. An encyclopaedia of architecture, historical, theoretical, & practical. New ed., rev., portions rewritten, and with additions by Wyatt Papworth. bi)ve given seems to be a safe guide to tlie ariliiiect. In the case of oblongarL-hes, the results must he obtained for each side. H56. In the case of grolnin;;s conipo-ed of many i)Mys, the chief care necessary is in tlieexternal piers, wliich will require especially to be of sufficient thickness. 1 hosa in themiddle, being counterb danced all round, have only to bear the weights of their respectivearciies, for which purpose they must have a propor
. An encyclopaedia of architecture, historical, theoretical, & practical. New ed., rev., portions rewritten, and with additions by Wyatt Papworth. bi)ve given seems to be a safe guide to tlie ariliiiect. In the case of oblongarL-hes, the results must he obtained for each side. H56. In the case of grolnin;;s conipo-ed of many i)Mys, the chief care necessary is in tlieexternal piers, wliich will require especially to be of sufficient thickness. 1 hosa in themiddle, being counterb danced all round, have only to bear the weights of their respectivearciies, for which purpose they must have a proportional area and be of such stone as theweight will not crush. But it ought to he recollected that in good construction the area(if tlie points of support should he so distiihuted as to establish for each a sufficient strength,because a single weak point will often endanger the whole fal)ric. 1457. In practice, a readier method will be wanting than that which has been just ; we therefore subjoin one which agrees well enough with theory and experiment,and it is as follows. Let ABCD (fy. 5S5. Mo. 1.) he the .space to be covered by a. groined vault supported in the centre by the pier E. Dividing each side into two equalparts, draw the lines HI, ¥G crossing each other in the centre E, and the diagonals A E,EB, EC, ED and H F, HG, IF, IG crossing each other in tFie points K, K, K, No. 2. draw the pier its half height to the level of the sjiringing, which half heighttransfer from K to L, and divide EL into twelve parts. One of these parts will be a halfdiagonal of the pier. For the intermediate piers H, F, I, G, after finding the diagonals ofthe half piers, produce them outwards to double their projection within, so that altogethertheir thickness may be once and a half their wiilth. For the angular piers this methodwill give an area of base 1.^ times greater, which will enable them to resist the thrust theyhave to sustain. 1458. When the width of the space to be vault
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