250 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[August, 



If now we suppose A F to be a rigid lever capable of turning about 

 F, and if the momenta tending to turn it in opposite directions be 

 eqoiil, we get 

 o, d, sin (p„ -\- a, rf, sin (p^ -{- b dn sin (p„ =z aS (R). Page xxxi. 



Tliis pqnation we may allow, but it must be observed that the pul- 

 leys E, B, are fixed quite independently of the main chain A P, and 

 we may thertfore suppose that the chain A P remains straight. a„ 

 a, Sec. are called subsidiary forces. 



At page xxxii. we read " If, instead of supposing the cords, to which 

 the subsidiary forces are attached, to be brouglit over pulleys and 

 stretched according to the intensities of their respective forces, let 

 them be simply attached to the prim.iry cord or chain A P, as repre- 

 sented figs. 7 and 8 following, then if stretched to the same degree by 

 means of the load which they are employed to support, the nature of 

 the action will be precisely the same as in figs. 2 and 6 &c." I am 

 quite at a loss to im.igine how any one, possessing the least possible 

 linowledge of mechanics, could make such an absurd and totally un- 

 warrantable supposition. If the subsidiary forces are to be anything, 

 they »!«s/ bend the main chain, — thus the position of the whole will 

 be altered, and consequently the tensions of the rods will be changed. 

 The main chain A P would of course be bent, and the arrangement 

 of the whole be so altered that all ihe previous investigation would 

 be rendered utteily worthless for the object in view. It appears that 

 this learned theorist has found his subsidiary forces to produce a great 

 s.iving in material, but although it may be always possible to attach 

 the ends C, H, &c., fig. Pi, to the platform, it is not generally prac- 

 ticable in actual constructions to find other ^md points, as E B, just 

 above to which we may tie the other ends quite independently of the 

 main chain. It does not appear necessary to continue the in- 

 vestigation any further, as its foundations are undermined. A 

 bridge built on this principle may st.md for two reasons, it is seldom 

 or never loaded to the full extent of its calculated power, and the 

 actual strength of iron is about three times as much as is used in the 

 calculation. 



Thus we see that Mr. Dredge's "principle" is built on the fallacious 

 assumption that we may attach one end of a supporting rod to the 

 pUtfoim, and the other end to some convenient point just above, quite 

 independently of the main chain. 



At pages xxxviii. and following, we have an example, and the ten- 

 sions i ij, &,.., a^, a„, &c., for that case are most obliginglv alTorded 

 lis with the greatest nicety, even to four decimal places, the above 

 fiKJire represents a part of the main chain, b„ b^, the tensions on each 

 side of the juint D, a^ the tension of the subsidiary force connected 

 to the main chain at D. It is found by applying the mathematical 

 Colculations to this particular case that 



6.= 151-G90G; b^= 10M270; a^ = 28-9517 



• V ^'""^ *5 + "it or two of the forces are together less than the 

 third. Now, since tliree forces, acting at a point, when thev keep it at 

 r-'st, are proportional to the sides of a plane triangle, formed' by drawing 

 lines parallel to the direction of the forces ; if this be true there may 

 be a plane triangle having two sides together less the third. But see 

 Euchd, Book I., Prop. xxT 



I have merely taken the values of the tensions for one point. The 

 seU of tensions (fi, 6^ aj, (6^ b, aj, (b, h, aj, and (b^ b^ aj when 

 applied at one point cannot keep it at rest for the reasons above given. 

 It IS a decisive proof that an author's calculations are erroneous 

 when they lead to an absurdity or an impossibilitr. 



I think I have already written enough to show 'that the principle is 

 wrong, and that its application to an example by the author leads to an 

 absurdity. I have compared Mr. Dredge's statements together and 

 with other accounts, and they are contradictory,— and I leave things 

 as I find them. ^ 



It has become usual for persons to speak of the Menai Bridge as a 

 complete failure— in one respect it has been a failure, in another a 

 triumph. The failure is, however, no discredit to the mathematical 

 abilities of Davies Gilbert nor to those of Telford the engineer. They 

 were not then aware of the effects that the wind could produce ; but 

 everything that they did take into account whs amply provided for. 

 Tills, however, will be no excuse for neglecting such lessons as eipe- 

 rieace bu taught, in future structures of a similar kind. 



If Mr. Dredge had examined the Philosophical Transactioni for 

 182(5 he would have found that the plan for tapering the chains was 

 no new discovery in 183(5, and perhaps he might have been led to 

 doubt the accuracy of his own conclusions, when he found that the 

 quantity of iron tliat could be thus saved with safety was so small as 

 not to be worthy of notice. 



All the patent bridges tliat have been constructed ought to be care- 

 fully examined ; theleigths and strengths of all the links, together 

 with their inclinations to the horizon, should he measured when the 

 bridge is loaded uniformly to the full extent of its estimated power, 

 it would then be possible to form some estimate of the security of the 

 structure. In the general case the data are insutficient for a mathe- 

 matical solution, but with given positions and magnitudes of all the 

 parts we may calculate the tension of each portion for a given loud, 

 and pronounce for or against after a comparison of the calculated ten- 

 sions with the capabilities of the several parts. We have in a great 

 measure to thank such writers as this theorist and Mr. Pole for the 

 distrust with which practical men regard theories. 



ON THE PREPARATION OF LIME FOR FRESCO AND 

 OTHER PURPOSES OF PAINTING AND ARCHITECTURE. 



It is amply known to most men that lime is a calcined chalk, or other 

 stone containing this earth, in the state of carbonate, and that we must 

 develope its caustic state by divesting it of carbonic acid by means of 

 the kiln, and still further change its ciiaracter by slaking, when it be- 

 comes a hydrate of the earth, which is now and lias long been consi- 

 dered a mere u'lion of water with oxide of calcium ; and, although I 

 demur' on the absolute correctness of the theory, it might have been 

 considered supererogation to have dwelled upon it here had it not 

 been industriously published to the world, especially to painters, — 

 first, that by washing, as practised by Pallomino, its caustic powers 

 and well known destructiveness among pigments, especially the sul- 

 phurets and carbonates, could be not only ameliorated but removed; 

 secondly, that the long continued burial of the hydrate in the state of 

 fine putty, as practised by Cornelius and other German painters in 

 fresco so pertinaciously that the director will use no lime which has 

 not been so buried from six to eight years ; thirdly, but it is almost 

 too silly to notice, that hydrate of lime is not formed by slaking, but is 

 a salt indigenous in all lime stones- .' fourthly, that to make a complete 

 job, we should dissolve lime, precipitate artificial carbonates, and 

 further deteriorate its powers by foolish experimental' mixtures ! 

 Alas, what shall we be told next ? 



Fourcroy published some forty-five years ago his valuable experi- 

 ments and many incontrovertible truths, but, as will always be the 

 case with the mere theorist as regards practical arts, many errors: 

 liydrate of lime is stated by him to be less caustic (the gieat obstacle 

 o( the misled fresco painter) than the earth before slaking. This 

 was an error of the clos't man; Fourcroy used, as an experimentalist, 

 Carrara marble; now, obviously the lime of Carrara marble, however 

 well adapted to philosophical purposes, must be a poor, trashy and 

 worthless one for building, tanning, fresco painting, c&c, nor does its 

 hydrate resemble that of Dorking lime. 



Convinced as I am that fresco painting is not at all adapted to 

 English taste, and much less so to English rooms or halls even of the 

 larger class — what, let us ask, is the essence of the art ? why, inherent 

 crudeness but real transparence and permanence, the very found Uion 

 of which is the permanence of the stucco. If, then, a caustic lime be 

 necessary to a permanent intonaco — and such intonaco be necessary 

 to fresco — obviously a caustic lime, in this climate especially, is the 

 sine qua von of a permanent fresco, and, as obviously, every attempt 

 to lessen the causticity of the lime, so as to adapt it to the pigment, 

 is a retrogradation ; the pigment must, in the nature of things, be 

 adapted to the lime, and the whole series of obstacles, hitherto re- 

 echoed from Pliny to Pallomiuo, sink before the ordinary expedients 

 of the painter's art. 



• Tliat a something more lakes places Is obvious, and was seen by tile older masters of 

 physic and painting j the first directed " all first waters in which lime had heen slaked to 

 be thrown away as ■ too furious for medicine ;' the last chose these first waters (in which 

 " lime had boiled up") to prepare Vermillion for fresco, which they do, not by "embuing 

 it with lime," but by abstracting the excess of sulphur. 



« An axiom actually promulgated in print by a lilr. Weld Taylor, who states also, that 

 Vermillion has a tendency to turn * black' by heat , apparently innocent of tlie fact ttiat it 

 is id)solutely a ' black' sulphuret of mercury turned red by heat I Vide his Essay on Fresc» 

 Paintinjf. 



» Dr. David Boswell Reld. Vld« tlie Royal CommiBslon on Fine Arts, 1st Report, 

 po^e 45 of the Appendix. 



