204 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



rSEPTEMBEK 



mense, and the conviction is, that the colliery will be eventually " won." 

 The engine power is ample, cancelling accidents, which have not been 

 frequent. The settling of the sand on the bucket on one occasion was 

 so dense as to be the means of lifting a column of 33 fathoms, of 22- 

 inch pumps, by the spears on the starting of the engine. The sand is 

 hard, and the feeder flowing principally from the south, has occasioned 

 great delay and expense by guttering. Fig. 4 is a representation of 

 the wooden segments that are being put in to get through the sand 

 previous to metal tubbing, which is now about half penetrated. The 

 liberality and public spirit of the owners deserves the most complete 

 success, which all parties earnestly wish may be the case. 



Another "winning" is now being made at Shotton, belonging to the 

 Haswell Company, under the manigement of Mr. Thomas Foster, where 

 the quicksand is very nearly arrived at. Should " any thing fresh" be 

 brought into play at this place, either in getting through the sand, or 

 the surface arrangements, it will appear in the Journal, with suitable 

 illustrations, so far as it cau be done without injury to the proprietors. 



DREDGE'S SUSPENSION BRIDGES. 



Sir — May I request the favour that the following remarks (on an 

 snonymous communication, signed G. F. F., which appeared in your 

 last Journal), may be inserted in your next. 



The curve of a taper chain either connected or unconnected with 

 the platform, is not a catenary, but one of very different properties; 

 it might be easily demonstrated, but let that pass — for your corres- 

 pondent makes as great a mistake in regard to the action of the oblique 

 suspending rods in connection with the chains, and which is the only 

 part of his letter I shall notice. 



Fig- 1- Let ABC represent a portion 



A of the cliain of a suspension 



"t _JE bridge, B D an oblique suspend- 



g - — " - ing rod having the same incli- 

 nation with the horizon as that 

 portion of the chain BA; then 

 C, the centre of the bridge. will the strain upon B D, and of 

 course upon B A, be proportional to the secant of the angle D A makes 

 with the horizon, and there being no resolution of forces from the 

 point B, there can be no tension in the direction BC. 



Fig- 2. Again, put ABC part of the chain 



A of a common suspension bridge, B A 



c B____— forming the same angle with the 



I horizon as A D did in the former 



curve ; then will the strain in the 

 direction B A be proportional to the 

 C, centre of the bridge. secant of the angle which it makes 



with the horizon (or the same as before), but by a resolution offerees, 

 there would be a tension in the direction B C, Ot as the radius, which 

 tension must be borne by a sufficient quantity of iron, and that iron 

 causing a strain on the curve Ot as the secant of the angle B A makes 

 with the horizon. 



I shall take no further notice of this anonymous communication, but 

 if your correspondent wishes further information, he must affix his 

 name to his next letter, and then be careful what he says, for though 

 the diagram he shows is totally different from the form proposed, his 

 demonstration if carried out, would only tend to support that principle 

 he is attempting to refute, and the several structures either in course 

 of, or about to be erected in various parts of the kingdom, will at once 

 silence every futile objection that can be raised against it. 

 I remain, Sir, your humble obedient servant, 



J. Dredge. 

 Bath, August IG, 1841. 



P.S. I would refer your readers vrho may be interested in this sub- 

 ject, to the drawings wliich have appeared in your Journal, and they 

 will at once perceive that there is not the slightest similitude between 

 them and that represented by your correspondent in the last cumber. 



*** We know not what right Mr. Dredge has to make the insinua- 

 tion which he has done in the above letter, with regard to an "anony- 

 mous communication." The article of G. F. F., was written without 

 the slightest taint of presumption or slur upon Mr. Dredge's invention, 

 it was a fair scientific enquiry into its merits, and such a one as every 

 Inventor must be ready to encounter, if ho be desirous of introducing 

 to the scientific world any new form or invention. For the puriioses 

 of free and open discussion, we do not see the necessity of corres- 

 pondents giving their names— and we shall leave it to G. F. F. to re- 

 ply to Mr. Dredge's remarks. — Editor. 



ON THE TRANVERSE STRAIN OF BEAMS. 



By Herdert Spencer, C. E. 



The following paper is an outline of a new system of investigating 

 the laws of the transverse strain, differing from the usual method, in 

 as much as it depends solely upon the position of the neutral axis. "The 

 results as here given, will probably not be considered sufficiently con- 

 cise for practical application; but they are published in the hope 

 that something useful may be elicited. 



Fig. 1. 



1. Let A B C D be a piece of timber, subject to the transverse strain 

 in the direction shown by the arrow ; and let P P' be assumed as the 

 plane of fracture, and N the position of the neutral axis. Take any 

 line P' R,to represent the resistance to fracture of all the fibres in the 

 bottom lamina, then by the theory of the lever, if N, R, be joined, and 

 any line be drawn parallel to P' R, and terminated by N P', and N R, 

 it will represent the relative effect of all the fibres in its latitude, and 

 therefore the whole triangle N P' R, will denote the resistance to 

 fracture of all the fibres in tension. In the same manner, a triangle 

 NFS may be assumed, which shall represent the resistance of all 

 the fibres in compression.* 



2. Now the mode of action of the fibres in resisting the force im- 

 pressed, involves the necessity of the equilibrium of the compressive 

 and tensive resistances, about the transverse line through N, that is 

 the neutral axis ; for suppose a saw-gate made down the line P N as 

 far as N, and the force to be then applied ; a deflection will immedi- 

 ately take place, and the surfaces of the opening will come into close 

 contact. Carrying out the idea it would appear, that the deflection 

 would continue, until the resistance to compression in the upper por- 

 tion P N of the plane of fracture, is equal to the resistance to tension 

 in the lower portion; or that in the uncut beam, the neutral axis ar- 

 ranges itself so that these forces are in equilibrium. 



As it is this theory upon v/hich all that follows depends, and which 

 if disproved, will invalidate the succeeding calculations, it may be well 

 to give a further illustration. 



Fig. 2. 



Let A B C D be a piece of wood as before, subject to transverse 

 strain, and let E F and G H be the planes of fracture; (the diagram 

 being necessarily greatly exaggerated to make the action clear) draw 

 the arrows K, and O, perpendicular to E F, and L, and M, perpendicular 

 to G H; then K, and L, will represent the direction of tlie resistances 

 of certain fibres to compression, and M, and O, those of the resistances 

 of other fibres to tension ; (the forces extending the fibres are acting 

 from H towards B, and from F towards C, and the resistances will ob- 

 viously be in the reverse directions) — now K, and O, being perpendi- 



* This theorem affords a simple demonstration, that the strength varies as 

 the square of the depth ; for if the depth be increased, (the neutral axis re- 

 maining constant) so that N P' becomes N P", the original supposition being 

 carried out, the triangle N P" R' will denote the new tensive resistance ; but 

 the triangle N P" K, is to the triangle N P' R, as (N P")= to (N P')- ; that is 

 the resistance of the fibres in tension, varies as the depth square, and the 

 same will be true of those in compression. 



