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OBSERVATIONS THE RE-BUILDING ' LONDON BRIDGE,
MSICK FOR THE 5EW BRUME hi. EVA 110 N - ^ i nter n : . mm TjTffSmp Wf: P |'4II ”iHti!liian!|l »IHIlj| Hm;:;nh":::::: iilH Joh/i Saward rci? 1824. R Smart sculp. ■SiXsSiSSMieiMis^s^iS^ fjftat.wt* vf-jBgg-- WSM '■^r r g j^ r JipupM 1 Published, bv Joshua Taylor lotufat.
OBSERVATIONS ON THE RE-BUILDING LONDON BRIDGE DEMONSTRATING THE PRACTICABILITY OF EXECUTING THAT WORK IN THREE FLAT ELLIPTICAL ARCHES OF STONE, EACH TWO HUNDRED AND THIRTY FEET SPAN : AN EXAMINATION OF THE ARCH OF EQUILIBRIUM PROPOSED BY THE LATE DR. HUTTON: AN INVESTIGATION OP A NEW METHOD FOR FORMING AN ARCH OF THAT DESCRIPTION. Ponderibus librata suis.—O vid. ILLUSTRATED «Y SEVEN PLATES AND OTHER FIGURES. By JOHN SEAWARD, Civil Engineer. LONDON: PRINTED FOR J. TAYLOR, ARCHITECTURAL LIBRARY, 59 , HIGH HOLBORN. m: ^ 1824 . • •
r 0N COLLEGE LIBRARY. J SOLD BY ORDER OP TBH president and governors 193 S, PRINTED BY RICHARD TAYLOR, SHOE-LANE.
PREFACE. It is generally acknowledged, that the constructing of a commodious bridge over a wide impetuous river is one of the noblest efforts of human genius. In no country that has made any advances in civilization has the art of bridge-building been wholly neglected ; on the contrary, it has every where been esteemed for its great utility, and has engaged the attentive care of enlightened men. In former ages, those persons who were engaged in constructing these important works w'ere honoured with distinguished favour; and the noble bridges which adorn this great metropolis are substantial proofs that the art has not in the present age lost much of its ancient reputation. During the last hundred years the most astonishing advances have been made in the art of
VI bridge-building; but, like other arts, it appears fated never to arrive at absolute perfection, and there is still an ample field for improvement: it may therefore be reasonably presumed, that every effort made for its advancement will meet with a favourable reception. The defects of this art may be attributed partly to the inattention of many bridge-builders to scientific principles ; and partly to the unsatisfactory methods pointed out by mathematicians : the latter relying upon abstract speculations only, and being but little acquainted with the operative parts of the art, it is no wonder that their theorems, though in themselves very beautiful, should be for the most part of but little utility to the practical engineer. The writer of these pages begs to acquaint the reader, that, having been employed, from his youth, in different departments of building and practical engineering ; and having had opportunities of acquiring an intimate knowledge of the practical parts of bridge-building in particular, which he has endeavoured to improve by much study and reflection, he presumes that he is enabled to offer to persons engaged in similar pursuits, some observations on the construction of bridges not undeserving their consideration; by
vii which he hopes to remove many of those difficulties which have hitherto so much impeded the advancement of this noble art, and which prevent that uniformity in theory and practice, which is so essential in this important branch of civil engineering. The present time appears to be peculiarly suited for publishing his ideas on this interesting subject, when the attention of the scientific world is so strongly excited by the building of a New London Bridge. Indeed, it may be proper to acquaint the reader, that the invitation given by the Corporation of the City of London to engineers, to furnish designs for that work, has principally induced the writer to compose and publish the following pages at this time; and he presumes that the plan which he now offers for the proposed structure, though somewhat late, may yet be serviceable to persons engaged in that or in similar works. The building a bridge over so noble a river as the Thames, which is to be designated after the first city of the British empire, is no common or trivial event: and it is earnestly hoped that the structure may prove in every respect worthy the dignity of its name.
viii To the New London Bridge foreigners will resort, as to an unerring standard, by which to judge of the state of intellectual improvement in the English people in this enlightened age. The author of the following pages, strongly impressed with this important consideration, contemplates the erection of a bridge, which, uniting simplicity with dignity of design and boldness of execution, shall not be surpassed b \ 7 any work of the kind hitherto attempted : how far the plan here offered is calculated to accomplish this great object, must be left to the judgement of the reader. The principal feature of the proposed design is, that the bridge be built of stone, and that it consist of three flat elliptical arches only, each arch of two hundred and thirty feet span. The proposal to build a bridge of stone arches, of a span so far exceeding any existing, will no doubt procure for the author from some persons the appellation of “visionary projector!” But he trusts that the candid and scientific inquirer will not indulge in prejudices hastily drawn, but will calmly weigh the reasonings contained in the subsequent pages; wherein, he flatters himself, he has submitted what will prove equally to the mathematician and to the practical engineer a satis-
IX factory demonstration of the practicability? the safety, and the propriety of the design. In the construction of great public works, it is to be presumed that a superior dignity and boldness will at all times, under a parity of advantages, be an adequate reason for preferring one design to another: it may therefore be inferred, that a bridge of three magnificent arches would certainly be preferred to one of five smaller arches, taking for granted it can be satisfactorily shown, thfit the former will possess equal stability, and that its execution will not be attended by greater risk or expense. But, independent of such considerations, the writer conceives there is a local propriety in a bridge of three arches, which is, the proximity of the Southwark bridge, consisting of three arches only : for it is not to be disputed, that whenever the obstruction of the present London Bridge is removed, the current of water will be prodigiously augmented both on the flood and ebb tides: in the narrowest part of the river, therefore, with two bridges so near each other, and with an increased velocity of the water, it requires serious consideration, whether it will be a prudent or desirable arrangement to have the water-ways of one bridge
directly opposed to the piers of the other, which will unavoidably be the case if the new London Bridge be built of five arches. But waving all further considerations of this question ; it will be desirable to state a few other particulars relating to the proposed design. It may, however, be proper to premise that the subject of bridge-building, in its various details, has engaged the thoughts and pens of some of the most intelligent men of this and other countries; of whom no one has acquired more deserved celebrity than our much respected countryman, the late Doctor Hutton. The Doctor many years since published a theorem for constructing what is technically called the arch of equilibrium. This theorem has, for its simplicity, perspicuity, and conciseness, been universally admired; and all attempts to improve upon it have hitherto failed :—and when it is also known, that the Corporation of the City of London, and other distinguished bodies, deemed it prudent to consult the Doctor upon various points relative to the construction of bridges, the reader will easily conceive how very important his opinions, on this difficult subject, have always been esteemed by enlightened men.
XI Yet, greatly as the writer venerates the Doctor for his mathematical attainments, he is not deterred from asserting, that this celebrated theorem, as elucidated by Doctor Hutton, is not of any real practical utility to the engineer or bridge- builder ; not that he would be understood to controvert the truth of the theorem ; on the contrary, no one can feel more firmly satisfied of its mathematical accuracy, though in its practical application it fails of being in any way serviceable. However, the Author takes this opportunity of stating that his design for the new London Bridge, elucidated in the following pages, is nevertheless founded upon this very theorem, although upon principles quite different from those adopted by the learned inventor. From this the reader will naturally infer, that the arch proposed for the new London Bridge is that which is appropriately termed the “ Arch of Equilibrium for, indeed, no other arch should ever be employed in constructing any work of magr nitude : all those formed on the common plan are known to be wrong in principle, and practically defective in strength; and it is to be hoped, that they will ere long be entirely discarded, and none employed but such as are constructed on true scientific principles.
xii A century hence, it may perhaps appear strange that in this enlightened age the arch of equilibrium should have required an advocate to recommend it to the favour of the bridge-builder ; the fact, however, will afford an easy explanation of the reason why our cotemporaries are so timid that they rarely attempt to construct an arch of stone beyond one hundred and thirty feet span: but when the true principles of the arch become generally known and attended to, there is no question that arches of two and three hundred feet span will then be undertaken with as much confidence, as is at present shown in executing an arch of half that span. The following work is divided into nine chapters. In the first chapter the writer has entered into a brief examination of those curves which appear to be most suitable for the arches of a bridge. The second chapter relates to the strength of arches generally ; and it contains the examination of the arch of equilibrium proposed by the late Dr. Hutton. The third chapter contains the investigation of a theorem for an arch of equilibrium on a new principle. The fourth chapter contains another theorem for an arch of equilibrium ; with its application to the forming an arch of 230 feet span. The subject of the fifth chapter is a popu-
Xlll lar illustration of the arch. The sixth chapter treats of the stability of an arch. The seventh chapter treats of the depth of the voussoirs. The eighth chapter of the abutment and bearing piers : and the ninth and last chapter contains observations upon the decorative parts of a bridge, the expense, and some concluding remarks. The reader is informed, that in several of the following theorems the writer has been under the necessity of employing the method of infinite series ; he would gladly have avoided doing so, but there was no choice, as the cases did not admit of any other kind of solution : and the summation of these series has been performed by the actual addition of their leading terms ; to this mode necessity compelled him to resort, as the more accurate modes of summation would not succeed, because, from the complex nature of the equations, it was impossible to discover the law of continuation of the co-efficients. The elegant rules given in Stirling’s Methodus Differentialis are wholly inapplicable to the purpose ; care, however, has been taken to collect, in every case, the value of a sufficient number of the leading terms, so that the results should be given accurately to three places of decimals, which it is presumed is quite sufficient for all practical purposes.
XIV Many of the computations are extremely tedious and operose; consequently some few errors may exist, notwithstanding all the care that has been taken : if any such should be discovered by the reader, his kind indulgence is therefore earnestly entreated. Walcot Place, Lambeth.
CON T E N T S. CHAPTER I. Page Of the most suitable Curves for forming the Arches of a Bridge 1 CHAPTER II. Of the Construction of the Arches of a Bridge. 11 CHAPTER III. To construct an Arch of Equilibrium, having a straight horizontal Boundary Line, with any Curve for the Intrados, and any required Depth of Voussoir. 28 CHAPTER IV. Of the forming of an Arch of Equilibrium with hollow Spandrels . 47 CHAPTER V. Further Illustrations of the Arch of Equilibrium. 71 CHAPTER VI. Of the Stability of an Arch. 91 CHAPTER VII. Of the Depth of the Voussoirs. 101 CHAPTER VIII. Of the Abutment and Bearing Piers . 118 CHAPTER IX. Of the Embellishments suitable to Bridges: of the Expense of their Construction: with a few concluding Remark?. 133
ERRATA. Page 15, line 26, for figures 9 and 10, read figures 8 and 9. 25, line 20, for passing, read pressing. 86, last line, for L/mP, readlhnV* _ 119, line 17, for zxl + r*§, read xx I + r*|£* 122, line 11, for Tg, read Eg.
OBSERVATIONS, fyc. CHAPTER I. Of the most suitable Curves for forming the Arches of a Bridge. In designing a bridge of any considerable magnitude, nothing demands greater care and circumspection on the part of the engineer than to determine with propriety the span, elevation and curvature of the arches. In all erections of this kind, the arches form by far the most prominent feature of the whole work ; and, unless they be contrived with due regard to beauty of form, the bridge itself, instead of being distinguished for its symmetry, will be condemned as a monument of bad taste. Beauty, however, is not the only consideration that should be attended to, for it must be combined with a certain conveniency of form, so that the arches may afford the most easy passage for the waters, and at the same time present the fewest obstacles to the purposes of a tree and secure navigation. There are three curves which appear to combine in B
2 an essential manner these advantages of beauty and con- veniency of form, and which, from their decided superiority in this respect over all other curves, appear to be almost exclusively adopted for arches by the practical bridge-builder. These are the circular, the elliptical, and the cycloidal curves: which, with their infinite segments, present to our choice an endless variety of arches. For brevity, I propose to confine my observations almost exclusively to the elliptic curve, although what is said of this will apply, with nearly equal propriety, to the circular and cycloidal curves ; for a circle is nothing but an ellipse, whose transverse and conjugate diameters are alike: and the cycloid approaches so very near to a segment of an ellipse, that it does not appear necessary to extend this small tract by any separate notice of it *. * The cycloid is as much admired for its singular beauty of form, as for its remarkable mathematical properties. FIG. 1. f Let ACB be a semi.ellipse; and put a equal AB, the transverse diameter; c equal 2CO, the conjugate diameter; i = Cm,
3 The ellipse, of all curves, is the most particularly deserving of notice, as no other curve can be so advantage abscissa; y — Pm, the ordinate; and p = 314159, equal the area of a circle whose radius is unity. And Jet the segment PCQP, cut off by a line parallel to the transverse diameter, be equal to three times the area of the circle C nmp, whose radius is — ■ And let PQ, the base of the segment, be to the altitude as 3-14159 to 1; that is, 2 y.x ;: 3-14159 : 1, (which are two known properties of the cycloid,) to determine the transverse and conjugate diameters of the ellipse. In the first place we have y = And y x, the fluxion of the segment PC m = -^ x And the area PC m = x FI.' sc c x — x 1 :— But the area PC m is, by hypothesis, equal to three times the semicircle Cmn, whose radius is —; and the area of the said semicircle is — — : therefore 3 Cm 8 8 But Pnt is equal -y = y = fcx — x *; therefore 3C»u - ——- X c x — x\ = segment PC m i consequently x^/cx — x' 1 = z x FI.' x sjcx — an d 3i* from wh ‘ cl) vve g et
30 , ll, Jll ~ r 24** " r 24CT + «/ + cy' -&c. 896< fi ‘ 2304/ e But when the ordinate y becomes equal AO=t, then x, the abscissa of the curve of direction, becomes equal to LH=5: therefore by substituting those values in the last equation, we shall obtain d 2 /-x at* . ct°~ Q*= T + 'W . ct* . ct- '' 240 896 + 2304+ &C - And Q: Whence we have ct* a T x Tc + i 24 4. _L_ 4. J_ 4 _J_. ' 240 ~ 896 ~ 2304 -& C. x=sx 2rf* t" Jl_ 4 jL 24^ ' 240< 6 + JL 4 -j— +& c. 896i 8 ' 2304t 10 ~ ~ + 2c ^ 1 '24' + 1 + 1 + 1 2304 240 ‘ 896 And putting n = a + - 0956c, we shall have + &c. cs nt 4 V i y' i A c "t" 12i J ~ 120^ + y 8 + -&c. 4481 s 1 11521 8 Therefore if different values be successively taken for y, the corresponding values of x will readily be had, and the form of the curve HE«C will thereby be easily determined. Thus if we suppose the semi-elliptic arch ACB to be 120 feet span and 40 feet high to the crown, and the depth of the masonry at the crown 6 feet; that is, f=60, c= 40, a=6; then n=a-\-‘0956c—9’S26. And assuming the value of s— LH=29‘5,58. Then if y be successively taken equal 2, 4, 6, 8, 10, &c., we shall thereby obtain the corresponding values of the abscissa x, as given in the first and second columns of the following table:
3 ) TABLE I. Of the Values of y, x and v, for an Arch of Equilibrium. Value of the Ordinate y - Corresponding Value of the Abscissa X. Corresponding Value of the Abscissa V. Difference of x and v. 2 •020 •022 002 4 •080 - -089 •009 6 •181 •201 •020 8 •324 •357 •033 10 •509 •559 •050 15 1-167 1-270 •103 20 2-030 2-287 •257 30 5-155 5-359 •204 40 10 T 03 10-185 •082 46-65 14‘844 14-844 •ooo 50 17-793 17-889 095 60 29-558 40-000 10-442 By the aid of this table of the corresponding values of x and y, so many different points may be ascertained of the curve of direction HEC, and by that means the curve itself can be described with considerable accuracy. The third column contains the values of v, the ab-
32 scissce of the elliptic curve of the intrados corresponding to the same values of the mutual ordinate y: by which means it will be easy to compare the two curves. The fourth column contains the differences of the values of x and v : or the vertical distance between the two curves at any particular point. If we examine the above table attentively, we shall observe that the corresponding values of x and v, the abscissae of the curve of direction and of the curve of the intrados, differ very little until we approach towards the vertical line AK; it is plain therefore that the two curves very nearly coincide all the way from the centre C, to a considerable distance beyond the point E, as to b : but beyond the point b the two curves separate very fast, as the ellipse is then approaching to its point of greatest curvature, while the curve of direction is at the same time degenerating into almost a straight line : it is therefore in this part, viz. between the points a and H, that all arches made after the common method are so singularly defective. And this clearly explains the reason why arches formed in the common way of flat, circular, or elliptical segments, approach so nearly to arches of equilibration, and w T hy they are so much stronger (provided the abutments be adequate) than arches formed of semi-circle9 or semi-ellipses. Of the Value of the Quantity s. . In the preceding description of the method of de-
33 scribing an arch of equilibrium, the reader will have observed, that in order to ascertain the nature of the curve of direction HEC (Fig. 13.) it was necessary to assume some determinate value for ,s=LH: but it must not therefore be concluded that this value can be assumed arbitrarily; on the contrary, it is a matter of very great importance, that a strictly correct value be given to this quantity. The value of s should be so taken, that LH may be as great as possible, but with the proviso, that the curve of direction HEC shall no where pass below or intersect the elliptic curve AEC. For it is to be observed, that the lower the point H can be placed, so much the less will be the lateral pressure or thrust of the arch : but at the same time, if the line of direction crosses or passes any w'here below the elliptic curve, it evidently must produce weakness in that part of the arch, and thus defeat the primary object of an arch of equilibrium. The value of s must therefore be such, that the two curves will coincide with, and touch, each other, in as many parts as practicable. Now the ascertaining of this precise value of s might be very readily accomplished, provided the curve of direction were a regular curve, similar to the hyperbola, ellipsis, &c., that is, if its radii of curvature, commencing at the vertex, uniformly increased or decreased in proceeding towards the springing: for, suppose that the radii of curvature continually increased; then, by assuming the two curves (i. e. the curve of direction and the D
34 ellipse) to coincide for an indefinitely small distance on each side of the vertex C, an equation would emerge from which the required value of s could be readily determined. But it will be found that the nature of the curve H E C is not of the foregoing description; for the point of greatest curvature is neither at the vertex C, nor at the springings A and B, but at the points n and n, near E &c., in which respect this curve approaches very near in form to the curve of equilibrium described in the third case of Dr. Hutton’s theorem: it is therefore quite plain that the value of s is not to be determined by the method here suggested. It will consequently be required, in order to have a clearer insight into the nature of this curve of direction HEC, to ascertain in the first place its radii of curvature for different points. Of the Radii of Curvature of the Curve HEC. The radius of curvature of all curves whose ordinates are applied to a straight line, is known to be R= ^ rr ° yx—xy And if y be put constant and equal unity, this expression will be R = But according to the equation No. 1, in this chapter, we have Q x—d-. d± ±y„jt*—ys, or oc=z Q Substituting
35 this value of x therefore, our expression for the radius will be A Q x J + x ‘] 2 _ Q d ± 7^-3 X 1+i 2 ! 2 ( No.2.) But it has already been shown, that .r= l : Q X a r 2 + + W 240i 4 + c r 896 1 6 4- ' 2ii04< 9 + &C. And if the fluxion of this be squared, it will produce Qi X + 9a + 5c *^ , &r c* ' Set* ~ 180tf 4 ' And putting u = a- we shall obtain _ U 3cF’ 9a - f- 5c y== 1¥Ort r ’ v _ 15a+7c ~ 840rt 6 &c. &c. x a f +&/ 4 +y.v“ +V + e y 10 + &c. 4]t #♦ But Q is found to be = 77—, and Q®= -7-7-. £ s ti Therefore our equation will then become * 2 = 777- X ay 2 ++ y/ +5j/ 6 +sj/'°+&c. which value of x* being substituted in the preceding equation, No. 2, it will at length come out, D 2 ■N-
n t* 2 s 36 R= 4c 2 s* d ±~r s/t 1 — y X H— ~Xay' , +fiy'+yy <> +h <> + &c ' fPV 1* or, 4c 7 s s __ . R= - x ~- 9 ++ $y“+yy‘ i + ty’+&c j t(t /“ '■'■ " tt o «> / Now if j/ be put = 0, which is at the vertex, then shall we have the radius of curvature of that point of the curve of direction: viz. R= n t * 2 s d ±- T - s /**-0 n t* = jLL = 1?L = 99-73. d—c TLas And the radius of curvature of the ellipse at the same point, is R = — = 90. Again, substituting 60 (=t) for y, we shall then have the radius of curvature of the point H, or the springing of the curve of direction; which is R= iilil v nH'd ^^ + af i + / 3i*+r< f! + ^+ & c. that is, R= 70-563. And the radius of curvature at the corresponding point of the ellipse is R = 26-666. Rut if we put y — 42 - 5, then the radius of curvature of that point of the curve answering to this value of y, will be R=:49'548, which is much less than the radius at the vertex or the springings, and is the smallest radius,
37 nearly, to be found in the whole curve. And the radius of curvature of the ellipse answering to the same value of y, is 11 = 55-129. From the foregoing, therefore, it plainly appears, that the nature of the curve is exactly as it has already been described ; for the point of greatest curvature is at n, n. But this peculiarity in the curve of direction, it is to be noted, would not have been of so much consequence, provided its quantity of flexure bad been no where greater than in the corresponding points of the ellipse: but from what is shown above, this appears not to be the case; for it seems that at the point where the radius of the curve of direction is only 49"548, the radius of the ellipse at the corresponding point is equal 55‘129 : it is therefore manifest that the curvature of the former increases much faster than that of the latter; and consequently, if the two curves had been assumed to coincide near the vertex, it is plain that the curve of direction would quickly have passed far below the curve of the intrados; which is exactly contrary to what is required. Having premised thus much as to the peculiar properties of the curve of direction HEC, we have now to resume our more immediate object of determining the right value of s, or HL. From what has been stated, it is clear that if the value of s be rightly assumed, the curve of direction will just touch the ellipse at the vertex, and also at some other point on each side, as at E; but without falling in any part below or cutting it. And it is also plain, that the
38 values of x and v, the abscissae of the two curves, must in that particular case be equal to each other, as well as their constantly mutual ordinates : that is, CF, the abscissa of the curve of direction, will be equal CF, the abscissa of the ellipse. But it is to be observed that, as s is a variable quantity, this equality of the abscissas may take place at any other point of the curves as well as at E, namely whenever the two curves are made to intersect each other, just the same as if they merely touched. Now if the point II, in the perpendicular line AK, be depressed so that the two curves may intersect each other near the vertex C, and then elevated in order that the intersection may successively take place in all the intermediate points between C and E; and be again depressed so that the intersection may occur in the successive points from E to A ; it is certain that when the tw'o curves just touch each other at E, the point H will then be at its greatest elevation; that is, the quantity LH will then have its minimumof value : consequently as s neither increases nor decreases, in that particular case, its fluxion must then be = 0. And hence we have a ready method of determining the values of y and s, in the required circumstances. For in that case, agreeably to what has been already shown, the abscissae v and a’will be equal; therefore substituting their known values in terms of y, we shall have, C t - - sc ay =T x-£i + y 4 12 < 4 y_ 120 < * + &c. c — n
39 From which we obtain ] — VP—y' n A ct l y y rj 12 i 4 ' 120 t 6 ‘ 448 t 3 &C. Bat we have already remarked that the fluxion of s will be = 0 in the proposed case; therefore we have yy 1 a/ 1 y‘ - v — v —4- —- 1- « ct^ \2t^ V20t* ,+ &c.-l-V^Z i X-X^+p + ^ B+ &c. > , ■n /» /? fl/ 4 I on *6 1 i y' . y" n ^ ct? " r 12 ii " r 120 ( 6 + &C.I Now reject the denominator and divide by -J- and we shall then have 1 ay * y* y 6 _ 2 a y l y* „ Divide both sides by 2 a c ' 3 t 1 ■ 20 1* multiply by which will produce ~ —I———I- &c. and 3 ji T w T a y* I y“ , _. r /• f 12 f» ~I~ 120 f 4 ~ 448 P ' ^ jit. i JL . _*!._*!_ i &c -■ ' 3< 2 ^20i 44 56 < 6 ^ Let the latter part of this equation be assumed equal to A y s - f- By 4 + C y 6 - f- Dj/ 8 + & c. Then if this value be multiplied into the denominator of the latter part of the said equation, and compared with the numerator, we shall thereby obtain the values of the assumed co-effici* ents as follows, viz.
40 A =- B = 24 at? ’ c =Sf> p ut /= D- cg 5 c —6a 360 ( _ 560 cf— 7 ac+ ‘295 a* Van* ’ g~~ 3360 ’ E = ch ' 2 a'f 8 ’ &C. &C. Therefore we shall have IOOSOcjt _ 1521 acf + 45a 9 c-210 a\ 60480 &c. &c. t Vt>-y' l —f—y — t jy*_ . g// _ e g'f , c %’° o. c- 2 24 a/ 8 "+ 2 a-t 4 2 a’< 8 '~ 2 aH* . /- i —3»* c ^ 4 | c ff c Sf , o or ^ <—y —t 2 24 at* 2 a“i 4 2 a 3 * 8 Now let this equation be squared, and it will give *»— tY=t*—t*y*— - ' ' - * 4 --y* x. And putting d = c + y a , 33 c _ Qil — y ax 2 + - g-.r — d=± j t/p—y' And by squaring both sides, and putting p(= d 2 — c 2 ) 9 c = 3 ac + > and f——\ we obtain, Q 2 i? 2 — — Q t ri; — 2d Qi? + 25 a 2 ^ 4 — ■^-axd 2 + + I5 — y dx +/> +/ 2 j/ 2 = 0: Now assume x = A y 2 + B?/ 4 + C3/ 6 + D1/ 8 + Ej/ 10 + & c. And by taking the first and second fluxions of this equation, squaring, &c. &c., and by equating the several ranks of homologous terms, we shall thereby obtain the C
53 values of the assumed co-efficients A, B, C, &c. as follows, viz. : A = 3 a Tq ; B = 40 c a Q- + 54a 3 ci 2 — 36act*Q — 81 a'P- _ 960^03 ’ 57600 Q 6 IP + B x 48CX) a O' + 5760 a‘cQ? — 30540a-i Q? - 160 c Q' + 729a 6 + 486a< + 81 cfi Q.’ 240007Q5 D = &c. &c. And supposing the arch to be of the same dimensions as in the former example, that is AO = t = 60, OC = c = 40, and PC = a = 4 : then if we assume the quantity Q to be equal 540, we shall from these values be able to ascertain the numerical values of the aforesaid co-efficients A, B, C, &c*. Now let t (= 60) be substituted for y in the equation, x = Ay 2 + Bj/ 4 + Cy 6 + I)y 8 - f- Ey 10 - f- &c. and it will produce #=20,000+5-037+-678+-307+-119 + &c.=26-204. That is, when the ordinate y is equal AO — t = 60, then x will be equal LH = 26'£ 04 = s. And if y be successively put equal to 10, 20, 30, &c. we shall thereby obtain the corresponding values of x, * For the sake of rendering the succeeding computations more easy, the common logarithms of the five first co-efficients A, B, C, &c. are here subjoined, viz.: A = Log. -3.744727 B = .. -7.589588 C = .. -11.162529 D= .. -15.262261 E= .. -19.297271
54 agreeably to the first and second columns of the table in page 62, by means of which so many different points of the curve of direction HcC will be obtained; and hence the curve itself may be traced out with great accuracy, as is done in fig. 15, Plate III., which is drawn to an accurate scale. Of the Value of the Quantity s. In the preceding chapter it was expressly stated to be of great importance, that the quantity LH (=s) be rightly assumed, so that the point H (the element of the curve of direction) may be kept as low as possible, but at the same time not to allow the two curves to intersect each other in any part. And in order to obtain a clear idea of the nature of the curve of direction, it was then deemed expedient to give in the first place the radii of curvature for different points of the curve : and for the sake of perspicuity it will be proper to adopt the same course in the present instance. The radius of curvature of all curves (whose ordinates are applied to a straight line) is R = 1 + x?\i But we have x — . _ t d - - s/ £ s — y x — — 3-f-aa;' 2 Q ; therefore R = QxT+^i# d-JL ^ s/ i 2 —y 2 ~q~ x + n (No. 1.)
55 But x = Ay 2 + By* + Ci/ 6 + Di/ 8 + & c. as is already shown, and x 2 = 4 A 2 y 2 -f- 1 6 A By 4 + 24AC + 16 B 2 X y r> + &c. Therefore substituting these values of x, and x 2 , in the equation (No. 1.), we shall thence obtain the radii as required : thus put y = 0 (which is at the vertex of the curve), then x, and x 2 will also be = 0, and our equation will become 11 = Q_ fa .540 TT = 90. That is, the radius of curvature at the vertex of the curve of direction is equal to 90. Now put ?/=60, and it will give R — 340 = 57*32, which is the radius of curvature at the point H, or springing of the curve of direction. And if for y there be successively put the values 10, 20, 30, &c., then we shall obtain the radii of curvature of the points of the curve corresponding to those values ; agreeably to the sixth column of the Table No. 11. On inspecting this column of radii of curvature for different points of the curve of direction HcC, it will be seen that this latterdiffers materially from HEC (Fig-14), the one exhibited in the former example; in which the smallest radius of curvature was neither at the vertex nor the springing, but at an intermediate point h :. from which point, proceeding both towards the ver-
56 tex as well as towards the springing, the radii continually increased. Moreover, at the point h in Fig. 14, the radius was much smaller than the radius of the corresponding point of the elliptic curve; whence the two curves tended to intersect each other towards the point E. But contrary to this, we shall observe in the present case, that the smallest radius of curvature is at the point H (Fig. 1.5), the springing of the curve of direction ; and that the greatest radius is still at the vertex, from w’hich point proceeding all the w'ay to the springing, we find the radii continually decrease, something similar to the radii of an elliptic curve. Moreover, if we compare the radii of the curve of direction HcC, w r ith the radii of the corresponding points of the elliptic curve of the intrados AEC (as given in the seventh column of Table No. II.), we shall observe that the radii of the ellipse are everywhere less than those of the curve of direction. It is quite clear, therefore, that if the two curves be made to coincide with each other at the vertex, they can have no tendency to intersect each other at any other point; because, from the nature of their radii of curvature, they will tend to separata more and more from each other, according as they recede from the vertex C. This peculiarity in the curve of direction of the present example presents us with much greater facilities for ascertaining a proper value for Q, and consequently for ,s also: for if the expressions for the radii of curvature, at the vertex of the two curves, be put equal to each
57 other, an equation will thence arise which will give the required values of Q and s. Thus the radius of curvature at the vertex of the curve of direction is R= as is already shown; and the 2 radius of curvature of the same point of the ellipse is 12 R= —: now' put these two values equal to each other, q 3 at* that is, —— = — ; whence we shall obtain Q = —— = \a c ’ 2 c 540; which is exactly the same value that has been assumed for Q in the preceding calculations. And when the value of Q is once determined, it is easy to ascertain the value of s; the method of obtaining which has already been explained in the former part of this chapter, it being = £6-204. From the foregoing it is manifest, that the making of the spandrels partly hollow is particularly advantageous, not only as regards the great saving of materials, but also from its rendering the curve of direction much more simple ; and as it approaches nearer to the form of the ellipse, it becomes much more suitable for the purposes of an arch, as is very apparent on comparing the curve HcC (Fig. 15) with the curve HEC (Fig. 14). Whatever objections might be made to cutting the voussoirs at right angles with the curve of direction, as given in the former example, I conceive those objections can have very little force as regards the curve given in the present instance: for the latter approximates so closely to the form of the elliptic curve of the intrados, that in the
58 practical application of the curve to the building of a bridge, I think it would scarcely be discovered that, in cutting the voussoirs, any deviation had been made from the usual method. It is true, that in the present case the point H (the springing of the curve of direction) is elevated rather more than in the former example: it might thence be in- ferred, that in that particular this curve is less advantageous than the former: if the lateral pressure were to remain the same in both cases, this objection would be perfectly reasonable; but it is to be remembered, that, by making hollow spandrels, the absolute lateral pressure is probably reduced one-third; therefore the raising of the point H two or three feet is a trifling inconvenience, compared to the advantage of the great reduction of pressure. In the preceding investigations the curve of direction HcC, has all along been assumed to coincide with the lowest point C of the voussoir at the crown of the arch. This, however, has been done for the convenience of computation only, and is not to be considered as an absolute condition in the investigating a theorem for forming an arch of equilibrium; because the curve might have been described from any other point in the vertical line PC of the voussoir at the crown; as from the middle, or from the highest point P. Thus, if vc, VH, &c. be made everywhere equal PC, then will the curve V v P be the curve of direction of the forces corresponding with the point P of the vertex : and we may conceive
59 that there exists an infinite number of other curves of direction, answering to so many points between P and C, all of which will be parallel to, and within the above- mentioned curve V T:I.jndon/. \
I PL Kg -7 ,V ’ V 14:, Bt JifcrEl-'' H ■Mit'a-i Mlt- Ir^HT i'mtbstied bv Joshid. Tavlor.JLo7idoTi ',
n. vl x Mg \29 & Yig.28 * 4 Puilish&i by JosiaA Taylor. London.
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a H'o/As published by J. Taylor, The CARPENTER and JOINER S ASSISTANT, cou- taining Practical Rules for making all Kinds of Joists, and various Methods of Hingeing them together; for Hanging of Doors on straight or circular Plans; for fitting up Windows and Shutters to answer various Purposes, with Rules for hanging them; for the Construction of Floors, Partitions, Soffits, Groins, Arches for Masonry; for constructing Roofs in the best manner from a given Quantity of Timber; for placing of Bond-Timbers; with various Methods for adjusting Raking Pediments, enlarging and diminishing of Mouldings, taking Dimensions for Joinery, and for setting out Shop-Fronts; with a new Scheme for constructing Stairs and Handrails, and for Stairs having a conical Well-hole, &c. &c. To which are added, Examples of various Roofs executed, with the Scantlings from actual Measurements, with Rules for Mortices and Tenons, and for fixing Iron Straps, &e. Also Extracts from M. Relidor, M. du Hamel, M. de Buffon, &c. on the Strength of Timber, with Practical Observations. Illustrated with 79 Plates, and copious Explanations. By Peter Nicholson. 4to. il. is. bound. The fourth Edition, revised and corrected. A TREATISE on the CONSTRUCTION of STAIRCASES and HANDRAILS, showing Plans and Elevations of the various Forms of Stairs, Methods of projecting the Twist and Scroll of the Handrail, an expeditious Method of squaring the Rail, general Methods of describing the Scroll, and forming it out of the Solid. Useful also to Smiths in forming Iron Rails, Strops, &c. With a new Method of applying the Face-mould to the Plank without bevelling the Edge. Preceded by some necessary Problems in practical Geometry; with the Sections and Coverings of Prismatic Solids. Illustrated by Thirty-nine Engravings. By Peter Nicholson, Author of the Carpenter’s New Guide, the Joiner’s Assistant, &c. &c. 4to. 18s. bound. The STUDENT'S INSTRUCTOR in drawing and working the Five Orders of Architecture; fully explaining the best Methods of striking regular and quirked Mouldings, for diminishing and glueing of Columns and Capitals, for finding the true Diameter of an Order to any given height, for striking the Ionic Volute circular and elliptical: with finished Examples, on a large Scale, of the Orders, their Planceers, &c. and some Designs for Door-Cases. By Peter Nicholson. Engraved on 41 Plates. 8vo. 10s. 6d. bouud. A new Edition, corrected and much enlarged. AN ESSAY ON THE STRENGTH AND STRESS OF TIMBER, Founded upon Experiments performed at the Royal Military Academy, on Specimens selected from the Royal Arsenal, and his Majesty’s Dock Yard at Woolwich ; preceded by AN HISTORICAL REVIEW OF FORMER THEORIES AND EXPERIMENTS. ALSO, AN APPENDIX, ON THE STRENGTH OF IRON AND OTHER MATERIALS. By PETER BARLOW, of the Royal Military Academy. 8vo. With numerous Tables and Plates. Second Edition, corrected. 18s. in Boards. PICTURESQUE VIEWS of the THEATRES of LONDON, and its SUBURBS. Drawn and engraved in Aquatinta, by Daniel Havf.i.l, on 14 Plates, elegantly coloured. With some Plans. Accompanied by an historical and descriptive Account of each Theatre. Quarto.
7 Architectural Library , High Holborn. A PRACTICAL TREATISE on the LAW of DILAPIDATIONS, Ecclesiastical and Common, Reinstatements, Waste, &c.; to which is added, an Appendix, containing Precedents of Notices to Repair, &c.; with Examples for making Valuations, Estimates, &c. By James Elmes, Architect. Second Edition, with Additions, 8vo. Price 4s. sewed. The RUDIMENTS of DRAWING CABINET and UPHOLSTERY FURNITURE, containing ample Instructions for designing and delineating the different Articles of those Branches perspectively and geometrically. Illustrated with appropriate Diagrams and Designs, proportioned upon Architectural Principles, on 32 Plates ; many of which are coloured. The Second Edition. To which is added, an Elucidation of the Principles of Drawing Ornaments, exemplified on 7 Plates. By Richard Brown. In 4to. il. ns. 6d. Boards. MODERN FINISHINGS for ROOMS; a Series of Designs for Vestibules, Halls, Stair-cases, Dressing Rooms, Boudoirs, Libraries, and Drawing Rooms, with their Doors, Chimney Pieces, and other Finishings, to a large Scale, and the several Mouldings and Cornices at full size, showing their Construction and relative Proportions; to which are added, some Designs for Villas and Porticos, with the Rules for drawing the Columns, &c. at large. The whole adapted for the Use and Direction of every Person engaged in the practical Part of Building. By W. F. Pocock, Architect. On 86 Plates. Quarto. 2I. 2s. bound. MECHANICAL EXERCISES ; or the Elements and Practice of Carpentry, Joinery, Bricklaying, Masonry, Slating, Plastering, Painting, Smithing, and Turning. Containing a full Description of the Tools belonging to each Branch of Business, and copious Directions for their Use: with an Explanation of the Terms used in each Art; and an Introduction to Practical Geometry. Illustrated by 39 Plates. By Peter Nicholson. Octavo. 18s. Boards. 21s. Bound. TAYLOR'S BUILDERS PRICE BOOK; containing a correct List of the Prices allowed by the most eminent Surveyors in Londou to the several Artificers concerned in Building: including the Jorneymen's Prices. A new Edition, corrected by an experienced Surveyor. Sewed, 4s. With a copious Abstract of the Building Act, and Plates of the Walls, &c. DESIGNS for SEPULCHRAL MONUMENTS, TOMBS, MURAL TABLETS, &o. By George Maliphant. Elegantly engraved, on 36 large Quarto Plates. BOOKS OF ORNAMENTS, &c. SELECT GREEK and ROMAN ANTIQUITIES, from Vases, Gems, and other Subjects of the choicest Workmanship. Engraved on 36 Plates. By H. Moses. With Descriptions. Quarto, il. is. Boards. ORNAMENTAL DESIGNS after the Manner of the Antique. Composed for the Use of Architects, Ornamental PaiDters, Statuaries, Carvers, Carpet, Silk, aud printed Calico Manufacturers, and every Trade dependent on the Fine Arts. By G. Smith. Neatly engraved in Outline. Royal Quarto, on 43 Plates. Price il. us. 6d. in Boards. A COLLECTION of DESIGNS for MODERN EMBEL- L 1 SHMENTS, suitable to Parlours, Dining and Drawing Rooms, Foldiug Doors, Chimney Pieces, Varaudas, Frizes, &c. By C. A. Busby, Architect. Neatly engraved on 24 Plates, 14 of which are elegantly coloured. Large Quarto, jl. 1 is. 6d.
8 Works published, by J. Taylor, An ELUCIDATION of the PRINCIPLES of DRAWING ORNAMENTS, exemplified on 7 Plates. By Richard Brown. In 4to. ics. 6d. Boards. DESIGNS for the DECORATION of ROOMS in the various STYLES of MODERN EMBELLISHMENT; with Pilasters aud Frizes at large. On 20 Folio Plates, Drawn and Etched by G. Cooper, Draftsman and Decorator, il. is. ORNAMENTS selected from the ANTIQUE, lithographed < 5 n 21 leaves Folio, il. is. Sewed. Exhibiting a Variety of Foliage and Fragments of Ornaments at large, in a bold and free Style. * ORNAMENTS DISPLAYED, on a full Size for Working, proper for all Carvers, Painters, &c.; containing a Variety of accurate Examples of Foliage aud Frizes, elegantly engraved in the manner of Chalks, on 33 large Folio Plates. Sewed, 15s. The SMITH, FOUNDER, and ORNAMENTAL METAL WORKER’S DIRECTOR; consisting of Designs and Patterns for Gates, Piers, Balcony-railing, Window-guards, Fan-lights, Varandas, Ballustrades for Stair-cases, Lamp-irons, Palisades, Brackets, Street Lamps, Stoves, Stands for Lamps and Gas Lights, Candlesticks, Chandeliers, Vases, Tripods, Candelabra, &c. With various useful Ornaments at large. Selected and composed by L. N. Cottingham, Architect. On 60 Quarto Plates. Sewed, zl. zs. WORKS UPON CIVIL ENGINEERING, MACHINERY, Sec. J. Taylor, having purchased the remaining Copies of the Reports of the late John Smeaton, Civil Engineer, proposes to sell them,for the present, at the following very reduced Prices ; viz. REPORTS, ESTIMATES, and TREATISES, on CA- NALS, Rivers, Harbours, Piers, Bridges, Draining, Embanking, Light- Houses, Machinery, Fire Engines, Mills, &e. &c., with other Papers, drawn up in the course of his Employment. 3 Vols. Quarto, with 74 Plates, engraved by Lowry. Boards, 4I. 14s. 6d. Published at 7I, 7s. MISCELLANEOUS PAPERS, comprising his communications to the Royal Society. 12 Plates. Quarto. Boards, il. is. Published at 1 1. its. 6d. The Reports and Miscellaneous Papers together, 4 Vols. Boards, 5I. 10s. Published at 81 . 18s. fid. An HISTORICAL and DESCRIPTIVE ACCOUNT of the STEAM ENGINE ; comprising a general View of the various Modes of employing Elastic Vapour as a prime Mover in Mechanics. With an Appendix of Patents and Parliamentary Papers connected with the Subject. By Charles Frederick Partington, of the London Institution. Octavo. Illustrated with Eight Copper-plates, and other Figures. 18s. Boards. PRACTICAL ESSAYS on MILL WORK, and other MACHINERY.—On the Teeth of Wheels, the Shafts, Gudgeons, and Journals of Machines ; the Couplings and Bearings of Shafts, disengaging and re-engaging Machinery in Motion ; equalizing the Motion of Mills, changing the Velocity of Machines in Motion ; the Framing of Mill Work, &c.; with various useful Tables. By Robert Buchanan, Engineer. The Second Edition. Revised, with Notes and additional Articles, containing new Researches on various Mechanical Subjects. By Thomas Tredgold, Civil Engineer. Illustrated by 20 Plat<£ and numerous Figures. In 2 Vols. Octavo. Price il. 4s. Boards.
0 Architectural Library, High Holborn. SMEATON’S EXPERIMENTS on UNDER SHOT and OVER-SHOT WATER WHEELS, &c. Octavo, with five Plates, ios. 6d. Boards. GRAY’S EXPERIENCED MILLWRIGHT, a Treatise on the Construction of some of the most useful Machines, with the latest Improvements, &c. With 44 Engravings. Folio. * 1 . 2s. Half-bound. NEW BRIDGES, &c. A PERSPECTIVE VIEW of the WATERLOO CAST IRON BRIDGE erected over the River CONWAY, in North Wales. By T. Telford. Elegantly coloured, il. ns. 6d. A PLAN and ELEVATION of the SOUTHWARK CAST IRON BRIDGE over the River THAMES. 12s. The celebrated WOODEN BRIDGE across the DELAWARE, Trenton, in America, ios. 6d. PLANS, ELEVATION, and SECTIONS of the CURIOUS WOODEN BRIDGE at SCHAFFHAUSEN, in Switzerland, built in 1760, by Ulric Grubenman, and destroyed by the French. 19 inches by 29. 12s. ELEVATION of BLACK FRIARS’ BRIDGE, with the Plan of the Foundation and Superstructure, by R. Baldwin ; 12 inches by 48 inches. 5s. PLANS, ELEVATIONS, and SECTIONS of the MACHINES and CENTERING used in erecting BLACK FRIARS’ BRIDGE; drawn and engraved by R. Baldwin, Clerk of the Work: on Seven large Plates, with Explanations, ios. 6d. ELEVATION of the STONE BRIDGE built over the SEVERN, at Shrewsbury; with the Plan of the Foundation and Superstructure; engraved by Rookeu. is. fid. A VTEW of the CAST IRON BRIDGE, erected over the River THAMES, at Vauxhall; elegantly engraved in Aquatinta, from a Drawing by E. Gyfford, Architect, il. is. A PLAN and VIEW of the CHAIN BRIDGE now erecting over the MENAI, at Bangor Ferry. 5s. A PLAN and VIEW of the PATENT IRON BAR BRIDGE of SUSPENSION, erected over the River TWEED, by Captain Brown. Elegantly engraved in Aquatinta. ios. A PLAN and ELEVATION of the WATERLOO BRIDGE, erected over the River THAMES. Elegantly engraved in Aquatinta. ios. A VIEW of the CURIOUS WOODEN BRIDGE over the SCHUYLKILL, near Philadelphia, America ; shewing the Construction and Scenery. 7s. 6d. A VIEW of the UPPER SCHUYLKILL BRIDGE at Philadelphia; Span of the Arch 340 feet. 7s. 6d. PLAN, ELEVATION, and DETAILS, of a BRIDGE, on the Principle of Suspension, constructed for the Islam! of Bourbon; Span of the Chain 300 feet. By M. J. Brunp.l, Esq. • ;s.
10 Works published by J. Taylor, A VIEW of the CAST IRON BRIDGE erected over the SEVERN, at Colebrook-Dale. 7s. 6d. WEST ELEVATION of YORK MINSTER, elegantly engraved from a Drawing by James Malton. 15s. A GRAND VIEW of the INTERIOR of ST. PAUL’S CATHEDRAL, taken from the great S. VV. Pier, and showing the magni- fieent Expanse of the Dome. Drawn and engraved by J. Coney. Size xt inches by Z7. Price its. On India paper, 15s. NEW WORKS OR NEW EDITIONS Preparing for Publication. ESSAYS on GOTHIC ARCHITECTURE, by the Rev. T. Warton, Rev. J. Bentham, Capt. Grose, and Rev. J. Milner. Illustrated with 1 z Plates of Ornaments, &c., selected from Ancient Buildings, calculated to exhibit the various Styles of different Periods. The third Edition, with a List of the Cathedrals of England and their Dimensions. Octavo. A PARALLEL of the ORDERS of ARCHITECTURE, GRECIAN and ROMAN, as practised by the Ancients and the Moderns. Illustrated by 66 Plates. Drawn and engraved in Outline by M. Normand Architect. The Text translated by Augustus Pugin, Architect. Folio. 3I. 3s. in Boards. _ A NEW TRANSLATION OF THE CHARACTERS OF THEOPHRASTUS; ACCOMPANIED WITH THE GREEK TEXT, AND NOTES ; AND ILLUSTRATED BY FIFTY piipstognomtcal ENGRAVED ON WOOD, BY THOMPSON, BllANSTON, HL’GHKS, 8 . c. TO WHICH ABE SUBJOINED, HINTS, PHYSIOLOGICAL AND ETHICAL, ON THE INDIVIDUAL VARIETIES OF HUMAN NATURE. BY FRANCIS HOWELL. Price 11. Is. Royal 8vo. ; and II. 11s. 6d. India Proofs. PRINCIPLES OF WARMING AND VENTILATING Public Buildings, Dwelling Houses, Manufactories, Hospitals, Hot-Houses, Conservatories, &c. AND OF CONSTRUCTING FIRE PLACES, BOILERS, STEAM APPARATUS, GRATES, AND DRYING ROOMS; With Illustrations, experimental, scientific, and practical. TO WHICH ARE ADDED, OBSERVATIONS ON THE NATURE OK HEAT, AND VARIOUS TABLES USEFUL IN THE APPLICATION OF HEAT. With 9 Plates, and several Woodcuts. BY THOMAS THEDGOLD, CIVII. ENGINEER , Member of the Institution of Civil Engineers; Author of Elementary Principles of C arpentry, an Essay on Cast Iron, &c. Ac. Rro. 15 s. Boards,
11 Architectural Library, High Holborn. DESIGNS FOR SEPULCHRAL MONUMENTS, TOMBS, MURAL TABLETS, &c. BY GEORGE MAL1PH ANT. Elegantly engraved on 36 large Quarto Plates. A PRACTICAL ESSAY ON THE STRENGTH OF CAST-IRON, AND OTHER METALS; Intended for the Assistance of Engineers, Iron-Masters, Architects, Millwrights, Founders, Smiths, and others, engaged in the Construction of Machines, Buildings, &c. containing practical Rules, Tables, and Examples; founded on a Series of new Experiments, with an extensive Table of the Properties of Materials. Illustrated by Four Plates and several Wood Cuts. By Thomas Tredgold, Civil Engineer, Member of the Institution of Civil Engineers, &.c. The Second Edition, improved and enlarged. 8vo. 15s. Bds. THE RUDIMENTS OF PRACTICAL PERSPECTIVE : In which the Representation of Objects is described by Two easy Methods ; one depending on the Plan of the Object, the other on its Dimensions and Position ; each Method being entirely free from the usual Complication of Lines, and from the Difficulties arising from remote vanishing Points. By Peter Nicholson. Illustrated by 38 Plates, engraved by Lowry. Octavo. 14s. Boards. TABLES FOR THE PURCHASING of ESTATES, Freehold, Copyhold, or Leasehold, Annuities, Sfc. And for the renewing of Leases held under Cathedral Churches, Colleges, or other Corporate Bodies, for Terms or Years certain, and for Lives; also, for valuing Reversionary Estates, Deferred Annuities, Next Presentations, &ic. Together with several useful and interesting Tables, connected with the Subject. Also the Five Tables of compound Interest. By W. In wood, Architect and Surveyor. In small Octavo for the Pocket. The third Edition, enlarged. 7s. Boards.
12 Works published by J. Tatlor, CHAMBERS’S CIVIL ARCHITECTURE. NEW EDITION, IN QUARTO. This Day is published, PARTS I. AND II. WITH THE ORIGINAL PLATES, AND THE TEXT OF THE THIRD EDITION, ENTIRE, On Imperial Quarto, in Twelve Parte, Monthly, Price be. each, A TREATISE ON THE DECORATIVE PART OF CIVIL ARCHITECTURE, ILLUSTRATED BY SIXTY PLATES, ENCRAVED BY ROOKER, FOURDRINIER, GRIGNION, Ac. BY SIR WILLIAM CHAMBERS, K.P.S. Late Surveyor General of Hie Majeety’e Works, ffc. ffc. THE FOURTH EDITION, CONSIDERABLY AUGMENTED. This highly esteemed Work, by the best Architect of his day, having been long out of print; has been much sought after, and copies which have occasionally occurred for sale have produced very high prices, and consequently can be obtained by few persons only ; to obviate this deficiency, and accommodate Architectural Students, as well as the Public generally, Josiah Taylok, possessing the original Plates of this scientific and useful Work, proposes to publish a new and improved Edition,
19 Architectural Library, High Holborn. on Imperial Quarto. The Plates, engraved by the elder Rooker, Fourdrinier, Grignion, and other eminent Artists, are the same as Sir W. Chambers originally published; the Text also will be entire, and without any alteration from the last Edition. The Plates will be printed on Imperial Folio paper, and form a separate Volume, in Folio, if desired. To accommodate this new Edition to the present state of the Art, an Appendix will be added, by An eminent Architect, of Examples of tire Doric and other Order*, from the best remains of Grecian Architecture; which will make Six new additional Plates, and will be accompanied by a Dissertation on the State, Taste, and Principles of Grecian Architecture : to which will be added, Notes and Observations on the original Work. And it is presumed, that this will be the most complete and interesting Book for the information of Students and Amateurs on the elementary Principles of Decorative Architecture. The Work, consisting of about Sixty Plates, Imperial Folio, with the Text entire, handsomely printed on Imperial Quarto, will be published in Twelve Parts, monthly, at 5s. each. The Plates will be folded, and the whole will make a very handsome Volume, of the largest Quarto size. Q3T Gentlemen who prefer having the Plates not folded f may have them delivered in folio, on signifying their desire to the Publisher. A few Copies are printed, with the Text, on Imperial Folio. Price 7s. each Part. The First Part was published on the 31st of March; and it will be continued on the last day of each succeeding month. Proofs of the Plates, which are iri the best state, may be seen at .1. Taylor’s Architectural Library, 59, High Holborn ; where the names of Subscribers are received, and inserted in the List to be regularly delivered. * # * Gentlemen are requested to order the Edition with the original Plates.
14 Works jiublished by J. Taylor, THIS DAY ARE PUBLISHED, Nos. I. II. III. IV. V. VI. CONTAINING SEVEN ENGRAVINGS EACH, Price 6s. Medium 8 vo.: 8 s. Imperial Svo.: and 14s. Medium 4to. with Proofs on India Paper, $rcf)ttecturai gliusitrattonfii OF THE PUBLIC BUILDINGS OF LONDON ; ACCOMPANIED BY HISTORICAL, DESCRIPTIVE, AND CRITICAL ACCOUNTS ; BY J. BRITTON, F.S.A., &c. AND AUGUSTUS PUGIN,—ARCHITECT. Vol. I. dedicated, by permission, to His Majesty George the Fourth. LONDON: PUBLISHED BY JOSIAH TAYLOR, ARCHITECTURAL LIBRARY, HIGH HOLBORN; J. BRITTON, BURTON COTTAGE, BURTON STREET; AND A. PUGIN, 105, GREAT RUSSELL STREET, BLOOMSBURY. prospectus. This Publication will comprise a Series of Plans, Sections, Elevations, and Perspective Views of the most interesting Edifices of the British Metropolis: viz. its principal Palaces, Churches, Chapels, Theatres, Halls, Mansions, Squares, Streets, Bridges, Museums, &c. When these are faithfully delineated, and brought into a compact and portable compass:—when they are examined in their true forms and proportions, and their ornaments carefully drawn :—when seen divested of extraneous objects, ar.d the confusing bustle of this much-crowded and ever-busy city, we shall find, that many of them are works of merit and of beauty. They have never yet been correctly and carefully engraved, and have consequently never been fairly appreciated. Two leading features of this Work, will be accuracy of delineation, and cheapness in price : towards attaining the former, the Authors will solicit the aid of the Architects of modern Buildings ; and they intend to have the old Edifices drawn and measured by competent Artists. To render the Work moderate in price, it is intended to have the Plates executed in a clear, but firm outline; by which means the architectural forms and
15 Architectural Library, Jliyh Holborn. characters of Buildings will be more carefully defined, than in finished, shadow ed prints. The Plates, to be engraved by J. Le Keux, J. Roffe, R. Sands, G. Gladwin, J. Cleghorn, &c., will be executed with a view of affording the Architect, Builder, Antiquary, and Connoisseur, accurate and scientific information ; by representing the real design and construction of each Building, respectively, and thus exemplifying the talents of its Architect. The letter-press will be devoted to History and Description, rather than to criticism and comment; and will be wholly limited to the two former, in its accounts of the works of living Artists. The Plates already published, are illustrated by Plans, Elevations, and Views, of the Churches of—St. Paul’s ; St. Stephen’s, Walbrook ; St. Bride’s, Fleet Street; the Temple ; St. Mary, Woolnoth; St. Pancras; Westminster Abbey; St. Martin’s in the Fields. Of Mansions, those of Uxbridge House, Burlington House, Mr. Soane’s, Mr. Burton’s. Public Buildings: the Custom House, King’s Entrance to the House of Lords, the British Museum, Bethleni Hospital, Russell Institution. Theatres : the Opera House, the Haymarket: those of Drury Lane, Covent Garden, the English Opera, and Astley’s Amphitheatre, are preparing. The following Subjects are drawn and in progress: The Bridges of Westminster, Waterloo, Blackfriars, London, and Southwark, will be shewn in Plan, Elevation, and Section. The Galleries of the Marquis of Stafford, Earl Gros- venor, Sir J. Leicester, Thos. Hope, Esq., B. West, Esq. The Bank, the India Mouse, the Mansion House, the Royal Exchange, the Tower, the Mint, the Trinity House, the London Institution, the Admiralty, Somerset House, Carlton Palace. This Publication is printed in Medium 8vo. at 5s. per Number; and Imperial 8vo. at 8s. per Number. A Number will appear at the interval of two months. Each Number will contain at least Seven Plates, and, on an average, about Two Sheets of Letterpress. The whole Work will be comprised in Twenty-four Numbers, forming two handsome Volumes, to which appropriate Engraved Titles will be given. A small number of Proofs on India Paper, Quarto, will be printed, to gratify the Connoisseur. Price 14s. each. *»* Gentlemen desirous of securing choice Impi-essions, are requested to forward their Names and Addresses, to either of the Publishers, where Specimens of the Work may be seen. A LIST OF SUBSCRIBERS WILL BF. PRINTED.
16 Works published by J. TAYLOR, THIS DAY IS PUBLISHED, In 2 Volumes, Medium 4to. Price Six Guineas; and Nitie Guineas in Imperial 4to. with Proofs: in extra Boards: SPECIMENS OF <§otf)tc Architecture; SELECTED FROM VARIOUS ANCIENT EDIFICES IN ENGLAND: CONSISTING OF Plans, Elevations, Sections, 8$ Parts at Large; CALCULATED TO EXEMPLIFY THE VARIOUS STYLES AND THE PRACTICAL CONSTRUCTION OF THIS CLASS OF ADMIRED ARCHITECTURE; ACCOMPANIED BY ^Historical anH Descriptive Accounts, AND A GLOSSARY OF ANCIENT TERMS. BY A. PUGIN,—ARCHITECT. %* Gentlemen having odd Numbers of this Work are requested to complete the same before Midsummer, 1824 ; after which time the Work will be made up into complete sets, and detached parts cannot be supplied. Printed by S. Gosnell, 8, Little Queen Street, Loudon.
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