18-16.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



73 



A Complete Treatise on the Oblique Arch. By Peter Nicholson. Third 

 Edition. London: Groombridge, 1846. 8vo. pp. 110; 43 lithographic 

 plates. 



This is a new edition of a work reviewed in a former volume of this Jour- 

 nal. The object of the treatise is confined to the explanation of the geome 

 trical forms and position of the Voussoirs of Oblique Arches, and does not 

 comprise the mechanical theory of these structures— the subject is in fact a 

 particular branch of Descriptive Geometry. The three preliminarv chapters 

 treat of those principles of plane and solid geometry which are neceisary to 

 the explanation of the construction of oblique arches ; the theory of which 

 IS divide-} into two portions-the theory of oblique arches, with spiral joints 

 and that of oblique arches with plane joints, the distinction between the two 

 kinds of arches is thus defined. 



J'^ oblique flrcA with spiral joint., is that in which the surfaces of the beds 

 and the surfaces of the joints are both spiral surfaces. 



If an oblique arch with spiral joints be executed accordine to the nrinci 

 pies here established and cut by a plane perpendicular to the axis of the cv" 

 bnder, the section w,ll exhibit a series of straight lines, dividing the are of i 

 circle^ into smaller ares, and the lines being prolonged, would meet in the 



An oblique arch with plane joints is that in which the beds of the stone, 

 are planes, passing through the axis of the cvliiider. The iilane-T nf ti 

 joints being parallel to the axis, intersect each face of the arch in verv 

 oblique angles, and only one of the joints can be perpendicular to tl"e flee 

 AI the her joints, as they recede from the centre, are more and m^,?; 

 oblique till they reach the summit of the arch. As eve v oblimie ini^f 

 the angWs made by the face and that joint to beve^y "i^qu^ 'eoM e::!' 

 will be muchstrongerthan that which is acute, theseandesbeinff ,,,„?! V 



t:fT"- Vr'^'l """'^"^ ^^^''^ "'«■ PlanrgLts'sh'o ^'"n'eTert 

 used where great strength is necessary; and where the angle of obliouftv is 

 very acute, tteobhque arch with spiral joints should only be emSe7 

 Im admit!"" '''"'"'' perpendicular to the face as' the construction 



Of course in a work like this one of the first requisites is simplicity and 

 precision language. The dimculty of conveying by words (and even by 

 diagrams) clear ideas of solid geometry can only be overcome by the mos 

 scrupulous adherence to the plain and uncomplicated modes of expression* 

 Our author seems to have generally paid great attention to this point" 

 Among the new portions of the present edition is a description of an oblique 

 budge over the river Gaunless, to which the following general observation, 

 are appended. ' 



it 'i'7^r" u"i" '" ""'''"' '''■' ""''■■'"'5' °f ^'""e is. in some countries where 

 It IS difficult to procure, verv expensive. However in nrrlp,- 1„ i -ij 

 which will be sufficiently strong at'a moderate pr" i s ecTs sary that "Z 

 imposts or spriugings should be of stone, and, to have thetppe^tf 

 .good work, the quoins which form the ring.stones and the head of the arch 

 should also be of stone Then the intermediate parts of the courses may be 

 of brick, (allowing perhaps fou, courses of bricks to each stone sprTn/erl 

 depenmng on thickness at the abutment. To work the springers and^ the 

 quo.n heads the same templets will be required as if the arch had been con 

 structed entirely of stone. Previous to setting the brick eourserthe board! 

 .ng or laggings should be truly adjusted and fixed ; and, for th; regularion 

 of the work, the bed-lines should be drawn thereon in the r true Sn^n 

 order to try the work as the bricklayer proceeds, he ought to use a ki, d of 

 set-square, made of thin board, containing an angle exactiv the reverse of the 

 templet; and, consequently, the curved edge will be concave instead of he ne 

 convex, as in the arch-square. The sides of each course being m de "o a'ef 

 vvith every application of the set-square, will be what it oSg" to be In 

 stone courses, if he stones are truly wrought, the spiial surfac^e of the'beds 

 w, I all agree with a set-square ; and, therefore, in this case it will be unne 

 cessary to provide one. uc unne- 



There are several useful trigonometrical tables appended to the work in 

 order that the mason may find in it all the information which he requires 

 without the rouble of referring to other books. The plates are well exe: 

 cuted. At the end of the volume we regret to see several '■ testimonials re- 

 garding the success which the author has had in the appHcaHon of his prin- 

 ciples to the execution of oblique arches." These testimonials appear to be 

 satisfactory in themselves, but thev arc nut nf „i„» <-. . ■ . 



' J. . ' "" ""^e out of place. Geometric princ pies 



are not patent medicines. '^ 



Coneise Tables to FaoilHate the Calculation of Earthworks required in the 

 Construction of Railways, &rc. Bv Tohv HTTr-nro w • r , 



T?(K k ITT-, ,„,f. ' ^ Hughes, Engineer. -London: 



Effingham Wilson. 1846., 12nio., pp. 26. 



This is a very useful litile book, and th^ portable form which it assumes is 

 not Its least recommendation. The object is to determine the volume of the 

 solid formed by earthworks in cuttings and embankments I 



There is this difficulty in determining this solid, Ihat'only one side of it ' 



is rectangular or of the same width throughout— namely, the plane sur- 

 face of the roadway itself,, which, in embankments, is the highest, and ia 

 cuttings the lowest side of the prismoid; the other sides of this solid vary 

 in all their dimensions, and though two sides opposite to each other may 

 be of unequal areas. For instance, in a cutting which commences at the 

 foot of a hill and terminates at a tunnel, the depth of the cutting gradually 

 increases, so that the perpendicular face at the mouth of the tunnel is of 

 greater area than the parallel vertical plane, supposed to be drawn at tho 

 base of the hill. The two oblique sides of the cutting also necessarily 

 widen as they approach the tunnel. Opposite portions of them may also 

 be unequal to each other, the depth of cutting to the right and left of the 

 railway depending on the original form of the hill. Mr. Hughes takes a 

 very simple method of ascertaining the solid content of the prismoid. He 

 imagines it divided into numerous small portions by vertical planes pa- 

 rallel to the faces at the commencement or end of the cutting: so that la 

 fact, the solid is considered as made up of numerous tliin slices of equal 

 thickness, but varying in their vertical areas, v.hicli are trapeziums. It 

 is clear, that by ascertaining the area of each of these trapeziums, takeo 

 at a certain determinate interval, the solid content of each slice may be de- 

 termined by knowing its thickness; and, adding all the solid contents so 

 found, we have the total volume of the cutting. The same method of 

 course, applies to embankments. It is important, however, to remark re- 

 specting the method here adopted, that the more numerous the cross 

 seclions are, the more closely will the result approximate to absolute 

 accuracy. 



It is clear also, that Mr. Hughes's method contemplates the case in 

 which the upper side of the solid is curved. The tables hitherto published 

 have referred only to the particular case in which the solid is bounded by 

 planes only. Tiie following extract may be introduced to show how far 

 the present work differs from those of an analogous nature which bavei 

 preceded it : — 



In extensive works, snch as railways and canals, the value of the earth- 

 work is about one-fourth of the entire cost of construction ; and, therefore 

 we find that engineers have given their attention to correct the approxima- 

 tions with which, in past times, the parties were satisfied, as well who 

 executed road and canal works, as their superintendents. The appearance 

 of the elaborate tables of Macnedl, and of those in a more condensed form 

 attributed to Bidder, went far to eradicate the practice, almost universally 

 prevalent, of taking average heights from a longitudinal section, or of 

 averaging the areas of the cross sections; a practice recommended by its 

 facility of application, and having nothing in its form, until reflection was 

 bestowed upon it, to excite suspicion of erroneous results in the minds of 

 those who were deeply interested in its truth. The damage to the interest 

 of contractors, in point of quantity, was, however, in all probability no 

 more than equivalent to the additional price paid to them for executing the 

 work ; but all arrangements which depended on balancing embankments 

 and cuttings were frequently found to be unavailable, and the disappoint- 

 ments from this source were set down to a change of bulk in the material 

 removed, which was assumed without sufficient examination, and which 

 until more competent persons took such arrangements into their own 

 hands, covered the ignorance of the surveyors from the eyes of their em- 

 ployers. 



Bidder's table requires that the longitudinal dimensions should be taken 

 with a Gunter's chain, a standard never introduced in the drawings or 

 specifications of the architect; and, as well as Macneill's tables, does not 

 extend to heights greater than 50 feet, whilst cuttiugs occur on railways 

 more than 100 feet in depth. At the entrance of tunnels they are rarely 

 less than 70 or 80 feet, and embankments of 80 feet in height are not un» 

 common. I naturally, therefore, directed my attention to the means of 

 obviating this inconvenience by employing the general formula for the con- 

 tent of a prismoid, of which Macneill gave a demonstration as applied to 

 a restricted case, and upon which restricted case both his tables and 

 Bidder's were calculated. The particular case taken by Macneill, is that 

 of a solid bounded by a horizontal rectangular plane at the bottom ; by 

 two parallel, trapezoidal, vertical planes, of unequal heights, at the ends; 

 by two trapezoidal planes, equally inclined, on opposite sides of the ver- 

 tical, at the sides ; and by a sixth plane at the top, passing through the 

 parallel bases of the end trapezoid. 



The Sdipension Bridge at the Falls of Niagara. — It is proposed 



to construct a auipenslon bridge above ttie Falls of Niagara, so as to join the Canadiaa 

 Railway and the United States. The execution of It is to be conSded to Mr. Charles 

 Ellett, of Philadelphia, or to Mr. John A. Roehliiig, of Pittsburg. Mr. Ellet lately visited 

 the spot, for the purpose of examining the locality, and to ascertain the practicabilUy of 

 erecting so great a desideratum, There is a bridge which exists about a mile and a half 

 belew the cataract, and near the gulph, or whirlpool, where the distance of the two chief 

 abutments, from oae side to the other, does not exceed (J40 ft. The expenses for con- 

 structing this bridge are estimated by Mr. Ellett at 43,200/., for wflich aum he offers to 

 build it, and he lubscribes Imngelf to the amount of 4,J20f. 



10 



