1S4.5.1 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



339 



v/i(iif thill Iht' demonstration teas »nine— which, not beinK the fact, is ini- 

 (c.^siblc; and then he must prove that the inveniion teas the conseqticiit nf it 

 — which is absurd ; failing at eilht-r of these and Iris arijunw iit fails, and 

 115 bolh are impossible his remarks, are worlhless. If Mr. Hashforlh had 

 .inly iiiUnded to undermine the argument, he should uot have extended 

 I 1. rtinarks lo the principle. 



if I hud told you that a pound weight placed upon the table caused a 



I itssun- of two pounds, I should have staled a manliest absurdity. Let a 



weight of 1875 tons be attached lo the point 15, lig. 1, then there 



^''l■• !• will be 1875 Ions of tension in the cord A 15, and 187.5 Ions of 



A passive resisliiuce at the point A. This is an example to which 



— ^ Jlr. ISashfortli ought to have applied his comparison, and not to 



that I gave in my previous letter, to which if you refer you will 



see that I supposed the cord to pass rouiid a pulley C,and a force 



or weight equal to 1875 tons attached at each end, A and 15 ; 



there is. therefore, 3750 tons of pressure, lb7.> tons of tension iu 



O the cord, and 3750 tons of passive resistance. 



n But to take an example which will directly bear upon my first 



expression. Suppose the poini A and B, fig. 2, to be in the same 



horizontal line, let a wire (^void of weight) .A. CB be suspended from them, 



Fig. 2. 



and let a weight W be applied at the centre C, ,i= Z D AC=: / D B C, 

 and T^lhe measure of tension in Ihe wire A C H ; Ihen 



T = J \V cos o. 

 But if W be supported in a projection at an Z = a, the tension excited 

 must be=W cos a. Let us see if this is not the case. At the point A 

 a resistance must be applied in the direction of the ariow = i W cos a, and 

 aimllarly at B a resistance is required = J W cos o, and the sum of these 

 resistances (which are solely caused by the action of the weight W,) is 



5 W cos a + J W cos a = W cos a, 

 Consequently the tension must be \V cos a, half of it (or J W cos o) acting 

 IN each direction. 



I believe 1 have now fully replied to IMr. Bashforth, and if anything is 

 passed it is an error of omission which does not proceed from a wish to 

 avoid discussion; I have no fear of the ordeal he talks about, and beg to 

 band you a proposition for his consideration. 



PkoPosition.— Let A B C, fig. 3, be a cord or string void of weight, and 



suspended freely between two fixed points A and C, lake B Ihe origin. 

 Suppose pressures applied to this curve, and let I'j U be a line repre- 

 senting the direction of one of these pressures, and (i/^ — y)=« (■'"i— ^") i's 

 equation, where .r and y are co-ordinites of the poiut 1' through which 

 it passes, draw P, T a tangent to the curve at the point P, so that 



rf ;, 



(!',-y) = 



(t, — x) where tan m = IV^V P,. 



Now I say that the smaller tan-' m is, the less is Ihe tension beyond the 



poiot P ; and finally, when tan-' m=tan-' 0, or tan-' a=lan-' — J, and 



d X 

 d y 

 the equation becomes (yj—i/)=-r^ {x^ — x)={y, — y\, that not any tension 



at all exists between the point P and the point at which the axis <if .r in- 

 tersects the curve, and consequently the segment P B may be removed 

 without at all ell'ecling the equilibrium of the segment P C. 

 I remain. Sir, 



Your obedient servant, 

 Banbiidge. Counttj Armagh, Ireland, James JJki'dge. 



October 4, 1845. 

 P.S. In your remarks page 307 you observe it can scarcely be supposed 

 but that there is some limit in the reduction of the central bars. There is 

 ♦10 limit, for in any bridge on my plan, however large, the central link may 

 be entirely laken away without affecting the stability of the structure, 

 niiich is evident from tie above proposition ; nay more, if the roadway be 



sufliciently strong to resist the compression, Ihe platform itself may be 

 diiiiled iu the centre, thus separating the bridge into two independent 

 biiulcets, and it wouhl still he us strong as ever to resist passing loads. 



l!y Ihe sentence " transferred lo and distributed, &c.," I do not mean 

 that the tension is lessened, this would be evidently absurd, excepting in 

 as fur as the reduction of tension from lessening the weight of the structure 

 is concerned. What I meau by " transferred" is this, ihat the horizontal 

 force, which is a constant quantity in the polygon of pressure, is transferred 

 fr.jin the chains to the plutrorni ; and by " distril/utcd," that the whole sec- 

 tion of the roadway is active to resist that tcnsiou. Those points must 

 necessarily be iliscussed if a controversy ensue with Mr. Bashforth, and 

 if it do not, then I will give you the particulars in a subsequent number. 



J. D. 



[Ue have inserted Mr. Dredge's letter at full length, that he might have 

 no reason to complain of injustice on our part. J5ut we must now beg to 

 remind him that there is a limit beyond which a controversy like the pre- 

 sent ceases to have any public interest. The discussion commenced with 

 the avowed object of eliciting the mathematical principles of Mr. Dredge's 

 bridges : but we have now, on the one linnd, the expressed opinion of Mr. 

 Basliforlh that the problem is not susceptible of an analytical solution ; on 

 the other, we have from IMr. Dredge a specimen of inathemalics, which, 

 to say the least of it, is totally dillereut from any thing iu standard works 

 on Mechanical Philosophy. 



The tension referred to in fig. 2 is wrongly determined. The horizontal 

 parts of the tensions of A C, B C respectively are T sin CAD and T giu 

 C B D, and the sum of these forces is 2 T sin o. Consequently 

 W 



T=:; — , instead of " i W cos a. 



2 sill a ^ 



This error pervades the subsequent remarks. The expressions "T=; 

 i M cos a" and " llie tension must be W cos o" are inconsistent with each 

 other. The notion of half the tension " acting in each direction" is not to 

 be found in any recognized treatise on statics. 



The " proposition" of fig 3 seems, as far as we can make any meaning 

 of it, as incorrect as Ihe preceding one. No demonstration of it is given, 

 cxcppt what may be supposed to be contained in tlie words '• I say that — ." 



'ihe most important part of Mr. Dredge's letter is, however, the post- 

 script. It is now put on record, by i\lr. Dredge himself, that a bridge on 

 his principle consists of " fu-o independent brackets ;" that •' the central link 

 may be taken airaij u-llhnnt uffcriing the stability of the structure;" that 

 ' the pliilform itself may he divided in the centre." 



It is now, thereVore, a question for the practical engineer to decide, — 

 whether the roadway of a bridge can be made sufficiently rigid to act as 

 the arm of a bracket perhaps 200 feet long. 



This question we sliall leave entirely to the solution of practical expe- 

 rience, for we cannot devote our space lo the particular kind of mathema- 

 tics which Mr. Dredge has originated.]— Ed. 



ATMOSPHERIC RAILWAY.S. 



ABSTR.iCT OF THE EVIDENCE BEFORE THE COMMITTEE OF THE HOCSE 

 OF COMMONS. 



fConlinued from page 317.J 



Obslrnctions. — The piston carriage might be constructed so as to remove 

 obstructions from the line — {lirunet.) 



" In the case of any impediment, upon the line, I think the weight of the 

 Incciniotive engine is an advantage in throwing the impediment over the 

 rails, as compared with the atmospheric train, which is much lighter. I 

 think it would be more than counterbalanced by many other circumstances 

 of safety; and I th^nk it would be very easy to construct the front of the 

 piston-carriage so as to throw any obstruction of that sort on one side, and 

 to (liiriinisli very much the chances of its falling immediately in front and 

 being run over. But I should observe that those things are very rare ; I 

 only linow of one instance on the Great Western Railway where any acci- 

 dent would have resulted, or did result, from running over an animal." 



Passing of Trains. — Suggestions as to the mode in v\-iiich the trains should 

 pass one another on a single line of railway ; amount of delay that will be 

 occasioned by this passing — [Vubitt.) 



" One train can pass another by instructions to the train arriving which is 

 to be passed, by a telegraph for that train to be detained on the platform till 

 the express train has passed it. As soon as the train is in from those in- 

 structions, the lever would be turned to bring the coming-in train through 

 tlie crossing into the other line ; it would then pass into the next pipe with- 

 out coming into contact with tlie train which is stopped. The train so passed 

 would be delayed only during the time that it would take to get up the va- 

 cuum in the next pipe ; three or four minutes. And the time that it would 

 require to run through the pipe.' — .\ltogether about eight minutes, perhaps. 

 To what extent would that delay the train beyond its usual time .= — Just 

 half that time, four minutes; because one of the operations would have to 

 be done for that train, namely, pumping out. Suppose that the train so 

 passed did not recover its lost ground by greater speed afterwards, it would 

 have the effect of delaying the train it met, would it not.' — To that extent; 

 therefore I think the thing is not so well adapted for express trains: excepc 



