18 Jo.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



377 



DREDGE'S SUSPENSION BRIDGES. 



We have to direct attention to the following Correspondence. 



Sir,— In publishing my father's reply to Mr. IJashforlh, in the No- 

 vember number of your Journal, you have made a very ridiculous error, 

 which is the more to be regretted in consequence of the remarks appended 

 to the letter. I say you made the error, because in the original draft of 

 the letter it does not occur ; and as I myself made the copy that went to 

 press, and took particular care that it should be correct, I feel convinced 

 that it is not in that. The part I allude is written, and should have been 

 printed thus : " Suppose the points A and B lig. 2 to be in the same 

 borizootal line, let a wire (void of weight) A C B be suspended from them, 



Rg. 1. 



»n(i let a weight W be applied at the centre Ca—iBA C= / BCD 

 aud T=tbe measure of tension in the wire ACS; then 



T = i W cose a.* 

 But if W be supported in a projection at au i = a, the tension excited 

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

 a resistance must be applied in the direction of the arrow = J W cose a, and 

 •imilarly at B a resistance is lequiredzzj W cose o, and the sum of those 

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



i W cose o + i W cose o =: W cose o, 

 Oonsequenlly flit tension must be \V coae a, half of it (or \ W cose «) acting 

 in each direction." 



The first part of this proposition is to be met with in every treatise on 

 statics; the latter part is self-evident, and is quite distinct from the prin- 

 ciple of action and reaction. If you doubt it, take a more general 

 example. 



From the periphery of the circle A B' B A' 

 let an infinite nninber of lines descend at 

 the same angle (a), all converging in one 

 point, C. From this point let the weight \V 

 be suspended, then will the tension in each 

 line be represented by cose a.dW; but to 

 obtain the full force excited by the weight, 

 W, we must integrate this expression, when 

 we shall have the amount ofiension due to 

 the action of the weight, W, 



Fig. 2- 



f= cose 



ydw = 



=W cose a 



which 13 the same as we obtain by the above proposition. Therefore as 

 a general rule (which cannot be disputed), multiply the weight suspended 

 by the cosecant of the angle of suspension, and the product will give the 

 whole amount of tension excited ; and if this be divided by the number of 

 sustaining lines the quotient will give the tension in each ' 



This is strictly in accordance with accurate mechanics, and with mv 

 father 8 proposition. If it does not agree with your pre-conceived notion 

 1 cannot help it. 



If jourefertothedilTerentialand integral calculus, by the Rev T G 

 Hall, third edition, pages 113 and 96, you will find that the pure mathe- 

 matics of the proposition fig. 3 is perfectly correct ; its application to the 

 mechanical problem under consideration is equally demonstrable, but 

 that was left for Mr. Bashforth to dispute. 



You will find it on record many times before the 1st of November that 



tf the roadway be sufficiently strong to resist the compression. Ihe pUl- 

 form, &c. 1 he words I have put in italics are omitted iu your remarks 



I deny the correctness of Mr. Bashforth's opinion, and corroborate my 

 father s statement, for " the problem is susceptible of analytical solution." 

 / hare done it, and have my MSS. by me ^ 



As this is an advertisement, for which the bearer will pay you I r»- 

 quest ym, will insert it vvithout any remarks. I have forwarded a' copy 

 to Mr Bashforth, that that gentleman might not be able to take advaota" 

 of the typographical error so opportunely laid before him." 

 Yours, &c. &c, 



Bath, Norember 7tb, 1845. '''"■'"" ^'''""'' ^''''' ^"S'"^^- 



• Co« (co.ec«,l) =„^ ifrad -1, lli« cose =-^cQntq»emly J W cose » 



The above letter was accompanied by the following : — 

 Sir, — I can perfectly understand the reason why the alteration in my 

 father's letter was made— but cannot admire the imprudence of risking an 

 exposure. I request that the accompanying advertisement be inserted 

 uitliout any riinarks in the body of the Civil Kngineer and Architect's 

 Journal, and the hearer will satisfy your demand fur it. An announce- 

 ment that this advertisement is to appear, is sent to the iMechanic's 

 Magazine, aud, I have no doubt, printed iu that journal of to-day. 

 You will see I have communicated with Mr. Bashforth on that subject, 

 so that he cannot take advantage of the blunder." 



I have the boDonr, &c. &c. 



W. Dredge. 

 To the Editor qf the Civil Engineer and Architect's Journal. 

 P. S. This letter is not intended to be published, unlets you please, and 

 not then as an advertisement. 

 Bath, November Sth, 1843. 



(Copy of Answer.) 

 No. 10, Fludyer-stteel, Whitehall, Nov. IC, 1845. 

 The Civil Engineer and Architect's Journal. 

 The Editor begs to inform Mr. Dredge that his paper shall appear in 

 the ensuing number of the Civil Engineer and Architect's Journal, with 

 all the correspondence relating tm it, and that a proof sheet shall be sent 

 to Mr. Dredge for his correction. As the paper cannot appear as an ad- 

 vertisement, the money sent in payment is returned. The editor reserves 

 to himself the right of reply, and of explaining what appears to .Mr. 

 Dredge an intentional typographical error. 

 '\V. Dredge, Esq. 



The following letter was sent with the corrected proof sheets : 



Herbert's Hotel, New Palace Yard, Nov. 22, 1845. 

 Sib,— I thank your courtesy for sending me a proof of my letter, which 

 was only put into my hand this morning, just as I was silting down to 

 dinner. In order that no time might be lost, I called upon the editor in 

 Fhidyer-street, that I might show the errors you have again committed. 

 V ou will, of course, understand my object for callinj; upon him personally 

 was, that no time might be lost in conveying an answer which you wished 

 to have by return of post. What I had to communicate, I therefore send 

 you in writing. 



I sent it to appear as an advertisement, — you have published it as a 

 letter; you will therefore please insert these short remarks, which are 

 referred to in the proof. Tlie letter at the foot of the proof was private ; 

 I have not any objection to its being published, it was not written unad- 

 visedly, nor in a hurry. 



Yours, &c. 

 W. Dredge. 



I had written the letter in London, but neglected posting it. If you have 

 occasion to write tome, address, Bath. 



Corrections : 

 The typographical errors are pointed out in the proof; where I want 

 inserted, in addition, is as follows ; 



• The steps of this deduction would have been sent at length, but for 

 the limits of advertisement, which it was intended to be. 



' Your expression of Mr. Bashforth's opinion would have been farther 

 remarked upcm but for the same reason. 



'^ No possible objection can be made to any remarks you please, pro- 

 vided you give an opportunity for reply. 



* This letter was private, but is published by your choice ; I have not 

 the least objection to it. W. D. 



The typographical error which forms the subject of the above letters 

 we readily acknowledge. It arises, we find, on referring to Mr. Dredge's 

 manuscript of his former communication, from his having written the word 

 cosecant " cose," whereas it is, we believe, uniformly expressed iu mathe- 

 matical books by the letters "cosec," or " cosect." It was therefore 

 concluded that in Mr. Dredge's paper the word " cosine," or its usual 

 abbreviation " cos," was intended ; and what we now find to be an " e " 

 was taken to be no more than a mere mark after the " s." This, we think, 

 satisfactorily explains the matter, without any supposition of intentional 

 alteration on the part of the compositor, or dishonesty on the part of the 

 editor. 



Allowing Mr. Dredge the full benefit of this acknowledgment (which 

 we here most explicitly do), there still remains enough to warrant us in 

 retaining our opinion of his mathematical knowledge. In his letter now 

 before us, the printer's proof of whiih has been corrected by himself, he 

 says,— let " T = the measure of the tension in the wire A C B ; then 

 T = J W cose o," and in the same sentence he says, " consequently, the 

 tension must be W cose o." Now, one of these assertions must be incor- 

 rect, for otherwise we must conclude that a thing may be equal to the 

 half of itself— ere is no need to tell the mathematical reader that the 

 former of the assertions is the correct one. 



50 



