Besides, we do not perceive how the cheapness of the commodity, on which a note is drawn, operates like a piece of machinery which abridges labour. Our experience of the power of paper in supplying the want of gold has taught us a valuable lesson: but there is imminent danger in placing too much confidence in ir, or in carrying this practice to excess.

ART. V. A Dissertation on the Construction and Properties of Arches. By G. Atwood, Esq. F. R. S. 4to. PP. 51. and 7 Plates.

7s. 6d. Egerton. 1801.

THE

HE proposal for constructing a magnificent iron-bridge of one arch over the Thames having excited much interest and discussion, and no specific plan of construction having been adopted, it was natural to suppose that ingenious and scientific men would direct their attention to that subject. Dr. Hutton has already presented the fruit of his researches to the public; and in his investigations, he has argued on the principle, adopted also by Emerson, according to which an arch is supposed to consist of uniform compacted materials, and to possess equal strength when on each point of it there is a ver tical pressure, sufficient to keep the arch in equilibrio. In this theory, all that is essentially required to be known is included in the determination of these two propositions: 1. from the intrados, or inner boundary of the arch, to determine the extrados, or outer boundary; and 2. from the extrados, to determine the intrados so that the vertical pressure on each point of the arch shall keep it in equilibrio:which latter is the most important, since the cuter boundary, along which the road runs, must always be a right line, or nearly so.

The author of the present treatise has considered the subject under another point of view, and supposes the bridge to be composed of parts having the form of wedges: consequently, the properties of the arch are made to depend on those of the wedge. Two principal problems are discussed by Mr. Atwood. In the first, it is proposed to adjust the weights of the section of the arch, to the angles contained by the sides of the section in the second, to adjust the angles made by the sides of the wedges to the weights of the wedges, supposed to be given quantities. These problems are solved geometrically, with great perspicuity and elegance; and rules are investigated for settling the equilibrium of arches, conformably to each of the two conditions above mentioned.

Several curious consequences follow from the result of Mr. A.'s investigations; first, that, if the materials of which an arch is constructed were perfectly hard and rigid, so as not to

be

be liable to the smallest change in their form, and the abutments were immoveably fixed, an arch, when the sections have been adjusted, although but little deviating from a right line, would be equally secure, in respect to equilibrium, with a semicircular, or any other arch;'-and, secondly, (within which consequence the former is in fact included,) that the curve line, which passes through the bases, may be of any form without affecting the equilibrium established on the supposition that the arch is formed of wedges.-Here is to be noted a remarkable difference between the results obtained by Dr. Hutton and by Mr. Atwood. According to the theory and deductions. of the former, if the exterior curve and superincumbent weight be given, then the interior curve is a determinate curve: but, according to the theory and deductions of Mr. A. whatever be the exterior curve and superincumbent weights, the inte rior curve needs not be of this nor of that form, but may be varied by varying the angles of the wedges that compose the arch. It is not surprising, however, (for it might indeed have been predicted,) that the two resu ts are very dissimilar, because the theories to which they belong are widely different. In one, the parts of the arch are supposed to be so compacted by the means of cement*, that the arch is in the same state as if composed of an uniform and equally coherent sub. stance; and, in this case, it is the vertical pressure or weight that is every where to be considered, in order to answer the conditions of equilibration. In Mr. Atwood's theory, on the contrary, the parts of the arch do not cohere by means of cement, but are joined the one to the other by the balancing powers of pressure downwards, and of resistance.

In practice, the choice of the theory which is to be adopted must depend partly, it should seem, on the size and hardness of the materials of which the arch is to be composed. If, for instance, it be made of bricks cemented with mortar, then Dr. Hutton's theory seems most proper to be adopted: but Mr, Atwood's appears to be the true theory when an arch is made of large stone wedges, put together with the intervention of scarcely any cement.

Admitting Mr. Atwood's theory, however, we meet with a practical difficulty which we think it is not easy to surmount,

* Emerson, however, (p. 148. Miscellanies,) intends his reason. ing to apply to an arch formed of parts and not cohering: for he bays, "here it is supposed that the stones have no cohesion with one another, but are entirely sustained by the figure of the arch," &c.— On this subject we would speak with caution: but, if we be right in certain opinions not yet matured, Mr. Atwood's and Emerson's principle, if applied under like circumstances, will lead to the same con clusions.

According to that system, if we assume the curve of the roadway to be horizontal, or nearly so,-and the weights of the sections of the arch, together with the weights of the wall superincumbent on the sections, to be given quantities,-then the magnitudes of the angles contained by the sides of the sections may be determined. Now, here, the weights of the wall superincumbent on the sections are supposed to be incorporated (if we may use such an expression) with the weights of the sections themselves: but, in practice, the difficulty will be to dispose and apply the weight of the wall on the section so that the effect should be the same as if that weight really existed in the section by its density being adequately increased. In the mathematical solution, is not the weight of the wall superincumbent supposed to be applied at the centre of Gravity; and what is to be the form of the upper part of the section or wedge, in order that the effect may be nearly the same as if the weight were applied to the centre of Gravity? Of this objection we find no satisfactory solution in the treatise before us: yet the question must have occurred to the author; and he seems to touch on it, in the following passage of his preface:

In the case when the arch is designed to support an horizontal plane or road, on which heavy weights are to be sustained, the intermediate space between the arch and the horizontal road way, ought to be filled up in such a manner, as not only to afford the support required, but also to add to the strength and security of the entire fabric. If this should be effected by columns erected on the arch, and acting on the several sections by their weight in a direction perpendicular to the horizon, rules are given in the following pages for establishing the equilibrium by adjusting the angles of the sections to their several weights, including the weights of the columns superincumbent, so that the pressure on the sides of each section may be a counterpoise to its weight, taking into account the place it oc cupies in the arch. But in structures of this description, the columns of masonry which are erected upon the arches of a bridge, as a support to the road way, cannot be expected to act on the sections of an arch according to the exact proportions required, which are assumed as data in the geometrical propositions, for determining the equilibration, as these proportions would probably be altered either by the differences of specific gravity which may occasionally be found in the materials used, or by differences in the cohesive force, which would prevent the columns from settling and pressing on the several parts of the arch with their full weights, such as the theory requires. Perpendicular columns of iron would not be liable to this objection: by adopting supports of this description, the weights of the columns, added to the weight of the road, would press on the interior arch, to be sustained in equilibrio, by adjusting the angles of the sections to the superincumbent weight, according to the rules determined in the

pages

pages which follow. But perhaps the space between the interior arch and the road might be more effectually filled up, by other arches terminated by circular arcs, drawn from centres situated in the vertical line which bisects the entire arch, so as to become united in the highest or middle wedge. The sections of these arches may be adjusted, by the rules here given, so as to become distinct arches of equilibration, which, when united, will constitute a single arch of equilibration, similar in form to that which is expressed in the plan of an iron bridge, of one arch, which has been proposed to be erected over the river Thames, as is represented in the engraving inserted in the Third Report of the Committee of the House of Commons, for the farther Improvement of the Port of London.'

We do not insist on the validity of the above objection, because our practical knowlege is not of great extent; perhaps the difficulty may be easily removed:- we speak with diffidence on this head,

The present disquisition deserves notice for its perspicuity and originality. With regard to the former point, any one who moderately understands plain geometry and statics may soon, and easily, make himself acquainted with its contents: with respect to its novelty, if any author has preceded Mr. A. in his view of the subject, it is unknown to us; and at present, therefore, we consider him as having an exclusive claim to whatever is clearly conceived, or logically deduced, or ingeniously suggested, in this Dissertation.

ART. VI. The Miscellaneous Works of Oliver Goldsmith, M. B. A New Edition. To which is prefixed some Account of his Life and Writings. 8vo. 4 Vois. 11. 16s. Boards. Johnson, &c,

1801.

WE

E believe that the present is the first complete edition of Dr. Goldsmith's Miscellaneous Works that has been given to the public; and we think that the scattered produc tions of very few modern writers, of this country, better merited preservation, and the benefits of editorial improvement : since Dr. G., to speak in the words of the preface, deserves by the peculiar graces of his style (both in prose and rhyme) to be esteemed as a classic in our language. With any account of these productions we shall not now detain our readers, because on former occasions they came in review before us: but we must observe that the collection of essays and prefaces here introduced is very numerous, and presents to our view several pieces which we did not before know to have proceeded from the pen of this writer. Of their authenticity, however, we by no

* Designed by Messrs. Telford and Douglass.'
9

means

means intend to express a doubt, since we think that they bear internal marks of being genuine; and we are aware that, in addition to his acknowleged performances, this author inserted several of his productions in the periodical works of the time. We must now confine our attention to the account of the life; which, according to the editor, is composed from the information of persons, who were intimate with the Poet at an early period, and who were honoured with a continuance of his friendship till the time when the world was deprived of this fascinating writer. Their names, were the editor at liberty to mention them, would immediately dispel all doubts as to the authenticity of the memoirs, and reflect distinguished credit on the publication.'

This biographical sketch, for it certainly does not deserve the character of a finished performance, is written with plainness and simplicity; and it introduces to our notice several curious particulars of which we were ignorant, though far from being unacquainted with the subject of them.—" The life of a scholar," Dr. Goldsmith had himself observed in his account of Parnell," seldom abounds with adventures;" his own life, however, was in opposition to the remark, since the events of it were varicus and checquered.

Of Dr. G.'s early life and character, and of some remarkable adventures at school and at college, an entertaining narrative was furnished by his eldest sister, Catharine, wife of Daniel Hodson, Esq. from which we shall make a considerable extract; because the anecdotes which it contains are new and amusing, and prove that the author, at an early period, was the same variable and eccentric being which in more advanced life he was universally known to be:

The Rev. Charles Goldsmith is allowed by all that knew him, to have been faithfully represented by his son in the character of the Village Preacher in his poem. He had seven children, viz. five sons and two daughters. Of his eldest son the Rev. Henry Gold, smith, to whom his brother dedicated his Traveller, their father had formed the most sanguine hopes, as he had distinguished himself both at school and at college, but he unfortunately married at the early age of nineteen; which confined him to a curacy, and prevented his rising to preferment in the church.

• Oliver was his second son and born very unexpectedly after an interval of seven years from the birth of the former child, and the liberal education which their father was then bestowing on his eldest son bearing hard upon his small income, he could only propose to bring up Öliver to some mercantile employment.

With this view he was instructed in reading, writing, and arithmetic, by a school-master in his father's village, who had been a quarter-master in the army in Queen Anne's wars, in that detach

ment