penetrate into futurity, or trace from their sources to their results, unless in some faint and general outlines, vague (or at least imperfect) comparisons, and uncertain speculations, the events that determine the late of

nations?

"Prudens futuri temporis exitum

con

Caliginosa nocte premit Deus :" To whose wisdom and power, as the Alpha and Omeg" of Existence and of Agency, we must leave what all our varied and most laboured inquiries are impotent to solve: fining ourselves more properly, in the limited sphere of human agency, to what most nearly concerns us, the fulfilment of our responsibility, whether in a public or private capacity. So shall we rear to ourselves, as far as human imperfection will allow, that "murus abeneus," whose mate rials must consist of our thoughts, words, and actions: and so shall we still further-But to return from this digression, which I think cannot well be called impertinent, as all things are more or less connected with the object of it, in proportion perhaps to their different degrees of importance, or of our disposition to refer them to it to return, I say, to Alfieri and his Plays, of which his Antigone is the one which most interested and affected

me.

It deserves, I think, in a much higher degree, the encomium that Pere Brumoy (in his Theatre des Grecs) gives to the same Play of Sophocles, "Dans une pièce où il s'agit simplement d'une dispute sur une Sepulture, tout ce que la Pitiè a de plus tendre, eclate au souverain degre." This, I think, you will find more fully verified in Alfieri's Tragedy, in which the gradual rise of interest is unequalled, except it is in the Oedipus of Sophocles; the deep interest, and the impressive and awful simplicity of which are perhaps unrivalled. In Alfieri's Plays, however, the calls for our admiration and sympathy are nearly as varied and multiplied as the subjects of them. They are, in short, what Dramatic Pieces ought to be, the finest and most interesting moral lessons: and their merit can only be done entire justice to, by the most attentive perusal in the closet, and the most perfect subsequent representation on the stage. The first we have in our power; the second is difficult (to say the least) to

meet with anywhere. Not to trespass further on your time and patience, by dwelling on a subject on which praise can hardly be exhausted, and having no motive for this Address to you but those first mentioned, being personally unknown to you, and, from my situation and habits of life, likely to remain so; I will contrast the retired obscurity of that life with the conspicuous and useful activity of yours, by signing myself, with all due respect and regard, Yours, &c. OTIOSUS.

Mr. URBAN,

MIL

Jan. 1. WILLER'S Gardener's Dictionary, when completed in folio, and sanctioned by public favour, was followed, at no great distance of time, by an abridgement, from the Author himself, in three handsome volumes octavo. How many editions of this might be printed, I am not fully informed. The Edition in my eye is dated 1753. The first Edition of the folio appeared in 1731: but I fancy it had seen more Editions before the Abridgement was made.

I am one of those who, not finding it convenient to go to the expence of the great Edition, completed in 1807 by Professor Martyn, have anxiously wished to see a good and judicious Abridgement of the work as it now stands. It could not perhaps be expected that the Professor, who had gone through the Herculean labour of republishing the folio, would choose to employ himself immediately in the task of abridging. But many competent persons might be found, and the work might as yet have the advantage of revision at least by the eye of the very worthy and learned Professor. I am persuaded that the number is not small of those who would be heartily glad of such a publication. The number could not fail to be considerable, in the present flourishing state of Botany and Horticulture.

It may be that such a work is actually preparing; if so, it will be gratifying to those engaged in it, to know that the work is so much desired. If it has not been thought of, I hope that this suggestion, thus made publc by the wide circulation of Mr. Urban's Magazine, may lead some spirited publisher to undertake it in a judicious manner.

As

YOUR Mathematical Readers (and

Y doubtless you have such) will infallibly be pleased with the following discussion of two different methods suggested for the Rectification of the Hyperbola. The one proposes to effect it by means of two Ellipses; the other shews that it may be better done by an appropriate Theorem. The former is Mr. Woodhouse, then Tutor at Caius College, Cambridge; the latter, Mr. Hellins, Vicar of Potters-Pury in Northamptonshire. The discussion refers to two Papers, published at different times in the Philosophical Transactions; that of Mr. Woodhouse, at Art. X. p. 219, in the Volume for 1804: that of Mr. Hellins, at Art. VI. p. 110, in the Volume for 1811. It was written originally for a respectable Journal, but by accident deferred, and finally prevented from appearing there. But considering it as a question interesting and important to Mathematicians, I am induced to forward it to you.

R.

N. B. It is written by a very emineut Mathematician and Professor. PHILOSOPHICAL TRANSACTIONS FOR

THE YEAR 1811. PART I. Art. VI. On the Rectification of the Hyperbola by means of two Ellipses, proving that Method to be circuitous, and such as requires much more Calculation than is requisite by an appropriate Theorem; in which Process a new Theorem for the Rectification of that

Curve is discovered.

The Rectification of the Ellipsis, and of the Hyperbola, are problems of the same class; and, by a judicious application of appropriate theorems, may be solved with equal facility. Yet, since the discovery that the latter of these problems might be solved by means of the former, that method of solving it has been considered as the best by several eminent mathematicians. The Rectification of the

Ellipsis is the main subject of Art. X. in the Philosophical Transactions for 1804; in which Paper Mr. Woodhouse, the writer of it, has applied the Rectification of the Ellipsis to the Rectification of the Hyperbola, and to the solution of a problem in Physical Astronomy.

It must be evident to every intelligent Reader, and appears also from Mr. Woodhouse's own references, that the greater part of the matter contained in his Paper was taken from other books, and no small part of it from French books, some of which were by no means easy to be procured, especially in time of War.

So scarce were the foreign books required, that two years elapsed before they could be procured. In that interval, however, and even to the present time, I have not heard of any correction which this Paper has received from its Author. But several of its errors have been pointed out in different periodical publications; and a few of them are noticed by the second writer, Mr. Hellios. A few brief remarks on Art. X. of the Philosophical Transactions for 1804 shall therefore suffice, with respect to that part of the subject.

The differential notation of Leibnitz, which is used throughout this Paper, instead of the fluxional notation of Newton, displays such a partiality for foreigners, and so much disrespect to the great inventor of Fluxions, as could not be expected from any Englishman, and parti cularly from a Member of the Uni-' versity of Cambridge. The new notation also of the co-efficients of a binomial quantity raised to a given power, proposed by Mr. Woodhouse (p. 227) to be used "for the sake of conciseness," is rather surprizing s since the Newtonian method of denoting such co-efficients by the letters A, B, C, &c. is both more simple and more concise.

The