300 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[Oct. 



tliat by a proper disposition of stispensiou rods, aa enormous saving of 

 niult-rial may be elfecleil. 



In some ofthe piiblislicd views of the Tubular Urid^^'e, llirre are repre- 

 sented curved chains, similar to those of coninion suspeusion bridges, meet- 

 ing llie tube at a very acute angle. The only points where these suspen- 

 sion-chains are attacked are their extremities, and as they are unprovided 

 ^ith vertical rods, their action is extremely indirect, the greater part of 

 the tension being revolved horizontally instead of vertically. A more in- 

 efficient contrivance could scaicely be suggested. 



If hov\ever ruii/infu/ rods be applied according to the plan explained 

 by Mr. Bashforth, in a former number of this Journal, the result is very 

 differenl. Let the diagram represent a section of part of the bridge and 



one abutment-tower. BD E one of the straight suspending rods joining 

 the points D and E of the bridge directly with the top of the tower. 

 Then the perpendicular distance of B E from the abutment is equal to 

 A C, and the moment of the forces about A is the tension of the rod multi- 

 plied by the length of AC. This length may be termed popularly the 

 leverage of the rod. But the leverage of the horizontal forces in F D will 

 never exceed A F, the height ofthe bridge, and consequently the efficiency 

 of the material in B D, over the material in F D is the proportion 

 A C : A F. If we suppose the height of the towers to be 80 feet, (the 

 height of the towers ofthe Hungerford Bridge), and E to be at the centre 

 of the bridge, we shall find by simple trigonometry the proportion A C : A F 

 equivalent to 2'985 to 1, In other words by putting the material in the 

 form of a straight rod the efficiency is in this particular case nearly trebled. 



The enormous increase of strength for a given quantity of material which 

 this reasoning demonstrates ought scarcely to be neglected. Even if we 

 look at the question practically without regard to definite mechanical prin- 

 ciples, it seems clear from a mere inspection of the diagram, that the rod 

 B D exerts au upward pull or strain applied directly to sustain the bridge 

 and that the action of F D is comparatively indirect and inefficient. 



But there is another great advantage in the use of suspending rods — 

 that they act by tension only. Where the metal is applied to exert a 

 thrust it will give way far sooner by bending than by actual disruption, as 

 the recent experiments abundantly prove : but where it exerts a tension it 

 can only fail by being torn asunder. If it were accidently bent, a thrust 

 would tend to bend it still more,— a tension to straighten it again. 



It will be seen by reference to Mr. Bashforth's paper that the effect of 

 the expansion of the rods in summer would be so small that it might safely 

 be neglected, and small as it is, it would be almost entirely compensated 

 for by the expansion of the masonry of the towers. The sinking of the 

 bridge from this cause would not be nearly equal to that due to a heary 

 load. The rods could never become loose and cease to exert a tension. 

 Even if we suppose they could do so, their value as means of security 

 would still remain the same : for this is certain— the bridge could never 

 actually give way under the elfect of a heavy load until the rods were 

 broken. 



The experiment of the applicalion of rods to the tube has not yet been 

 tried. If this were done, it may be safely predicted that the amount of 

 the breaking weight would be very greatly increased. It would be diffi- 

 cult to calculate beforehand the exact increase of strength, but if the com- 

 parison be fairly instituted by experiment between a bridge with cellular 

 compartments and without suspending rods, and one with suspending rods 

 and the material collected in masses at the angles of the bridge, it may be 

 confidently anticipated that the strength would be increased to three times 

 probably many more times — its former value. 



The suspension chain should be relied upon as the principal means of 

 security, the masses at the angles of the bridge as the principal means of 



rigidity. By thus assigning to each part its separate appropriate office, 

 the efticiency ofthe whole is most likely to l.'e ascertained. 



The preceding invesliga'ion has been earned to so great a length tiiat 

 many things are necessarily omitted which are important with respect boih 

 to the theory and to the practical construction ofthe bridge. The circum- 

 stance of the eiperimeuls being confided into such hands as those of 

 Messrs. Fairbairn and Hodgkinson has prevented the appearance of many 

 suggestions which otherwise might not have been superlluous. If however 

 the remarks here oflered conduce to any improvements in the particular 

 structure which has been here considered, or should facilitate the applica- 

 tion of simple slaiical principles to the general theory of the strength of 

 materials, the labour of the writer will not go unrewarded. 



H. C. 



SETTING OUT RAILWAY CURVES. 



Sir, — In reference to Mr. George Heald's communication to yon on the 

 subject of laying out railway curves, I beg to say that I have occasionally 

 used a method which is, I think, more simple and accurate, which is as 

 follows: — 



Take any given curve, and fix the two extremities of tt by two polea 

 and flags. Then run a right line between these two points, which will, of 

 course, be a chord to the curve. Divide this chord line by two, which 

 point of division will be its centre, and each half will = sine of i the 

 whole arc, and iis versed sine will be the perpendicular to set off at this 

 point; and this r.s. is found by multiplying the tubular t.s. by radius of 

 curve. 



Then proceed to ascertain, in a similar manner, the centre points of each 

 of the two halves of the curves, by running chords, dividing them in two 

 parts, and setting off the perpendicular from the centre by means of its 

 versed line. 



When the curve has been divided into a few parts in this way, the small 

 divisions, being now equal and close at hand, may be ascertained by strik- 

 ing one of them on a large size, and, by a scale of equal parts, ascertain 

 the ordinates of one part, which serves for ail the other parts, 

 I am your obedient servant, 



An Engineer out of Employment. 



Oswestry, July 18, 1846. 



[The suggestion above is well worth recording. The method described 

 by our correspondent appears to be very practicable, and is geometrically 

 accurate. Whether, however, this method, or that requiring tables of rail- 

 way curves, similar to those reviewed by us last month, require the least 

 labour, can only be determined by actual experience.] — Ed. 



THE PROBLEMS IN "PLANE SURVEYING." 



Sift — Such communications as those of your correspondents, Messrs. 

 Byrne and Turnbull, are little calculated to support the high credit to 

 which your work aspires, and to which by the general ability of your 

 articles it has attained. In common, therefore, with other of your readers 

 with whom I have conversed on the subject, I could not but feel indignant 

 at the unwarrantable pretensions to originality which characterise both ; 

 and still more, at the accusation brought by one of them of bad faith on 

 the part of the late Dr. Olynthus Gregory. At the same time, it was a 

 source of real regret to see your pages made the medium for claims, 

 which, to say the least, are preposterous; but much as I should dislike 

 any personal dispute, or other inlercouse, with either of those writers, I 

 consider that the importance of any otherwise unworlhy statement which 

 may appear in your pages, is so far enhanced by that circumstance, that il 

 ought not to be alhiwed to pass into currency without a caveat from those 

 who set an estimate upon truth, and are iheniseives cultivators of science. 



In the first place, Mr. Byrne's "fundamental principle," upon which he 

 sets such extraordinary value, was given by C arnot, nearly half a century 

 ago, in his Ge'uin&'trie dt Position^ and in his Essai sur la Tke'orit det 

 Tranxiersates. The application of it to the problems in question have been 

 given over and over by Dr. Gregory in successive editions o! HiUtnn's Ma- 

 Ihematict, and there they still remain in the last edition of that work, pub- 

 lished in 1842, in a form only differing so far from that in youi pages as 

 would follow from a wish to conceal their origin. So much for Mr. Byrne's 

 boasted '■ quality of being original." 



With respect lo your other correspondent, Mr. Turnbull, 1 have in the 

 second place to admit, that against his opponent his claim is conclusive for 

 as much as it is worth. That worth is however, inconsiderable, in a prac- 

 tical point of view, at least ; and beyond being useful exercises in trigo- 

 nometrical reduction, they have no scientific value whatever. Under either 

 aspect, no person whose inventive powers in mathematics is ofthe average 

 order, would consider the discovery worth a moment's dispute. It is 

 to the grave charge made against Dr. Gregory by Mr. Turnbull, (who 

 should have been the last man to make that charge against him) that I 



