. An encyclopaedia of architecture, historical, theoretical, & practical. New ed., rev., portions rewritten, and with additions by Wyatt Papworth. es, or those whose Rise is less than the 11 Jf Span. 1407. For the purpose of arriving at just conclusions relative to surbased arches, threemodels were made of the same thicknesses and diameters, witli a rise of 35 lines, and inform elliiitical, cassinoidal, and cycloidal. We however do not thinkit necessary, from the similarity of application of the rules, to, givemore than one examjile, which is that of a semi-ellipse {Jig. 577.),in which, as bef
. An encyclopaedia of architecture, historical, theoretical, & practical. New ed., rev., portions rewritten, and with additions by Wyatt Papworth. es, or those whose Rise is less than the 11 Jf Span. 1407. For the purpose of arriving at just conclusions relative to surbased arches, threemodels were made of the same thicknesses and diameters, witli a rise of 35 lines, and inform elliiitical, cassinoidal, and cycloidal. We however do not thinkit necessary, from the similarity of application of the rules, to, givemore than one examjile, which is that of a semi-ellipse {Jig. 577.),in which, as before, the formula is .= ^/ 2j) + 2/7rf- 2mc i^ I) The lines described in the foregoing examples being drawn, we have KL = 45-5iK= 8-5. IT, represented by d in the formula, MK - _ -nilj X AB representing the thrust (37 x 9) givesthe value of/) . - . 2p therefore TI, represented by d, being 24-84, we have 2pd -7H, is KM x AB, will be 14-66 x 9, which gives c, representing iK, being 8-5, 2mcI), which expresses the sum of the vertical efforts m + »i(39-5 x 9) 24-8414-66 333-00666 -00 o, being always 120, - z= ^oq is - T *i ^*Lastly, -^. Substituting these values in the formula, we have .r= \/666 + j?!-^3;44^^2242-94 ^ g -76 - 2-96 = 25 -22 lines, or a little less than 25\ lines. 1408. In the model it was found that a thickness of 26 lines was necessary for the pier,and the lower voussoirs were connected with it by a cementing medium. Without whichprecaution the thickness of a pier required was little more than one tenth of the o]) the square root of double the thrust, that is, of 666, we have 25-81, about the samedimension that the graphical construction gives. The experiments, as well as the applica-tion of the rules, require the following remarks for the use of the practical architect. 1409. I. The cassinoid, of the three curves just mentioned, is that which includes thegreatest area, but it causes the greatest thrust. When the distance between the intradosand
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