378 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[December, 



In the CESS referred to in fig. (2) the tension is said to be " cose a d W." 

 This assertion is not accompanied with any proof. It is incapable of one, 

 for this simple reason — that there can be but six equations for the equi- 

 librium of a system (three of translation, and three of rotation), and in 

 the present case there are an infinite number of tensions to be determined. 

 We presume that Rlr. Dredge knows that simultaneous equations are 

 soluble only when their number equals that of the unknown quantities. 

 The problem is, in fact, an indeterminate one. 



Mr. Dredge next refers to the " pure mathematics of the proposition 

 fig. 3," in our last number. Now, as we said before, we can discover no 

 demonstration whatever of the proposition, except that which may be sup- 

 posed to be contained in the words, " I say that." This'i;(S£ dixit appears 

 to be the only argument employed ; for, as far as we can make out, it is 

 not even professed, that any use or application is made of the pure mathe- 

 matics here written down. It may be very true that the diflerential ex- 

 pression for a tangent is correctly copied from Hall's " Differential Cal- 

 culus," but here no use seems to be made of it. The " proposition" ex- 

 pressed in intelligible language, freed from analytical symbols which have 

 nothing to do with it, seems to be this — that if a chain hang iu a curve 

 between two points, and be acted upon by any forces applied at different 

 points, that then, if oue of these forces be tangential, the tension of the 

 chain is zero between the point of taugency and the lowest point of the 

 curve. This is not true. It certainly may happen for a particular case, 

 where certain relations hold between the amounts and directions of the 

 pressures, that the tension in question becomes zero. But Mr. Dredge 

 asserts this as a general and necessary proposition, which it most decidedly 

 is not. 



It was also stated in the former paper that " the horizontal force is a 

 constant quantity iu the polygon of pressure." It seems scarcely too 

 severe to characterise this as perfect nonsense ; and it may almost be sus- 

 pected that here mathematical phrases are used without any apprehen- 

 sion of their meaniug. 



On these mathematical points we certainly think further discussion 

 unprofitable. If Mr. Dredge will reply to what has just been said, we 

 suppose he must be allowed to do so : but he must excuse our giving any 

 further answer lo his mathematical observations. 



We follow Mr. Bashforlh in this determination of giving up fur- 

 ther argument, and nothing will induce^ us, to alter our resolve, unless 

 Mr. Dredge can bring the written declaralioo of some really competent 

 mathematician, explicitly confirming his mathematical notions. 



Let it not, however, be concluded hence, that, because we condemn 

 Mr. Dredge's mathematics, we consider his invention a useless one ; on 

 the contrary, there is one part of it which we consider very valuable, and 

 that is, the varying thickness of the main chain. We will briefly state 

 our reasou for this. M'hen a heavy chain hangs in a curve between two 

 points, the tension is greatest at these points ; and the less the inclination 

 of the chain to the horizontal, the less the tension. Consequently, the 

 lowest point of the chain is the point of least tension, and therefore less 

 strength of the material is required at this point than at any other. The 

 same remark holds good where the chain is equally loaded throughout — 

 that is, where the weight of the platform is distributed equally, and at 

 equal horizontal distances along the chain. 



Unfortunately, however, Mr. Dredge, like all other inventors, has 

 carried his principle too far. Because the lowest point of chain is the 

 point of least tension, he concludes that it may be arranged that there 

 shall be no tension at all at that point : that the chain may actually be 

 severed there without danger, and that the two parts of the platform will 

 stand as two independent brackets, if sufiicienlly strong to resist com- 

 pression. He lays great stress ou the words " if the railway be strong 

 enough to resist the compression ;" but the fact is, the railway must, if the 

 bridge be cut into two, be strong enough lo resist not only compression, 

 but the slightest bending also. For if it be conceived that a bracket, com- 

 posed of several parts hinged together, is suspended half across a river by 

 chains from the bank, it is clear that if one piece of the flexible bracket 

 be displaced in the slightest degree the whole must, so to speak, collapse. 

 This may be illustrated by the following simple experiment; let a number 

 ofbeams A^B, B C, C D, D E be hinged together at B, C & D, and 



let them be made to stand out from the wall at E, being also suspended 

 by oblique strings as in the diagram. Now if this fragile structure be in 

 the slightest degree disturbed so as to present the following arrangement 



the whole must fall together. In fact, the structure is no securer than a 

 child's house of cards. 



It is very true, that if the platform be made perfectly rigid it can never 

 assume the position of the second diagram. But then if it have this 

 rigidity it becomes a girder-bvidge, and the increased strength of the main 

 chain requisite lo support the increased weight of the girder would be so 

 great, that it would be belter to dispense with the chains altogether, to 

 unite the two independent girders which we suppose banging over the 

 river, and when they are connected at the centre, to let the whole rest 

 upon abutments on either bank. 



The |only bridges which we have of Mr. Dredge's, those in 'the Ee- 

 gent's Park, certainly have not the rigidity of girder bridges : they have 

 quite pufticient flexibility to produce the etlect explained above, supposing 

 they were divided at the centre. We do not tliiuk that any one who has 

 seen them, except, perhaps, the inventor, would like lo stand on them 

 while the experiment was being made. 



It is to be remembered, that the bridge at Calcutta gave way by break- 

 ing at the centre, 



Ou the whole, therefore, it seems clear, that Mr. Dredge's system of 

 lessening the thickness at the chain at the centre has a limit. We are 

 convinced that no practical engineer of reputation would consent to con- 

 struct a suspension bridge without a very ample provision in this re- 

 spect. 



The other distinguishing feature of Mr. Dredge's invention is the 

 obliquity of the suspending rods. On this point we will not speak posi- 

 tively, but our present impression is, that this arrangement does not permit 

 any saving of material in the main chain. On the contrary, it seems that 

 the obliquity of the suspending rods demands a greater strength iu the 

 main chain than would otherwise be required. Our reason for this 

 opinion is as follows, though it is tu be understood that we do not in this 

 place speak with abslule certainty. 



It is clear that with either arrangement the vertical parts of the tension 

 of the main chain must be together equal to the weight of the platform 

 (neglecting the weight of the suspending rods)— that, is the upward force 

 exerted by the main chain must, on the whole, be equal lo the downward 

 force exerted by the weight of the platform, however it may be sus- 

 pended. We know that if a man raise a weight attached lo two strings, 

 he must use the same exertion, whether the strings be parallel or converge 

 to a point. If, then, the upward parts of the tensions of a main chain of a 

 given curvature must be the same for both Mr. Dredge's and the old plan, 

 it seems to follow that the strength of material must be at least as great 

 iu his plan as the other. And when we add to this the consideration that 

 the obliquity of the chain necessitates an increased amount of the hori- 

 zontal part of the strengih of the chain, and also that the platform niust be 

 made stronger to resist the horizontal parts of the action of the oblique 

 rods, it seems that we have two items to add to the account in estimating 

 the requisite strengih of material, which would not appear if the rods 

 were supposed vertical. 



We have thus, as well as we were able, stated what appeared the merits 

 and defects of Air. Dredge's plan. It were much to be regretted that 

 any remarks here made should impede the introduction into general 

 practice of the valuable part of the invention. We again repeat, that the 

 diminution of the ttiickness of the main chain towards its centre is a most 

 useful aud philosophical method of reducing its necessary weight ; but 

 we must couple with our commendation the opinion that Mr. Dredge has 

 carried this principle beyond its just limits. 



One point more we have to allude to before quitting the subject. Mr. 

 Dredge commences one of his letters by saying " I can perfectly under- 

 stand why the alteration iu my father's letter was made." This, if it mean 

 anything, implies intentional dishonesty on the part of the editor. Surely 

 »o grave a charge ought not to have been made without some reason, how- 

 ever trifling, being alleged in confirmation. So severe an allegation might 

 well provoke an angry retort ; but a scientific journal is not the proper 

 medium of expressing personal feeling, however justly it may have been 

 aroused. The discourtesy is not only gratuitous, but excessively ungene- 

 rous : for, throughout the discussion, we have treated Mr. Dredge with 

 every consideration — we have allowed him ample room and verge 

 enough for the discussion of points of comparatively personal interest — 

 we have publicly acknowledged his candour and readiness in supplying 

 us with iiiforniatiun— we refrained from any expression of opinioii till 

 compelled by the extraordinary nature of his doctrines — and we have the 

 satisfaction of thiukiug that even in the present reply, himself will be un- 

 able tu discern any traces of vindictive feeling. 



