1S4I.1 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



253 



the hope that you may think them deserving of a place in your forth- 

 coming number. 



The two characteristic features of Mr. Dredge's bridge appear to 

 be the unequal thickness of the chains which taper from the middle 

 1 oint of the curve to its extremities, and the inclined position of the 

 suspension rods. 



A chain whose thickness is equal throughout being suspended from 

 its extremities, assumes the form of a curve which has received the 

 name of the Catenarian curve ; the tension to which the chain is sub- 

 ject by its own weight, varies as the secant of the angle made by the 

 tangent on any point, with a horizontal line, or, which is the same 

 thing, as the secant of the angle contained by (lie tangent and ordinate. 

 It is obvious, therefore, that the tension will be least at the lowest 

 point of the curve, and increase towards the points of attachment, 

 where it will be a maximum. In a chain of equal thickness its strength 

 cannot therefore be proportionate to the stress to which it is subject, 

 and it therefore naturally occurs that the chain should not be of equal 

 thickness throughout, but be increased in sectional area from the lowest 

 point of the curve to the highest. By mathematical analysis, the form 

 of chain has been determined whose sectional area is always propor- 

 tional to the tension ; and a chain constructed upon this principle has, 

 I believe, been actually adopted for the large suspension bridge erect- 

 ing over the Avon by Mr. Brunei. 



The idea of a chain of varying thickness is not therefore new, and 

 as regards Mr. Dredge's bridge, the utility of the form of chain he has 

 adopted appears to depend upon whether the sectional area varies as 

 the tension at each jioint. Considering the chain in the first instance, 

 as simply affected by its own weight, this point would be determined 

 by comparing its form with that in which it is known the sectional 

 area varies us the tension. I have not at this moment with me the 

 means of making the comparison, but it is evident that if the two forms 

 are identical, there is no novtlty in this part of the invention, and if 

 they are not, Mr. Dredge has proposed a form which is inferior to one 

 that would always be employed when rendered proper from attendant 

 circumstances. Except in large bridges it has not, however, been 

 considered desirable to vary the thickne.~s of the chain according to 

 the tension, as the ditference of thic;kness at ditterent points is found 

 too inconsiderable to merit attention. It seems, therefore, extremely 

 probable that Mr. Dredge by varying the thickness of his chain in a 

 very rapid ratio has far exceeded the increased thickness required by 

 the tension. 



Abstracting now for the sake 

 of argument, the effect pro- 

 duced by the weight of the 

 chain itself, and regarding only 

 that occasioned by the tensions 

 of the rods, it will be observed 

 that these tensions are much 

 increased by the inclined p<isi- 

 tions which the rods are made 

 to assume. This is illustrated 

 in the tigure. A B C is the 

 chain, X Y the horizontal plat- 

 form, and a b, a' b, &c. the 

 suspension bars. Let us sup- 

 pose that the tension of the bars has been adjusted so as to be equal 

 for all, and that the weight of the platform is known. If it be homo- 

 geneous in its structure, the centre of gravity will be at 6, and the 

 weight maybe conceived as a force B D, acting in a vertical direction 

 through this point. Each of the pairs of forces acting along the rods 

 a b, a' b, &c., will have a resultant acting in the direction D B, oppo- 

 site to that in which gravity acts. These resultants Vidll also be equal 

 to one another, and, supposing the platform suspended from two chains, 

 their sum will be a force equal in magnitude (though opposite in direc- 

 tion) to half the force B D, the weight of the platform. Hence if this 

 weight be given, we obtain the resultant of each pair of forces acting 

 along oppositely inclined rods, by dividing half this weight by half the 

 number of rods attached to one chain. Let the angle made by the 

 rods with the vertical be e, w half the weight of the platform, and u 



the number of rods, then the resultant of each pair of forces^ t—' 



4 n 



Hence 



And b the tension of each rod is i X 



5 n COS. e n cos. 9 



6 Ct Ct sec. 9, and is consequently least when sec. S is least, j. e. 



COS. 8 



when sec. 9=: 1, or the rods are vertical. This arrangement, then, 

 appears disadvantageous, since it not only requires that the rods 



should be made of increased size to resist the increased tension to 

 which they are exposed, but subjects also the chain to increased pres- 

 sure from the rods in the ratio of sec. 9 ; 1. 



Although the forces acting upon the two halves of the chain are in- 

 clined in opposite direction, it will be observed that the two halves 

 are precisely similar, for if we imagine one-half to revolve round the 

 axis B D, till the plane in which it is situated, coincides with the 

 plane of the other half, the suspension rods of the two halves will ex- 

 actly coincide, and consequently as the forces produced by them are 

 equal, coincident in direction, and have similar points of application, 

 the curves produced will be identical in all respects. Being produced 

 by equal and parallel forces uniformly distributed along the curve, they 

 belong to aCat'mary whose ordinate is at right angles to the directions 

 of the rods. Hence the tension caused by the action of the rods varies 

 according to the law already stated, and if it be required to equalize 

 the sectional area and tension of the chain, it must be constructed of 

 the form already determined for the Catenarian Curve. Whether, 

 then, we consider the effect of the weight of the chain itself, or the 

 pressures produced by the suspension rods, the chain should be con- 

 structed upon precisely the same principles as in the onlinary suspen- 

 sion bridges. For these reasons I cannot but regard the plan proposed 

 by Mr. Dredge as inferior to the ordinary method of construction, and 

 I have accordingly, a contrary opinion having been maintained in your 

 pages, ventured to offer these remarks to the consideration of your 

 readers. 



I am, Sir, your's obedientlv, 



G. F. F. 



Sandon Bury, July 1-1, 1841. 



MR. PARKES' NEW THEORY OF THE PERCUSSIVE 

 ACTION OF STEAM. 



In this highly enlightened age, when long established theories 

 crumble to dust under the all-searching glance of modern science, and 

 the discoveries of our fathers, eclipsed by the surpassing splendour of 

 the productions of modern genius, hide their diminished heads, it 

 would perhaps be a mark of weakness of intellect to express astonish- 

 ment at any new doctrine, however contrary it may be to our precon- 

 ceived notions, or apparently so to the fundamental laws of nature. 

 If, then, we were not surprised, at least our interest was excited in a 

 high degree by the perusal of Mr. Josiah Parkes' Paper " on the Ac- 

 tion of Steam in Cornish Single Pumping Engines," published in the 

 Transactions of the Institution of Civil Engineers, Vol. 3, Part 4, 

 wherein he developes, or rather announces a new principle of Action 

 of Steam in Cornish Engines, which seemed at the first glance to point 

 out a means of increasing almost indefinitely the dynamic effect of 

 steam in steam engines ; though why he considers it to operate in these 

 engines only we know not — we are of opinion, that, if it obtains in 

 them, it should obtain a fortiori in Locomotives, where the density and 

 velocity of the steam entering the cylinder are so much greater. This 

 new Principle is denominated by its discoverer the Percussive Action 

 of Steam, and is announced in the following words, page 268 : 



" Steam, in its action on the piston of an engine, has hitherto been 

 consiilered as simply exerting elastic force." 



" Steam, however, possesses another important property, equally 

 inherent in its nature with pressure and expansibility. This property 

 is the velocity and consequent momentum due to steam of high elasti- 

 city ; a force which comes into play under the peculiar conditions of a 

 Cornish engine. The velocity of steam, in passing from a dense into 

 a rarer medium, is immense ; and the momentum of this steam must 

 be very considerable. On the sudden and free communication effected 

 between the cvlinder and boiler of a Cornish engine, the steam in the 

 cylinder receives an instantaneous action, proportionate, in amount, to 

 the velocity of the entering steam, and this action, by the property of 

 fluids, is transmitted to the surf.ice of the piston. This action, thus 

 transmitted to the piston, and due to the communication suddenly 

 established between the highly elastic steam in the boiler, and the 

 steam in the cylinder, may be likened, I conceive with great propriety, 

 to the force of percussion ; by which term I propose to distinguish it 

 from the action of the steam's simple elastic force." 



This force is illustrated in a note at the foot of the page by a com- 

 parison with the Pile-driving Machine and Hydraulic Ram; we think 

 the following illustration much more appropriate. 



Let d ef g in the annexed diagram represent the section of a cylin- 

 der, in which the piston;; can move air-tight, let the latter be con- 

 nected by a link a to one end of the vibrating beam b, a mass M being 



