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THE CIVIL EN(;iNEI<:il AND ARCHITECTS JOURNAL. 



[Jul 



ON OBLIQUE ARCHES. 

 (IN' Reply to Mr. Buck, C.E., &c. &c.) 



Sir,— III Konseiiuence of what has already appeared in yoiir .Tournal, 

 I trust to your candour to insert my answer. I consider, Sir, tliat tlie 

 insertion of it is not only due to me, individually, hut to all who are 

 interested in pradical attainments. The facts which I state in reply 

 are plain, and whilst they expose unilue pretension, they have the 

 merit of being in themselves irrefutable. 



I am, Sir, very truly your's, 



Peter Nicholson. 



My attention was accidentally called, about the first instant, to an 

 article in the Railway Magazine, of the 25th of January, ISIU, written 

 by Mr. G. W.Buck, of Ardwich, Manchester, in reply to some remarks 

 which appear in my Treatise on the Oblique Arch, respecting some 

 inconsistencies in certain formula-, &e., in his "Essay" on the same 

 subject. Mr. Buck says in his reply,—" At page 8 of' his preface, in 

 speaking of the forms of his templets which are necessary for working 

 the stones, Mr. Nicholson says — ' they are not shown by any other author 

 vyho has wrote upon the subject.' Now, if Mr. Nicli'olson will refer to 

 the 3rd chapter of my "Essay," he will find thatcliapter to be exclusively 

 devoted to an explanation of the method of making the temj)lets anil 

 working the voussoirs ; moreover the fifth plate contains eight diagrams 

 exhibiting the forms of these templets." Now, Sir, I /lare examined 

 the third chapter of Mr. Buck's " Essay," and I can find no method ex- 

 plaining the making of the curved edges of the templets, Nos. 1 and 2, 

 plate 2G, in my work, to which I refer when I say "they are not shown 

 by any other author who has written upon the subject ;" and I have 

 also examined the fifth plate in his " Essay," which, Mr. Buck says, 

 contains eight diagrams exhibiting the forrns of these templets, and I 

 have been equally disappointed, for lean find iwnnc/i tcmpkU txhibited. 

 Mr. Buck does not even show how the radius of curvature of these 

 templets may be found ; neither does he give a hint that thev are ne- 

 cessary. The arch squares, Nos. 3 and 4, entirely depend upon the 

 curved edges of No. 2, and No. 1. Now, Sir, that Mr. Buck should 

 have made these assertions is, to me, a matter of the utmost surprise, 

 seeing that he must have known, when he made them, that lie was 

 deliberately stating that which was incorrect. The only method which 

 Mr. Buck gives for working the arch stones is a very complicated and 

 a very clumsy one, the principle of which he has taken from the 'i5th 

 page of my work on Stone Cutting, published 12 years ago, and which 

 method is much more difficult, even for a person possessed of con- 

 siderable mathematical knowledge, to work by, and at the same time 

 imich more liable to error, than the method which I give, and which, 

 in order to guard against error, I have adapted to the understanding of 

 the most ordinary mason. In fact, it requires very little more attention 

 than a common square segmental or semicircular arch, and the rules, 

 or squares by vvliich the stones are wrought are exceedingly simple in 

 their construction. On this point it may not be amiss to add that 

 although every mason is naturally inclined to work the bed of a stone 

 tirst, yet, the first conception which I had of forming the stones of an 

 oblique arch was certainly the most rational : first to foniL the sotTit, 

 then one of the beds, and lastly the other bed. And I did this because 

 it was easier to conceive how the spiral surface might be obtained from 

 the cylindric, than the cylindric surface from the spiral surface. This 

 method of working the arch stones was, I believe, adopted from the 

 year 1828, when my book on Stone Cutting was published, and con- 

 tinued until the year 183G, when Mr. Fox published a small Tract, as 

 an original work on Obliipie Arches, supposing himself to be the in- 

 ventor of all lliat was known upon that subject. He says : — " But I am 

 not aware that any rule has been published that would enable the 

 stones to be wrought at the quarry into the desired form." The tem- 

 plets ndiicli Mr. Fox uses are shown in my Treatise on Masonry and 

 Stone Cutting, plate 17, where the two equal circular-edged rulesj Z, Z, 

 tne straight edge Y, and the arch square 7 are those which he employs. 

 Mr. Fox, after some trials in working arch stones, preferred to form 

 the bed to the spiral surface of each arch stone first; and he was cer- 

 tainly the first to apply the winding straightedges for working the 

 spiral surface of the beds, and to show the angle of the twist. 



Mr. Buck next goes on to reply to the inconsistency which I noticed 

 in certain formula-, in his "Essay," and in one part of his Letter he 

 says :— " Here 1 take the opportunity of saying that, after making tlie 

 discovery of the mutual convergence of the chords of the curves of the 

 joints of the face of the arcli, and after obtaining the formula; appli- 

 cable thereto, I long sought in vain fur a dcmonnlraliun of the gene- 

 rality of this property. On applying to my mathematical friends, 

 both in London and in Cambridge, 1 was equally unsuccessful. 

 Under these circumstances, being experimentally quite certain of the 

 existence of this property, I assume it as a postulate in the "Essay," 



and the whole of the investigation contained in the Tth, a conehidiiig 

 chapter (/lie nnbj part if the murk ivitich lamsiikr thconlical ) is based 

 upon it. The publisher, Mr. Weale, well knows how anxious I was to 

 have given a demonstration in the work, and that 1 was finally under 

 the necessity of publishing it without, allhongh no one appears to have 

 noticed this deficiency." This, Sir, I consider to be a sufficient ad- 

 mission of the justness of my remarks, and one which renders it per- 

 fectly unnecessary for me to allude further to those remarks at this 

 time. Mr. Buck also says: "It is not my wish or intention to be. 

 drawn into a review of Mr. Nicholson's book, but I think it richt to 

 make the following few remarks. In problem '.1, referring to plates 28 

 and 29, he gives directions for radiating the joints of tlie face of the 

 arch in two different ways. By his first method the joints are to be at 

 right angles to a tangent to the elliptic curve ; by the second method 

 they will radiate to the point of convergence, which I have denominated 

 the focus ; this latter method is that given by me, and which Mr. 

 Nicholson has here adopted. Now, if the voussoirs be worked in 

 spiral beds, according to /lin rules, they must necessarily radiate in this 

 way ; and consequently they cannot be made to radiate as described in 

 his first method, unless tlie beds a^e /corked in some other matj, the direc- 

 tions/or irhich he has not given. This dilemma leads me to infer that 

 Mr. Nicholson is not practically familiar with the subject on which he 

 has written. I hive confined myself to the points referred to bv Mr. 

 Nicholson's strictures, or I might have added more on the subject." 



Now, Sir, I will reply to these "remarks" in their order, premising 

 that I never have objected to anyone reviewing my vioxks pro cidtd 

 that they are competent to the task, and provided also that they come to 

 the performance of that task in a fair and manly spirit! Now, Sir, 

 first, as to the radiation of the joints. The lines b h, c i, dj, &c., Cplate 

 28 in my book) are not the joints, neither are they intended to be re- 

 presentations of the joint lines ; they are merely to direct the con- 

 struction of fig. 2, in the same plate, in order to find the angles made 

 by lines approximating nearly to the joint lines of the face of the arch, 

 and tangents to the bed lines, or the angles made by these approximat- 

 ing lines to the joints on the face of the arch and tangents to the bed 

 lines at the points in which they meet the plane of the face of the 

 arch; and, in speaking of these lines in my work, at page lii, I say 

 that the method is a near approximation, and that its simplicity is 

 ample compensation for its introduction. Plate 29 of my " Guide to 

 Railvvay Masonry," was engraved at the same time as plate 20, and is 

 the same in every respect, as regards the construction of the two de- 

 velopements. Plate 20, and its explanation in page 6, was published 

 in Part 2, May 11, 1839, and is referred to at page 27, as being neces- 

 sary in the construction of plate 29. From the difficulty of getting the 

 proofs from the printer, the third part was divided into two half parts; 

 the first of which was published in August, and the second in Novem- 

 ber, at Newcast'e-upon-Tyne, Mr. Buck's work being published 

 in July, and the 29th plate in my "Guide," showing the method of 

 drawing the joints, and which Jlr. Buck says I have " adopted" from 

 his work, being published in August, there was not time for me to have 

 "adopted" his plan, even if I had been driven to such a strait as to 

 think of, or to stoop to, such a thing; and, moreover, I can prove by 

 ray engraver that all the plates in my book were finished four months 

 before the letter-press could be got from the printer, and a very consider- 

 able p,eriod before the pvblication of Mr. Buck's "Essay." The joints 

 in the elevation of the arch, plate 29, are drawn by an entirely different 

 method from that used by Mr. Buck, although it may, perhaps, amount 

 to the same thing, and are found by making the developemeuts of the 

 intrados and extrados of the arch, and transferring the points made in 

 each developement by the joints to its corresponding curve in the ele- 

 vation. These points being joined form the chords of the curves which 

 form the joints in the elevation. We all know, Sir, that "facts are 

 stubborn things," and I leave Mr. Buck to reconcile these facts with 

 his somewhat fugacious assumption that I have " adopted" his plan in 

 my book. 



I now proceed to the second part in which Mr. Buck says — " this 

 dilemma leads me to infer that Mr. Nicholson is not practically familiar 

 with the subject upon wdiich he has written," S;c., and upon this point 

 I will refer Mr. Buck 10 the luth page of the History of Obli([ue Arches, 

 in my work, wliich will, I think, convince him, if he be capable of con- 

 viction, that I was perfectly aware, when I wrote my work, of the 

 nature of the joints in the elevation of an oblique arch ; in addition to 

 this, I may say that I have seen nine oblique bridges on " the New- 

 castle and North Shields Railway," and /fo on " the Brandling Junction 

 Railway," all executed in stone, on the principle laid down by me, 

 making, upon the two Railways yoK/tei; bridges within a distance of 

 about eight miles from Newcastle, luid built, as it were, under my own 

 immediate inspection. To this I may add, that one oblique bridge 

 was built on "the Hartlepool Railway" in 1834, precisely on my prin 

 ciple, and that I have had the satisfaction of seeing all the stones 



