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Some years ago, a very extensive fumigation of the Milbank Penitentiary was conducted under the direction of Dr. Faraday: and so copious was the evolution of chlorine, that, upon looking through a plate of glass inserted in the door of each long gallery, the whole of its atmosphere appeared intensely yellow.

In such extensive fumigations, the operators are often dreadfully annoyed by the accidental inhalation of the gas; and, indeed, as I have before stated, it is most distressing. The remedy already mentioned may be resorted to, or a sponge soaked in weak liquor ammoniæ, may be folded in a handkerchief, and held close to the mouth, whilst operating; the ammonia or volatile alkali neutralizes the chlorine, and prevents its access to the lungs.

Chlorine is a very heavy gas; compared with hydrogen, its specific gravity is as 36 to 1, and compared with air, as 2.500 to 1.000, so that it may be poured from one vessel to another; in making this experiment, and indeed, all others in which it is concerned, remember to guard against inhaling it.

Chlorine was discovered by the celebrated Scheele, and he called it dephlogisticated muriatic acid, that is, muriatic acid deprived of an imaginary combustible principle called phlogiston. The French chemists called it oxymuriatic acid, imagining it to be muriatic acid containing loosely-combined oxygen.

Sir H. Davy examined it with masterly skill, and found that it contained no oxygen : that it could. not be resolved into any simpler form of matter ; that it was not a compound but an element, for which he proposed the name of chlorine, as involving no theoretical notions regarding its nature, but simply implying its yellow colour; and should it at any future time be decomposed, and shown to consist of two or more bodies, still the term chlorine will remain unobjectionable. How different is this precision of nomenclature to that of the French school regarding oxygen!

If you imagine Scheele’s phlogiston to have been hydrogen, you will at once perceive, how near the true clementary nature of chlorine he had arrived, when he called it dephlogisticated muriatic acid.

Now you still more fully see the absurdity of calling oxygen the universal supporter of combustion, for here is chlorine supporting combustion, with an equal, if not a superior energy; and the absurdity of the term, universal acidifying principle, will become fully apparent hereafter; it is slightly so at present, for chlorine and hydrogen produce muriatic acid.

Such is a slight sketch of some of the most popular properties of chlorine, its evolution, its power of supporting combustion, of destroyir. colour, and contagious or infectious matter. All these the chemi well acquainted with, but of the ultimate nature of this singular stance he knows nothing.

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296

THE MATHEMATICAL MISCELLANY. No. I.

CONDUCTED BY PROFESSOR GILL, FLUSHING INSTITUTE, LONG ISLAND.

NEW YORK, 1836. It can never be an object of indifference to Englishmen, to witness the efforts made for the extension of science by their Transatlantic brethren. Those efforts have been in every sense gigantic: but especially in all that relates to the arts of life and civilization. Still, till very recently, America fell far behind ourselves in those fundamental branches of science which must form the real basis of every solid scientific structure, the mathematical. Prior to the publication of Dr. Bowditch's translation of Laplace, and the excellent notes appended to it, the American press could not boast of one single mathematical work comparable to hundreds published in the mother country. The cause is easily explained, and has been pointed out over and over again by American writers,—the slavish prejudice which prevails, amidst all the personal vanity of the Americans, that nothing can be produced in America at all comparable to the works published in London. In the arts of life they felt themselves free, and less shackled by fiscal imposts than the parent-country, and there they put forth all their strength; but in pure science, as well as in literature, they have fallen as far below us as in commercial and manufacturing efforts they have surpassed us. We are not sure, however, that the American publishers do not find it more to their advantage to keep up this delusion, than to use any effort to dispel it: inasmuch as they thus avoid the expense of purchasing “copy,” but find it made ready to their hands in the form of printed books imported from London! No English work of eminence, and adapted to the taste or wants of their own population, issues from the press in this country, which is not, as if by magic, circulated throughout America, and from a dozen American presses simultaneously, in less than three months after the most favoured town reader” has perused it! Happy the publisher who gets a single week the start of his competitors! He makes half a fortune in that single week,-provided the book is one calculated to have a “good run.”

Though we are ready to admit that much of the literature, as well as of the science of America, is inferior in every point to our own, yet it must be obvious that this does not arise from want of good models,- for all that we have, they have too. It arises from the discouragement of American effort, and from this alone. Our advantage may possibly be found in this; but it certainly is not intentionally consulted. American patriotism would dictate a different course; and it is improbable that after the splendid efforts of Washington Irving, Webster, and Cooper, in literature, and of Bowditch in mathematical physics, that great country will look so coldly on the labours of her own children. It is her interest to foster the genius of her own soil; and she cannot be much longer blinded to it.

It is well known to every well-read mathematician, that in this country pure science was cultivated in comparative silence and obscurity, by means of certain periodical works more or less exclusively devoted to them (and especially the Ladies' and Gentlemen's Diaries) whilst in our

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own universities they lay dormant, or were taught as a mere matter of course, studied by hardly any, and considered only as matters of idle curiosity by nearly all. We live in better times: yet few of us are sensible of the great obligations which we are under to those modest and unpretending works for the present spirit of inquiry which is now become so general in respect of pure mathematical science and its innumerable applications. As we were, so America is, at this moment. Bowditch was little known to the general scientific world before his present undertaking: yet, so to speak, Bowditch was the child of Diarian nursing. His efforts were first made in those obscure American periodicals which are, except to perhaps half a dozen persons, unknown in this country, and almost as unremembered in their “ father-land." Knowing this as we do, we cannot look with indifference upon the attempts which are made in that country to establish a superior class of such publications, dependent for their support on native or adopted talent. Were we to recount the names of those who in this country were made mathematicians by the English Diaries, Repositories, Bees, Correspondents, Companions, Receptacles, &c.,—were we to recount the names of Simpson, Landen, Dalby, Burrow, Lawson, Bonnycastle, Crakelt, Saunderson (George), Robertson (Dr. Abram), Wales, White (Thomas), Wildbore, Vince, Brinkley, Maskelyne, Hutton, Harvey, and a hundred others, already passed away,—were we to recount the names of Gregory, Leybourn, Lowry, Ivory, Wallace, Barlow, Davies, Swale, Mason, Young, Woolhouse, and a hundred others amongst the living -we are sure the importance of these publica

, tions would be at once admitted. Can we then but augur well for America from an undertaking like this? Or, still more, from the very superior manner in which this is conducted? Can any one who peruses this single number with attention, fail to be struck with the power of American mind? We think not.

The plan of the work assimilates more with that of Professor Leybourn's Mathematical Repository than with any other type: and we think Professor Gill could scarcely have selected a better model, as to general feature. Should he succeed, even to a partial degree, in effecting by his publication the real good which Mr. Leybourn has done, he will deserve well of his countrymen.

We shall give a brief analysis of this number, and our readers will then see that we may most cordially recommend it to their notice and support, assured that they will find much to compensate them for its cost.

The first article is the investigation of a formula for the longitude when the rhumb is invariable. In this case, the course is the loxodrome, and the expression, for the longitude arrived at is known to be accurately (omitting the spheroidal figure of the earth) x – X, = tan. v log. tany where x and x, are the longitudes of the limits, y y, the polar distances of the same limits, and v the angle of the rhumb; and the formula is well adapted for calculation*. The method has, however, been virtually

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We shall probably have occasion to solution of this problem, as to comparative make some remarks on the various me- facility, in a future number of this magathods which have been proposed for the zine.

anticipated by several European writers, and we may add that it is not the one most in favour amongst us.

The next is an excellent solution of the problem.—“In a given ellipse to inscribe the greatest equilateral triangle.” It is shown that the triangles vary from the least to the greatest continuously; or, in other words, that there is only one maximum and one minimum value of the side; though obviously there must from the symmetrical form of the curve be four different positions in which they may be drawn.

Thirdly, a new discussion of the problem:-“Upon a horizontal plane a rectilineal path is traced, in which p is constrained to move uniformly. This body is connected by an inflexible and inextensible line with another body, m, which is posited in this plane, and which is supposed to have received some primitive impulse in the direction of this plane. It is required to find the nature of the curve described by the body m, and the other circumstances of the motion, abstracting all consideration of friction.” This problem was first considered in connexion with several analogous ones by Clairault in Mém. de l'Acad., 1736, in a discussion with Fontaine and others, who considered the curve to be the Tractory or Equitangential Curve. It has been subsequently discussed by Gergonne, Dubuat, Français, and others, (Ann. des Math. tom. iv.); and by Professor Lowry in Leybourn's Repository, vol. v., as well as in the Ladies' Diary for 1779 by the Rev. Charles Wildbore.

Mr. Gill obtains the equations of motion with great elegance, and differently from anything we have seen. His mode of integrating is similar to that of M. Français. He annexes the discussion of several collateral problems. This paper is on the whole a very instructive one to the young geometer and physicien*.

The fourth and final article, as well as the most elaborate and important one, is a paper on Spherical Geometry. This is a branch of science exclusively English, and of very recent growth in any regular form. It seems to have taken a definite character from the researches of Mr. Davies, concerning the “Nature of the hour-lines on the antique sun-dials,” published in the Edinburgh Transactions, vol. xii.; and has been followed up by two other papers on the general principles and equations which are involved in the fundamental idea. An abstract of it has also been published in the appendices to the Ladies' Diary for 1835–6; and several interesting questions concerning spherical loci have been interspersed through the Diaries and Leybourn's Repository, by Messrs. Davies, Woolhouse, and Rutherford. The abstracts above spoken of seem to have turned Mr. Gill's attention to the subject, and his

processes are, in some cases, material improvements upon those of his predecessor, though, in others, they fall short of them. This article ought not to be passed over by any one who feels interested in this important branch of geometry.

* Some singular discussions took place tercation, the sons of Esculapius appear to at the Bristol meeting of the British As- have compromised this important question sociation, respecting this term. It was by allowing the cultivator of physics to thought very hard that the medical | adopt, after the French non-medical sapractitioner should monopolize the term vans, the title of “ Physicien.” Much physician," and after considerable al- | ado, indeed, about-nothing !

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We feel, however, disposed to take an exception to Mr. Gill's notation. Mr. Davies had employed the Greek* letters to designate spherical co-ordinates, so as to distinguish them completely from the notation of the linear system. Mr. Gill employs, contrary to the analogy which is suggested by the uniform practice of modern writers, the Italic letter. Even in plano, the angle made by the radius vector and the angular origin is written X, 0, or $; but Mr. Gill has employed y to designate the spherical radius vector, and the polar angle. We are at a loss to account for the motives of this change; and as a uniform system of notation is essential to a successful cultivation of any branch of analytical science, we trust that Mr. Gill will yet accede to that which he found in use, except he can show that it violates some of the essential rules of a good notation, and that his own is free from that charge.

We shall conclude, by referring our readers to the remarks on the present state and probable tendency of spherical geometry to be inserted in our next number; and with cordially recommending Professor Gill's labours to the notice of our American as well as our English readers.

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REMARKS ON CRYSTALLIZATION,

BY MR. THOMAS GRIFFITHS.

In the Journal of the Royal Institution, (vol. xiv.,) I inserted a short notice respecting the method “of colouring alum-crystals,” together with a few observations on the best nuclei for them to form on.

I there state, that “ coke with a piece of lead attached to it, in order to make it sink in the solution, is the best substance for a nucleus, or if a smooth solid surface be used, it will be necessary to wind it round with cotton or worsted, otherwise no crystals will adhere to it.”

This fact was afterwards noticed by Dr. Faraday, in his Chemical Manipulation, as follows:-“ Prepare a solution of alum for crystallization by diminution of temperature; hang a thread across it, or leave in it a glass rod with a thread wound round it, and observe the greater tendency to deposition on the one substance than the other.”

Now, I believe, that these are the only two published notices respecting the influence which the mechanical texture of a nucleus has on the deposition of crystals from solutions ; I have been at work a little on the subject from time to time, and more especially, lately, in preparing illustrations for the lectures in the Chemical school of St. Bartholomew's Hospital, and have obtained several results, which, although

The employment of the Greek cha- | only to take the radius vector constant, racters has a perfect analogy with the es- and the polar equation of that locus (or tablished practice of all good writers on those points, when the given locus is the geometry of co-ordinates, and on a line) becomes identical with the spherical physical astronomy. In truth, if the in- equation of the curve (or points of intertersection of any locus, linear or super- section. This notation is therefore in ficial, with a sphere concentric with the perfect keeping with pre-established ones. origin of co-ordinates be sought, we have

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