272 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[Sept. 



the bar is currerl, or polygonal, as it necessary must he in the case of a 

 chain employed in the actual construction of abridge, the process be- 

 comes a little more complicati'd, since it requires all the composant 

 forces to be referred to, the several portions of the chain as resultants, 

 vtf iiiean such portions as are comprehended between any two con- 

 tiguous bars. In every other respect the principles which regulate 

 the calculations are the same, and for this reason it will be sufficient 

 to establish the theory in reference to the straight line only, since the 

 reader, who is familiar with the composition and resolution of forces, 

 will find no difficulty in extending the procss to a ctirve, and he who 

 is not, will derive but little benefit from a perusal of the subject which 

 is now laid before him." And now with regard to the investigation, 

 without qui'stioniiig whether the author was capable or incapable of 

 fully satisfying the conditions of the problem proposed by Sir John 

 Macneil, yet considering the slender data it was possible for him to 

 obtain in 1S41, and tlie simple mathematics he used, the work was 

 satisfictorv, even though at the end he jumps at conclusions rather 

 than deduces them from previous reasoning. I do not wish to uphold 

 it as a specimen, but I do say that if he did not succeed in a complete 

 solution of the problem, he' deserves credit for what he did, for he 

 was the first who attempted it. 



Mr. Bashforth next, after alluding to much that has been written, 

 says, "but most unfortunately not one of the writers even ;)rq/£ss^s to 

 have a knowledge of mathematics, and consequently all their opinions 

 are worthless!! I" Practical men will thank mathematicians very 

 little for such compliments as these. What, Sir, are plain common 

 sense statements "worthless?" Are experiments "worthless?" Is 

 (iract'cal experience "worthless?" Is the successful com|iletion of 

 twenty bridges in four years "worthless?" Is the adoption of the 

 plan in foreign parts "worthless?" Is the increasing reputation it 

 has always obtained " worthless?" I could continue, but then it would 

 be "worthless," compared with a mathematical investigation, well, 

 let it be so, and I will yet meet Mr. Bashforth on his own ground, for 

 J am a mathematician, and every thing that bears my signature is the 

 result of rigid investigation. Although 1 do not wish to make a parade 

 of what little learning I may possess, yet I fear no attack on this point, 

 even from a Fellow of St. John's; and since Mr. Bashforth has com- 

 m'-nced, it may not be presumptuous in me to express a wish to try 

 his strength as an analyst on this subject, it you, Sir, will kindly allow 

 Ui the use of your p iges for that purpose. 



In reference to the weight of the chains of the Menai Bridge, the 

 statement of 1935 tons is taken from a small pamphlet, an abstract of 

 Mr. Provis work, (I purchased at Bangor); I have it somewhere 

 amongst my papers, but caimot at this mument find it. Mr. Bashforth 

 speaks of 774 tons, but this refers to the weight between the points 

 of susjiensiun only, whilst the 193 J tons includes the whole of the 

 chains outside the towers, and the immense masses of iron work at- 

 tached to the chains in the retaining tunnels. I have always been 

 very careful to put forward nothing but what I could substantiate, and 

 if this be an error, it is an error of the pamphlet from which I copied 

 it. Lord Western also makes a similar statement in his letter, which 

 his Lurdship copied from the book I lent him. The weight of iron 

 r^-quired in the chains of a bridge, such as the Menai, on my plan, 

 would be about 70 tons instead of 1935. 



Mr. Bashforth next remarks, "Again we are informed that the (en- 

 siun ol the chaiu must be nearly 3750 tons, half acting in each direc- 

 tion." This, I believe, is only part of a sentence, the context of winch 

 would shew the meaning; but as it here appears, it requires some 



explanation. Theiefore let ABC, fig. 1, be the chains of the Menai 

 Bridge, D E F the roadway. Su|ipose a section B E of the chains, and 

 platform when made, then each half ABED, and C B E F would ex- 

 ert a horizontal force of lb75 tons,* which, when the chains are con- 

 nected at the point B, would counteract each other. Now since each 

 lialf of the bridge causes 1S75 tons of horizontal force, the whole 

 bridge must cause double that, one-half of which is reached by the 

 other. 



* " Suppose the whole suspended weight of the Menai Bridge, with its fair load, to be 

 iUUO tuns, then the tension at the middle wsuld be XUli tons. — Orewry, page 167. 



^: 



To put it in another light, let A B, fig. 2, be a 

 Fig. 2. cord passing freely round the pulley C, and su|ipose 



at each end A and B, animal force were applied in 

 the direction of the arrows equal to 1875 tons, now 

 it is evident that if each excited a force of 1»75 

 tons, the amount of work done by both would be ^ 

 3750 tons, but because one counteracts the other, 

 the strain in the cord is only 1875 tons. These 

 examples will illustrate my meaning. 



I think I have now said enough to shew that the 

 principle is not so wrong, nor my statements so 

 conflicting as the author of the "Remarks" would 

 make it appear, and having reconciled those which 

 he made somewhat contradictory, "I leave it for 

 the world to judge, and Mr. Bishforth to reply. 

 There is no occasion. Sir, for searching the Phil. Trans, in 1S26 for 

 what was known long prior to that period, for the tapering of the 

 chain for a catenary bridge is fully exemplified in the " princi|ile of 

 the polygon of pressures," but then it is so smad as not only to be un- 

 worthy of notice, but impossible to be carried out in practice, and I 

 must repeat to Mr. Bashforth the same I told Mr. Mosely, when he 

 committed a similar error, that my pian bears no analogy to the catenury. 

 As we have been talking about the Menai bridge, I will take that 

 structure to exemplify this by comparison. Drewry, page 167, states, 

 " The chains of the Menai bridge contain 260 square inches of iron, if 

 therefore they were proportioned throughout to tinir tension, they 

 should contain at the middle about 251 square inches." Now in the 

 chains of a similar bridge, on my plan, there need not be any section of 

 iron ah the centre, because there is no tension existing there. I will 

 make one more remark and then have done. 



In the conclusion of the paper, Mr. Bashforth says, "In the general 

 case the data are insufficient for a mathematical solution," &c. ! And 

 yet he has "undermined the foundation," shewn "the principle to be 

 built on afallacious assumption," and proved "it to be wrong," anathe- 

 matizing the whole as though he rigidly investigated it and almost 

 with acknowledged insujficiency of data." I therefore return Mr. 

 Bashforth his compliment, viz., (that if the opinions of men who are 

 not mathematicians are " worthless," the opinion of a mathematician 

 without data is equally " worthless," ergoj his remarks are "worth- 

 less," and mathematicians, I am sorry to say, have in a great measure 

 to thank themselves " for the distrust with which practical men regard 

 theories." 



I must apologize. Sir, for writing to such a length, but could hardly, 

 with courtesy, to Mr. Bashforth, have replied in less. 



I remain, Sir, your obedient servant, 



James Dbed&e. 



Bath, August G, 1845. 



*^* Mr. Dredge disavows Mr. TurnbuU's papers, he is therefore not 

 responsible for the errors in it; but as he s.iys that he hiiLself is a 

 mathem itician, does he not suffer his zeal to exceed his knowledge 

 when he defends a paper which he confesses "jumps at conclusions 

 rather than deduces them from previous reasoning," and in which it 

 seems that the writer assumes that if three forces keep a point in 

 equibrio, one of them may be greater than the sum of the other two ? 

 Such nonsence could never by any possible contingency have been 

 written by a mathematician, and is so obviously beyond all defence, as 

 to be scarce worth attacking. But it must be allowed in justice to 

 Mr. Dredge that " erroneous argument proves nothing but the inability 

 of the disputant," and therefore does no/ prove Mr. Dredge's inven- 

 tion to be either valuable or valueless. The real question, the only 

 question in which the public have any interest is — whether, weight 

 for weight, Mr. Dredge's bridges are stronger than those or ordinary 

 construction. Of Mr. Turnbuh's paper quite enough has been said — 

 if the discussion be continued, it ought to refer exclusively to the real 

 merits of the question. — Ed. 



OxTGEN AND LiTHARnF, — At a s'tiing of the Jcnrlemre lies Sciences M 

 Millon gave nn account of some expenmeiita as to the influence exercised by very smal 

 quantities of loreigo substances, in the decomposition of water by metals. M. BarVeswil 

 noiv explains this inflaence in the fulloiving manner:—" We may admit," says he. " that 

 II zinc, tin, and lead, ate atta. ked by hydrocliloric acid with greater energy under the in- 

 fluence of only afewdropsof as.)iution of ihe salt of platina, than without this influence, 

 it is because the precipitated metal (plitina), in contact with the Jjrecipitating metal, con- 

 stitutes a true voltaic element. In fact, if instead of a solutinn of platina we make use of 

 a piece of platina wire, and touch with it the metal to be dissolved, we obtain the same 

 result. If aisenic accelerates, as we all know it floes, the decum position of water by z nc 

 (a phenomenon analogous to the presence of platina), whilst it checks the action of acids 

 upon iron, this apparent anomaly arises from the fact of the deposit formed upon the zinc 

 being porous, whilst that which covers the iron is impenetrable, like gilding. The proof 

 of this is, that if we scrape a surface of iron thus arsenicated, and replace it in the same 

 li lUid, the re-action becomes strooper than upon the same iron when entirely cleaned for 

 the process. This protecting envelope is not necessarily metallic ; it suifices for it to be 

 Impenetra'de to liquid, adherent, and insoluble In the bath. Thus marble is not diBsoIved 

 in concentrated nitric acid, because it covers itself with an Insoluble coating of nitrate of 

 lim<. 



