1840.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



275 



doubt will properly appreciate the value of the complement here paid 

 to their ;icquiremeiits by Mr. Nicholson. But I am happy to say that 

 not one with whom I have the pleasure of being connected is deficient 

 of the mathematical knowledge requisite to understand it; indeed, I 

 have in my employ a stonemason, acting as iaspector, who makes use 

 of the formulae, and prefers them to the circuituous and "c/«)«8;/" 

 rules given bv Mr. Nicholson. " Mine is intended as a purely practical 

 work," says he; nevertheless the third part of his "Guide" is headed 

 " Theory of the Oblique Arch." But the fact is, in consequence of 

 his not being " praclically familiar wilh the subject on which he has 

 nri/'tn," his work is altogether theoretical, and in some respects very 

 objectionable in practise, which I could easily show, were I disposed 

 to waste my time in doing so. 



Mr. Nicholson calls his letter an address to me, and concludes it in 

 a dreamy vision of the fame to be awarded to him by '^ posterity," and 

 assuming the motto of the hero of Trafalgar, seems almost ready to 

 exclaim, "Victory, or Westminster Abbey," but to prove how easy is 

 the transition from the sublime to the ridiculous, he closes by saying, 

 " I have now done with him." Very like Nelson indeed ! — He fires 

 his pop-gun and runs away ! 



Your most obedient servant, 



George W, Buck. 



Manchester, July IS, 18 tO. 



To The Editor of the Railway Magazine. 



Sir, — Mr. Peter Nicholson has recently published a work under the title 

 " Guide to Railway Masonr)', comprising a complete Treatise on the Oblique 

 Arch." In his preface and introduction he has made some observations and 

 references to a work on the same subject published last June by me, and to 

 which I am anxious of making the following reply, requesting the favour of 

 your inserting it in your valuable Journal. 



At page 8 of his preface, in speaking of the fonns of the templates which 

 are necessar)- for working the stones, Mr. Nicholson says, " they are not 

 shown by any other author who has wTitten upon the subject. Now, if Mr. 

 Nicholson will refer to the 3rd chapter of my "Essay," he will find that 

 chapter to be exclusively devoted to an explanation of the method of making 

 the templates and working the voussoirs ; moreover, the 5th plate contains 

 eight diagrams exhibiting the forms of those templates. 



At page xiv of his " History," at the commencement of the " Guide," Mr. 

 Nicholson says, "The formula CO = (r + ?) cot 9 tan 3, is due to Mr. Buck. 

 It gives the distance below the centre to the point 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 they are not exactly ; liavuig given 

 the angle of obliquity =8, and the angle in which the bed lines cross the axis 

 of the cyUnders =^, or the angle which a bed line makes with the adjacent 

 springing hne. In this formula also r= the radius of the cylinder, r + e the 

 raihus of the extraJos, e being the breadth of the bed or thickness of the 

 arch." In reference to tins remark. I beg to obsene that not only is the/or- 

 muta due to me, but so also is the discovery of the beautiful and remarkable 

 property of the obUque arch to which it applies. At page 5 of the " Essay," 

 I stated that the joints of the face " are not straight lines, but curies concave 

 on the upper side " : and at page 6 I stated that the chords nf these curves 

 produced, meet in the point to wliich I have given the name of the focus of 

 the elliptic face. I no sooner discovered this property than I made it sub- 

 sen-ient to practical utility, of which any one may be conrinced by reference 

 to the " Essay." The stabiUtj' of oblique bridges is intimately connected 

 with, and dependent upon, this property, and the investigation of the problems 

 relating to the limit of obhquity, and the best proportions for oblique arches, 

 cannot be made without it. At the same page Mr. Nicholson, alluding to 

 myself, writes as follows: — "He says the expression 00 = (r + e) cot. 8, tan 3, 

 included among some others, ' are general, that is, they are appUcable to 



c cot.- S 

 segments as well as to semicircles ; but in page 9 he gives (»• -;- e) 



= CO, the eccentricity or focal distance below the axis of the cylinder in the 

 oblique segment.' " 



This way of stating it will lead any one to the erroneous inference that I 

 have fallen into a discrepancy, and given irreconcileable formulse. The ex- 

 planation is as follows : when it is said " these expressions are general, that 

 is, they are applicable to segments as well as semicircles," reference was 

 made to the two formula: then immediately before given, namely, CO = 

 r cot e tan *, and C0 = ^r + e) cot 9, tan 0. 



Now at pages 6 and 7, it is shown that the tangent of the intradosal angle, 

 or of the angle which the bed line makes with the springing line in an oblique 



cot 9 

 semicircular arch, in particular cases, = -j — and when it has tlus valuei 



thenC0= —^ — ■ (r + e). But because, in practice, this value of the intra- 



dosal angle ought sometimes to be departed from, then the distance CO may 

 be obtained by either of the two before-mentioned general expressions. 

 Again, at page 8 of the " Essay," treating of segmental arches, the tangent 



c c cot- 6 

 of the intradosal angle is given = - cot B ; and in this case CO = 



{r + e). But here, again, as before in practice, this value of the intradosal 

 angle ought not to be always adhered to (it requires adjustment to the par- 

 ticular case, as fully explained in the work), and then the distance CO is to 

 be found by one of the two general formulae before referred to. 



Mr. Nicholson's concluding sentence of his " History " is in the following 

 words :— " One thing which we consider defective in Mr. Bucks' ' Essay on 

 Oblique Arches ' is, that his ir.structions are not enunciated under regular 

 hearls, so as to call the attention of the reader ; he gives no reasons for his 

 rules, nor does he show the principles upon which his formulae depend. The 

 height of the point CO, Fig. 7, will depend upon the breadth of the bed." 



I am really at a loss to conceive what could have induced Mr. Nicholson 

 to make the several incorrect assertions contained in this short paragraph ; 

 and to which I shall reply in their order. 



First, as to my intentions not being enunciated under regular heads : the 

 table of contents, consisting of the heads of the seven chapter into which the 

 w-ork is diviiled, affords a sufficient refutation to this charge. 



Secondly. " He gives no reasons for his rules, nor does he show the prin- 

 ciples upon which his formula; depend." To this it is only necessary to add, 

 that by reference to the work itself it will be evident that the reasons which 

 are geometrical and mathematical, flow naturally from the first principles and 

 contain their "wn demonstration — the best of all reasons. 



Thirdly. "The heiglit of the point 11, figure 7, will depend upon the breadth 

 of the beds." Verj' profound, indeed ! inasmuch as the formula informed 

 him of it. because e in that expression denotes the breadth of the beds. 



Mr. Nicholson, at the same page, in speaking of my " Essay," says some- 

 what affectedly, " as far as we have had leisure to examine it.*^ Surely be- 

 fore any one can be competent to criticise a work he mnst read it, otherwise 

 he will naturally and inevitably fall into such mistakes as Mr. Nicholson has 

 here been guilty of. 



It is not my wish or intention to be drawn into a renew of Mr. Nicholson's 

 book, but I tlunk it right to make the following few remarks. In problem 

 9, referring to plates 28 and 29, he gives directions for radiating the joints of 

 the 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 points of convergence, which I have denomi- 

 nated 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 his own rules, they must necessarily radiate in this way ; and 

 consequently they cannot be made to radiate as described in his first method, 

 unless the beds are worked in some other way, the directions for wliich he has 

 not given. This dilemma leads me to infer that Mr. Nicholson is not practi- 

 cally familiar with the subject on which he has written. I have confined 

 myself to the points referred to by Mr. Nicholson's strictures, or I might have 

 added more on the subject. 



Here I take the opportunity of saying that after making the discovery o£ 

 the mutual convergence of the chords of the cui-ves of the face of the arch, 

 and after obtaining the formulae appUcable thereto, I long sought in vain for a 

 demonstration of the geuerality of this property. On applying to my mathe- 

 matical friends, both in London and Cambridge, I was equally unsuccessful. 

 Under these circumstances, being experimentally quite certain of the existeuce 

 of this property, I assumed it as a postulate in the " Essay," and the whole 

 of the investigation contained in the 7th, or concluding chapter {the only 

 part of the work which I consider theoretical,) is based upon it. 'The pub- 

 lisher, Mr. Weale, well knows how anxious I was to have given a demonstra- 

 tion in the work, and that I was finally under the necessity of publishing it 

 without, although no one appears to have noticed this deficiency. 



However, I have now the gratification of adding that about four months' 

 back my highly scientific friend and assistant, Mr. W. H. Barlow, son of Pro- 

 fessor iJarlow, of Woolwich, has accomplished a beautiful geometrical de- 

 monstration, which, in the event of another addition being called for shall, 

 with his permission be given therein, together with some further practical 

 information and additional investigations which I have recently made. 



I am. Sir, your's truly, 



George W. Buck. 



Ardwick, Mamhester, January 21, 1840. 



MR. BARLOW IN REPLY TO MR. NICHOLSON. 



Sir— I perceive in your last number a commuDication from Mr. 

 Nicholson purporting to be a reply to Mr. Buck, and to the remarks 

 signed W. H. B., which appeared in your Journal for May last. Being 

 the writer of those remarks, I trust j^ou will allow me to say a few 

 words respecting that part of Mr. Nicholson's communication whicli 

 refers to them. 



Mr. Nicholson's observations are chiefly confined to the problem for 

 finding " the curved bevels for cutting the quoin heads of an oblique 

 arch," relative to which I stated that there was considerable obscurity 

 as to what species of joints it referred. He replies, " Now, Sir, I 

 assert that W. H. B. mtist either have been very inattentive or very 

 stupid not to have observed to what species of joints the problem re* 



