152 



THE CIVIL ENCilNEKR AND ARCHITECT'S JOURNAL. 



[May, 



A FEW KKMARKSON THli: CONSTRUCTION oK oni.K^UE 

 ARCHES, ANU ON SOME RECENT WORKS (JN THAT 

 SUBJEC'l'. 



IIntil witliii) the last few years, the construction of oblique briilges 

 lias been but little nnilerstooil, from a iloiibt as to their stabililv, and 

 I'ruiii the dilliiHilty of their conslnidion, they were regarded to a cer- 

 tain degree with distrust, and the engineer would only have recourse 

 to tbeui when the circumstances of the case were imperative; the 

 superior scientific acquirements of the engineers of the present dav, 

 liovvever, the assistance of various books on the subject, and the great 

 experience (jbtained in this species of construction, l)y the demai d. 

 occasioned for them in the large railway undertakings which have 

 lately occupied so niucli*of the public attention, have contributed 

 luaterially to remove the veil of mystery whi(d) formerly hung over 

 them; the doubl wbicli was at one time entertained of their stability 

 is removed, the oblique bridge is now generally adopted, and the only 

 ])oint remaining to be cleared up is, as to the iiest nietliod of working 

 the parts togetlier, so as to obtain the desideratum of engineering, 

 \iz., stability, economy, and beauty of appearance. 



Since the connnencement of the London and Hirniingham Railway, 

 fcair authors have written on the construction of obli(pie bridges, Mr. 

 I'dx, .Mr. Hart, Mr. 15uck, and Mr. Nicholson. It should be observed, 

 with refereme to the two latter, that Mr. Buck's work appeared be- 

 fore the third part of Mr. Nicholson's was published. The announce- 

 ment of a work on this subject, by a person whose reputation as an 

 author, stood so high as that of Feter Nichelson, naturally gave rise, 

 in the practical world, to the hope tliat the diUlculties which had 

 lierelofore attended the constructing of oblique bridges would, with 

 his powerful assistance, be much reduced, if not entirely removed, 

 but lliat our most reasonable anticipations are sometimes doomed to 

 disappointment, was never more signally shown than in this instance. 

 A feu quotations will be sufficient to give a specimen of the errors 

 and inconsistencies which, we regret to say, cl;araclerize this book. 

 IMr. Nicholson says in his preface, " In this undertaking, the general 

 reader is not supposed to be nuich acquainted with scientilic re- 

 searches," and he accordingly goes on, in the introduction, to inform 

 him that a right angle contains ninety degrees, that bu niinut<'s make 

 a degree, and (hat " a number having a small zero or cypher placed 

 over the riglit hand shoulder of the iigure or last tignre, shows this 

 number to be as many degrees as the figure or figures express." At 

 page XX of the introduction, he says, " If a spiral surface be cut by a 

 ])laue obliquely to the axis of the cylinder, the section will be a cuive 

 <;f contrary flexure, and if the spiral surface be cut by another plane 

 passing along the axis, perpendicular to the first [ilane, the section, 

 which is a straight line, will intersect the curve of contrary flexure at 

 the point of retrogression." The first of these paragr.iphs appears 

 intended for a person who has only learnt to read and write, while the 

 second, it must be admitted, seems little adapted to the understanding 

 of tlmse who are unacquainted with scientific researches. 



In Section IV, jiage xxiii, which treats of the trihedral, he states 

 thai " If a trihedral be cut by a plane perpendicular to one of its 

 oljlique edges, the section shall be a right angle." Now a trihedral 

 7nay have all three of its edges oblique, or one obtuse and two oblique 

 edges, or one right and two ob'.ique edges, and the above assertion 

 only holds good with regard to the latter ; with such a glaring error 

 as this among the definitions on which his trihedral svstem is founded, 

 it is of course unnecessary to examine it further. One part of the 

 subject in which Mr. Nicholson has been very unfortunate, is relative 

 to the sections of s)>iral surfaces; of this we will only give one in- 

 stance here, as we shall have occasion to return to this subject. He 

 .says, page ■24, "the transverse section is, Ihcrclore, the onlv section of 

 the spiral surface v\hich is a straight line." \\'liereas, in introduction, 

 page .\i-\, we find, "If a spiral surface be cut by a ))lane, either per- 

 pendicular to or passing along the axis, the section will be a straight 

 line. 



The history and theory of oblique bridges is, liy some system of 

 arrangement peiadiar to the author, placed after the problem for con- 

 structing the teiiqilets for working arch stones, and is followed by a 

 practical method for obtaining the templets. This history, so curi- 

 ously placed, a|i|)ears to be introduced chiefly for the op|iortunilv 

 thereby alforded the author of making his own sirietures on other 

 works; but in his anxiety to detract from the merits of ;dl authors 

 but himself on this subject, he has again fallen into so many errors, as 

 to leave no doidjt of his being but superficially acquainterl with the 

 subject on which he writes. 



Mr. Fox has assrrted, in common with other writers on the oblique 

 arch, that, " when the soflit i.i developed, the edge wdiich formed the 

 face of the arch gives a true spiral curve." Upon this Mr. N. re- 



marks, " It must, liowcver, be observed, that the edge of the devel- 

 loped sciui-ellipse is neither a spiral line nor (ho projection of a spiral 

 line." In this remark Mr. Nicholson is decidedly wrong, for it is easy 

 to dennjustrate that the curve above mentioned is the projection of a 

 true spiral, whose radius is equal (o half the obliquity of the arch, and 

 whose length is equal to the semieireumfereuce of the lylinder on 

 which the arch is assumed to be built. With reference to Mr. Fox 

 having stated that (he joints in the face are curves, Mr. N. says, " if 

 they had been curves, the curvature v.ould have been so small, that 

 the joint lines would nut have varied sensibly from straight lines. 

 The true curvature (jf the joint could not, therefo.e, have been ex- 

 pressed in lines," Now if Mr. Nicholson had ever had occasion to 

 put his rules into practice in a bridge of considerable obhqnily, he 

 would have found that the face joints near the springing are not only 

 curves, but very jierceptible ones. There is, moreover, nothing im- 

 possible in constructing the curves formed by the face joints, it is 

 nearly as simple as the construction of the sijiral itself; but this is 

 a part of the subject on which Mr. Nicholson is throughout \uiforlu- 

 nate. 



Mr. Buck's Essay on the Oblique Bridge next falls under our author's 

 scrutiny; that it should receive his entire disapproval, is not perliaps 

 surprising. Mr. Buck has had the advantage of Mr. Nicholson in 

 being able, while engaged on the London and Birmingham and oilier 

 railways, to put his rules into practice, and prove them to be right 

 before he laid them before the public ; he has, for the same reason, 

 been able to select the useful parts, and pi-esent them to the reader 

 unencumbered by the superfluous luid weary waste of words through 

 which Mr. Nicholson's readers are doomed to wander. Relative to 

 this work Mr. Nicholson proceeds to say, "The formula cu = C/-|-e) 

 cot fan B is due to Mr. Buck ; it gives the distance below the centre 

 to the puiuf of convergence, into which all the joints in the elevation 

 of the arch meet in the axis minor, supposing that the joints are 

 straight lines, which thev are not exactly." This having reference to 

 the section of the spiral surface, no wonder Mr. Nicholson is again 

 unfortunate. Mr. Buck does not wish bis readers to tin-n the curves 

 into straight lines, wdiich peculiar operation, if pr<q)erly conducted, is 

 to cause the straight lines to converge to a ])uint. He simply gives 

 the point to which the chords of the said curves so converge, and the 

 formula for finding this point is not all that is due to ]\Ir. Buck, but 

 (lie discovery of the fact (hat (hey do converge to a point, and the 

 uses to which this discovery can be applied in facilitating the con- 

 struction of tlie bridge. 



Mr. Nicholson next complains that Mr. Buck has given, besides his 

 general formuki for finding the |)oint of convergence, another formula 

 which lia|)pens to be more convenient when making the necessary 

 calculations for the segmental arch. He concludes at once that the 

 results of these forniulie must dill'er, and puts forth bis assertion to the 

 world as if the book were in error. His concluding paragraph rela- 

 tive to Mr. Buck's book is, " One thing which we consider defective 

 in Bn(d>.'s Es.say on (Jblique Arches is, that his intentions are not 

 enunciated under regular heads, so as to call the attention of the 

 reader ; he gives no reason for his rules, nor does he show the prin- 

 ciples upon which his formulae depend. The height of the point o, 

 Fig 7, will depend upon the breadth of the beds." 



The first part of this remark we will leave Mr. Nicholson to settle 

 with bis conscience in the best way he can. As regards the second 

 part, we would ask «liat is the K in Mr. Buck's formula if it is not the 

 breadth of the beds or the thickness of the arch, which is one and the 

 s;ime thing ? Mr. Nicholson ought, in justice, to ascertain that an 

 error really exists, before he implies that such is the case. That he 

 has not long been acquainted with the fact of the chords of the joints 

 in the face converging to a point below the axis of the cylinder, is 

 evident from his book on stone cutting, in which the joints are drawn 

 at right angles to the curve, and that he was unaware of the utility of 

 knowing this point is equally evident, or he would never have given 

 the laborious and complicated construction for finding the joints in the 

 face, beginning at page 17. 



Mr. Nicholson gives rules for what he terms two kinds of oblique 

 bridges, namely, those in which the joints of the stones are planes, 

 and those in wliicli they are spiral surfaces; these rules are so jumbled 

 up togetlier, that the reader is at a loss to know to which of the two 

 species of bridges they refer. At page 15 there is a problem, " To 

 find the curved bevels for cutting the cproin heads of an oblique arch." 

 The reader being unable to learn from the heading of the problem 

 whether it rel.ites to square or spiral joints, naturally proceeds to 

 wade tlirougli it, with tlie lio|)e that it may aliijrd some means of as- 

 certaiuing this fact, but licre he soon becomes lost in a labyrinth. You 

 are told to divide the arc ABC into as many equal parts as the ring 

 stones are in number, and through the points of division draw b k, c i, 

 dj, &c., perpendicular, to the curve A D E. ABC and A D E being 



