have been attended with very serious conséquences"-Editorial Remark,

P. 144.

With due submission to this learned editor (whose bad writing might be excused were there any thing to compensate for it), he has helped to disgrace his pages with a great deal of rank nonsense on the subject of the portable gas-lamp; and the sooner he bids adieu to the subject the better. In this very Number, while he talks so gravely of the danger from "the expansive force of thirty atmospheres," He quotes (unconscious, possibly, of its bearing) the overwhelming fact, that Mr. Perkins has just con'structed a steam generator, "" which has been proved to sustain the enormous and incredible pressure of

TWENTY THOUSAND POUNDS UPON EVERY INCH OF ITS SURFACE"!!! p. 148.

MECHANICS'

INSTITUTION AT

NEWCASTLE-UPON-TYNE. At a Public Meeting held on the 26th ult. it was resolved to establish, under the title of "The Literary, Scientific, and Mechanical Institution of Newcastle-upon-Tyne," an in'stitution calculated to place a knowledge of the arts and sciences, and of literature in general, "within the reach of the humblest individuals in the community." Mr. George Stephenson, engineer, who contested with Sir Humphrey Davy the honour of having invented the safety lamp, and who has risen to eminence by the ubaided force of his own talents, was called to the chair; and the movers and seconders of the resolutions were (as their worthy chairman once was) mostly all of the operative classescarpenters, masons, printers, &c. The report of the proceedings which we have perused in the Tyne Mercury is altogether extremely gratify ing. The good sense and good feeling which seconded the speeches delivered on the occasion, promise the happiest results. We doubt not that the establishment of the Institution will prove, as one of the speakers predicted, "a new era in the moral history of Newcastle."

May we hope that the name of this

Institution is not irrevocably fixed? A Literary, Scientific, and Mechani cal Institution sounds queerly; the sense in which the word is here used is unusual; and we should like, besides, that the mechanics of Great Britain, acting in brotherly concert, would abide by the simple title of "Mechanics' Institution," as, beyond all others, distinctive and clear,

CUBE ROOT.

London, March 9, 1824. GENTLEMEN ;—I observe in your last Number a few remarks upon the use of logarithms, and on my reply to the question in your förmer Number on the best method of obtaining the cube root of a given number.

I am not much disposed to enter into a controversy with your cotrespondents J. T. and J. Y., being of opinion that in proportion to the investigation of the subject, so will be the preference given to the use of logarithms, over every other method, when expedition is desired, with such a degree of accuracy as will be deemed sufficient by all practical men, and I think I might have ventured to have stated, without much risk of being refuted, that in nine instances out of ten, the twelve-inch sliding rule, which is simply a scale of logarithms, will be found fully sufficient for the common purposes of extracting the squaré and crbe roots of numbers, and that by simple inspection.

It was not my intention to say that no cases occur where more than four or five figures may be required; but this I might have said, that when a greater number of figures are required, they may be obtained by a small additional operation, with the aid of log'arithms, sufficient to satisfy every case of real practice.

Your correspondent inquires where logarithms may be found to twenty figures of natural numbers? I am not able to inform him, nor do I know the real utility of such high numbers. The common tables of Gardener and Hutton are carried to five figures of natu

ral numbers, and are very easily extended to two more, and the logarithms are given to seven figures.

I should be glad to learn what cases of real practice occur, in which the root, or power of any number, to a sufficient degree of accuracy cannot easily be obtained by logarithms?

I can readily admit, that some hypothetical and theoretic calculations may require more than seven figures, and also that there may be an occasional error in the tables; but it is well known that the errors are few, and easily detected by any person acquainted with the subject, by taking the differences between the proposed number and the adjoining numbers.

Your correspondent will possibly admit, that long and complicated calculations, even by common arithmetic, are occasionally liable to

error.

It may be expected that I should explain the reason why I adopted the number 287500 instead of some other numbers: so far as I can now recollect the reason, it was to show, that in matters of real practice, the first four figures are the most essential, and that the remaining two are of but little comparative importance; another reason might be, that of having at the time of writing the paper no other tables at hand but Didot's stereotype pocket-edition: the example given was explanatory of the manner of using the tables, and not as a proof of the number of figures to which the answer could be carried. If Hutton's tables had been at hand, I might possibly have selected the number 288888, the logarithm of which is 6-4607307,

of which is 2.1535769, answering to the number 142:422, the root nearly.

I also beg leave to observe, that any inaccuracies which may have crept into my former or the present paper, may in part be ascribed to their being written in a public and crowded coffee-house..

I am, Gentlemen, yours, &c.
B. BEVAN.

CONTRIBUTION TO THE HISTORY OF PERPETUAL MOTION.

Grange-street, Bermondsey, Feb. 13, 1824. GENTLEMEN; I have often, with no small share of regret, witnessed the attempts of the "visionary" to find out a machine fit to be denominated a "Perpetual Motion," and I am inclined to think that a vast deal of study, expense, and vexation may in future be saved to the ingenious but misled mechanic, by putting him in possession of a knowledge of the labours and bitter disappointments of our ancestors, in their endeavours to get at this "forbidden fruit."

In a treatise by Bishop Wilkins (which I have now before me), entitled "Dædalus on Mechanical Motions," there are several attempts of this kind mentioned, and some very ingenious reasoning on them, and I think that he with great justice applies the appellation which he says some one spoke wittily concerning the philosopher's stone, namely, that it is "casta meretrix" (a chaste wanton), quia multos invitat, neminem admittit" (because she allures many, but gratifies none).

66

One of the attempts mentioned in that work (with the exception of of water being used instead mercury), very nearly resembles that of your correspondent" Philo-Mechanicus" (page 361), and therefore, if it is not trespassing too much on the limits of your very useful Magazine, I will trouble you with the two following designs, and descriptions of them, verbatim, which I think may save some future tyro the trouble of reinventing them. You will, no doubt, perceive that it is the last which I refer to as so much like that of "Philo-Mechanicus."

1st. "But amongst all these kind of inventions, that is most likely wherein a loadstone is so disposed, that it shall draw unto it, on an inclined plane, a bullet of steel, which steel, as it ascends near the loadstone, may be so contrived as to fall down through some hole in the plane, and so to return unto the

tages attendant... Apon logarithmic operations, such as the probability of errors in the tables, a thing of no ancommon occurrence, even in our best tables; all which circumstances tend to show that logarithms should be used only when other methods of computation do not present them selves, or when, if they do, they require much greater labour and trouble.

Within these last few years, several new methods have been proposed for extracting the cube-root; some of your readers may be able to decide upon the merits of these several methods, and by making public that which is most easy and expeditious, through your Magazine, will, I dare say, do a service to many of its readers, and particularly so to

Your obedient servant,

J. T.

GENTLEMEN';- Your very respectable correspondent Mr. B. Bevan, has sent you a method of simplifying the extraction of the cube-root by logarithms, as an answer to J. T. It is all very good and very correct in its results, provided we can find tables of logarithms, whose natural numbers extend to twenty or thirty places; but I have never seen tables extending to more than four places. He has very sagaciously, but not very mathematically (inadvertently no doubt) taken the number 2875, with two ciphers annexed; for he well knew where to find the logarithm of 2875, which, with its annexed ciphers, would make its index equal to 5; but it often happens that we have a quantity which may extend to a far greater length than six places to find the root of; and unless we have tables whose natural numbers extend to such a length, we shall find that the

J. Y.

Mr. Picket will perceive, that in his answer on this subject he was anticipated by Mr. Bevan: his offer to teach J. T. gratis in logarithms, "if not already acquainted with them," at his house, Brook-street, Ratcliff, is liberal, and not the less deserving of thanks; that J. T. seems, from the reply which we now publish, to be an inquirer of a very different stamp.

ENGLISH METHOD OF CASTING MEDALLIONS.

230 Brownlow-street, Feb. 25, 1824. GENTLEMEN;-A subscriber of Lincoln's-inn wishes to know the French method of casting medallions. Although I am ignorant of the method adopted by the French, yet I am inclined to think the English mode is quite as good; as I have both seen cast, and have myself cast medallions which I have considered in every respect equal to those cast in France. The

left will make us play a very foolish game, and will by no means be sufficiently near for practical purposes. Your numerous readers who may be acquainted with the tables of logarithms, but ignorant of the principles upon which they are constructed, may apt to

taking the mould in plaster of Paris, the fineness of the texture of which enables a mould to be drawn off in the greatest state of perfection, need scarcely be remarked that the mould should have the moisture thoroughly eradicated prior to its being cast in. Your correspondent is perfect ly right respecting the nature of the

metal. It usually consists of one-fifth antimony, and the remainder lead (it should be tea-lead). I have at present by me a small cast (the bust of -Shakspeare) which I should be happy to show your correspondent.

a

I am yours respectfully,

AN OLD CASTER.

METHOD. OF MAKING ALUM,,
BASKETS.

GENTLEMEN;-As some of your correspondents might wish to employ a leisure hour in contributing to the amusement of the ladies, I beg to offer a method of making alum baskets. Form a small basket, about the size of the hand, of iron, or split wire, or split. willow; then take some cotton, such as ladies use for running into flounces; untwist it, and wind it round every limb of the basket. Boil a pound of alum in quart of water, or in that proportion; let it boil well, stirring it all the time; when completely dissolved, pour it into a deep pan, or other convenient vessel, and suspend the basket in it to a good depth, so as that no part shall touch; let it remain perfectly at rest for twenty or twenty-four hours, and when you take it out, the alum will be found very prettily crystalized all over the basket, making a very neat chimney ornament to hold flowers, &c. The alum may be coloured pink, purple, or yellow, by boiling Brazil logwood or French berries with it. Sometimes, however, the crystals will be too large, and the basket not uniformly covered; therefore, if any of your correspondents know how to prevent this, or any better method of proceeding, they will, by communicating it, very much oblige,

Gentlemen, yours, &c. &c.

VECTIS.

HOW TO POLISH PEBBLES, CORNELIANS, &c.

Rub the pebble to a surface upon thick piece of lead, with emery, mixed with sweet oil or water; first with coarser, then with finer, as the Furface improves next with the different Scotch grits, proceeding as with the emeries, until all the scratches left by the emerics disap

款

pear; this being done, provide yourself with a block of wood, well planed on one side, intended to be the uppermost, about 14 or 15 inches by 4 or 5, and as many thick; cover it with a thick coarse flannel, called fearnought; on this fasten a piece of coarse linen cloth, double at least, and upon it rub the stone, prepared for polishing, with tripoli, finely powdered, and mixed with either sweetoil or water; then rub it on soft washleather, and afterwards on the thick part of the hand, which process will bring the polish to its highest pitch.

1

TO MAKE BRUNSWICK GREEN.

The Brunswick green colour used in paper-hangings, and other coarse kinds of painting in water-colours, is prepared in any close vessel of wood or earthenware, filled half full of copper filings or clippings, on which is poured a saturated solution of sal-ammoniac, which together will form the muriate of copper, the ammonia being at the same time disengaged. In a few weeks almost the whole of the copper may be converted into oxide: this being well washed, and slowly dried in the shade, is pare Brunswick Green. Three parts of muriate of ammonia, or sal-ammonia, and two of copper, yield six parts of green.