriages from falling, by adding two small wheels to the shafts. But suppose the horse should fall (which he will do sometimes), would not the shafts be instantly broken in spite of every precaution, the hinder part of the carriage thrown up, and the company ejected from it into the street? I think that such an accident would be prevented by having the shafts to let down, the same as the shafts of a four-wheeled waggon, which may be seen every day in the streets; so that, if the horse should fall occasionally, the shafts only would fall, and the carriage would remain as upright as before. All the other parts of the

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REMARKS ON MR. PALMER'S SUSPENSION RAILWAYS.

carriage might be made as Dixon Vallance proposes, except the shafts, which should be made as above.

I am, Sir,

Your very humble servant,
WILLIAM Downes.

111, Aldersgate-street.

REMARKS ON MR. PALMER'S SUSPENSION RAILWAYS.

(See Mech. Mag. page 287, vol. III.) Mr. Palmer asserts that his plan will cause a great saving in embankments, bridges, culverts, and drains, and that the carriages will be moved on it with less friction and resistance than on the railways hitherto in use; averring that a horse can draw a load on it, when level, of 33,750 pounds two miles and a half in an hour, which on the best performing edge railway that he had heard of (that near Newcastle-onTyne), could move only 17,773 pounds at the same rate.

We should be greatly at loss to account for this superiority of performance of Mr. Palmer's railway, and even to suspect exaggeration, could we not see, in the nice adjustment of Mr. Palmer's apparatus, and in his curious contrivance to lessen the friction of his wheels (which we are, bythe-bye, inclined to attribute to its bringing a larger surface of the axle and hollow box of the nave into contact, instead of the oil being prevented by it from assuming the shape of a wedge, as Mr. Palmer asserts), somewhat to justify the validity of the experiment; to this we have to add, that the shape of the surface of this rail, which is the segment of a circle, and the hollow rim of the wheel being also of the same circular form, will at first give a great superiority to the performance of the apparatus, which the power of adjusting the level, or inclination of the rail by the wedges, to unusual nicety, must greatly assist. But as all these circumstances are equally applicable to the common double railroads of the edge form, we think that farther trials than those made previous to the publication of his book will be necessary, impartially conducted, with wheels, axles, and both parts of the apparatus, equally good and perfect in the other species of railroads, before the question can be fairly decided.

That the form of the surface of the rail and rim of the wheels, being seg

ments of circles, will at first much facilitate the draft, as we have just stated, depends upon the well-known geometrical problem, that a circle described within another circle can only touch it in a point; therefore, as long as these forms continue perfect, the lateral friction of the projecting part of the rim of the wheel against the side of the rail will be avoided, and so long will a great source of resistance, which is experienced in other railroads, be overcome.

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The Penryn railway, which was originally formed in this manner, had, at first, all the advantages stated but, according to the authority of Mr. Benjamin Wyatt (for which see Repertory of Arts, second series, vol. 111. page 285), the two circular surfaces of the rail, and of the wheel's rim, as they wore, excavated the latter so much, and caused it to fit so tight, as to occasion much friction, and make it necessary to change the wheels so often, that another form of rail and wheel became necessary; from which it follows, that time is needful in experiments of this sort as much as any thing else, and that it is requisite new kinds of railways should be in perfect operation for a reasonable period before their superiority can be allowed.

A railway of Mr. Palmer's construction has been erected at Cheshunt, near Waltham, to carry bricks from Mr. Gibbs's fields, about a mile, to the river Lea; it is constructed of wood, with posts about five feet high, and ten feet apart, as we are informed, and has the surface of the rail covered with an iron plate. Nothing, at present, can be learned from this experiment, but that the plan is feasible, which we never doubted; but, for the reasons stated, we must wait for the effect of wear and of the weather upon it, before we can decide how far the posts will maintain their upright position, and the rails their level, the first of which points we do not think sufficiently provided for by the patentee. In point of expense, a wooden rail can be no guide for those to be made of iron; and when formed of this latter material, we think the patentee deceives himself in supposiug that his railway can be made cheaper than a common double one; for, supposing his made with rails of the same strength as they are, and of course requiring supports, as they do, at every three feet, or thereabouts, now his pillars being three feet at least above ground, and as much more below the

SINGLE-WHEEL CLOCK.

earth (according to his drawings), and requiring to be of considerably greater substance, it is evident that they will take at least double the weight of iron for their construction, which would be necessary for the second rail, saved by his plan; and if, as he proposes, they be set farther asunder, nothing will be gained in this respect, since the rails then must be made so much stronger in proportion (to which must be added, that they must in all cases be made of double the strength of common rails, one of them having to sustain the load of two of these); and as for the lengths of ten feet between the posts sug gested, their weight, to carry the usual loads, must be so much greater than that of any now used, that we much doubt if any of them, of iron solely,

will ever be constructed.

That erecting numerous lofty pillars of iron, as proposed by the patentee, can cost less than embankments of earth (in general the cheapest mode known of raising an elevated surface), we cannot in any respect credit, and can still less give faith to the advantage of making railways of this kind ten feet high above the level of the earth, advocated by some of his friends. We have further to remark, that loads carried as designed on this railway will, from their pendulous arrangement, be extremely liable to be knocked against the posts in high winds, to the great damage of the goods carried, as well as to the obstruction of their conveyance, which, in case of a storm, blowing across the rail, may be sometimes so great as to render the railway totally impassable

for the time of its duration.

The injury from unequal loads at the two sides of the carriages, we do not think would be found so slight as asserted by the patentee, who states, that all acquainted with geometry must be of his opinion on this point. Now, in the first place, it remains with him to show what problem of geometry can be brought to bear on the question, and that he has not used the word geometry here in the vulgar sense of equilibrium; and, in the next place, to point out how he prevents the danger incurred by the oblique position of the wheels, which this must occasion, of the carriage being entirely dismounted. The rods which connect the loads with the axles, being jointed to them so as be at right angles to them in all their oscillations (which, we suppose, is what is meant by their being inflexible),

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though it will, when the centre of gravity of the load is placed below the rail, keep them from tumbling off directly, yet will not prevent the risk of the accident mentioned, while it will increase that of their being knocked against the posts.

In conclusion, were we obliged to decide on the question in the present stage of this experiment, which, however, we do not wish to do, we would say that the plan of single railways them constructed at Cheshunt, as they should be confined to that species of would be much too costly if formed of iron, for the reasons before stated. The great defect of the wooden framing would be its want of durability, cularly in the posts, which would be and the expense of its repairs, partiextremely liable to rot at the level of the ground; for which, in order to show that we have no ill will to the plan, from being able to see its defects, we will point out a remedy which will make them more durable and facilitate the repairs-which is, to have square cast iron sockets, two or three feet long, placed so as to occupy this portion of them, let down firmly, for half their length, on the lower part of the posts, secured in the earth as before described, and the other half forming a receptacle for the bottom of the upper portion, which should be formed so as to project a little beyond it at every side, to throw off the rain; and in order that the fitting between the wood and the iron socket might be more perfectly tight, the wood in this part should be previously impressed by screws-a method already practised to great benefit in the preparation of staves for casks; to facilitate which process we have advised the sockets to be made square instead of cylindricala form which, in other respects, might at first appear more advisable.

Repertory of Patent Inventions.

SINGLE-WHEEL CLOCK.

SIR,-Having seen, in your valuable work (page 319, vol. III.), an account of a clock with one wheel, by B. P. C. No. 10, Wolcot-place, Lambeth, I immediately set to work, and made one according to his direction; but when finished, I was disappointed to find it did not answer. The clock, when wound up, unwound itself in two

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prevent its rapid descent. Length of the line.. Spindle....

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.......4 feet.

.4 inches. .7 inches.

I should feel very much obliged if B. P. C., through the medium of your valuable publication, would give us the measurement of his clock.

minutes: we could not, by any weight, in diverging lines; but as the momentum of such minute particles is very inconsiderable, this diverging ..1 foot 1 inch. tendency is soon overcome by the mutual attraction of the particles, and the stream thus gradually diminishes in diameter until it reaches the earth. Now, Mr. W. considers that the tube, when applied to the aperture, draws, by its capillary attraction, a portion of the stream towards its internal upper surface, and passes it along that surface until it reaches the extremity; peventing, by this means, the stream from assuming its natural converging conical form, and producing a sort of vacuum in the stream, which the water from the vessel immediately rushes to supply.

I am, Sir,

Your obedient servant,
A SUBSCRIBER AND JOURNEYMAN
CARPENTER.

Royston, July 15th, 1825.

HYDROSTATICS-SINGULAR FACT. SIR, Mr. N. Webster has recently, in several parts of Cornwall, delivered courses of very useful lectures on Experimental Philosophy. During the course which he delivered at this place, he showed us the following experiment :-A cylindrical vessel full of water was placed on the table; through an aperture in the side of it, a certain quantity of the fluid was discharged in 24 seconds. A straight tube was then attached to the aperture, and the same quantity of water flowed through it in 21 seconds; on the straight tube being exchanged for a diverging conical tube, the water passed in 18 seconds. The cause of this effect, Mr. Webster observed, has not yet been explained by philosophers; and the manner in which that gentleman accounts for it is the following:-It is well known, that the figure described by a stream of water, issuing forcibly from an aperture in the side of a vessel, is that of a converging cone; and the reason why the diameter of that part of the stream which is near the orifice is greater than that of any other part of the stream, is, I imagine, owing chiefly to the pressure within the vessel towards the orifice, operating not only in a line in the direction of the axis of the stream, but also in lines proceeding from every direction in the interior of the vessel; thereby giving to the particles of the fluid a tendency, on isauing from the aperture, to fly off

This is the opinion of Mr. W. on the principle by which the effect, now under consideration, is produced: but as it is not at all satisfactory to me, I beg to submit an opinion of my own to the judgment of your scientific readers.

When the water issues from the mere orifice, without any tube affixed, as the lines of pressure towards the aperture proceed from every direction within the vessel, they must, by acting against one anoth~, diminish considerably the effect of the aggregate pressure, and consequently diminish also the quantity of water discharged in a given period; but when the tube is affixed, and the water flows from the end of it, the whole pressure exists nearly in a line with the axis of the stream, and therefore acts in the most advantageous manner to facilitate the discharge of the fluid, without one part of the pressure impeding another part. And if, from the cause I have just mentioned, there be any impediment to the free passage of the water from the vessel into the tube, and a vacuum should thereby exist in the tube, that vacuum would instantly be supplied, by its affording a greater facility to the passage of the water through the orifice. Another circumstance which conduces to the more rapid discharge of the water through the tube, than through the mere orifice, is, I consider, the pressure of the water in the vessel

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