418 On the different Theories f)/' Arches, Faults, ^c. 



as of, 0/5; tlie force whicli it exerts to fall being always 

 constant. Prolong the radii, and make «/', ab equal oi, oi ; 

 through bb draw the exlrados; (or, from any point a draw 

 ck vertical and equal BV-', and draw kO horizontal, cutting 

 the radius through o, in b, which is the point required) l>a, ba, 

 are infinitely ihui voussoirs. On anv voussoir ^(7 construct 

 the paralleiograni, cutting the base-line mt of the abutment 

 jn fn \ 7nbl'V is the extrados of the arch and abutment. To 

 find the voussoir ab to produce the least al)utment : Draw 

 Ic horizontal, equal id or bk, and C7« vertical, cutting bni, 

 drawn I'erpendicular to bo, in m ; ihrouoh y and w draw 

 the curve ;;??/, cutting the base line in m ; join mo, and on 

 it as a diameter describe the semicircle iribo, touching the 

 extrados in b, the extremity of the voussoir required : the 

 curve V7?i is a catenaria. It is remarkable, that upon re- 

 ference to Table I. in this work, the key-stone being 1, 

 the voussoir at the haunch will be 1,4 14, which is a propor- 

 tion conformable to what Mr. Simpson recommended for 

 Blackfriars Bridge, and what was adopted in that structure. 

 Mr, Gwilt has since published a work entitled, A Treatise 

 on the Equilibrium of Arches, with a view to render the 

 tracts on this subject by Emerson and Dr. Hutton useful 

 and more easily understood. He considers them at present 

 "of little if any use in practice :" and in the alteration of 

 the dress, the subject is rendered more familiar ; but no- 

 thing new has been exhibited; and indeed, what has been 

 considered the great and important discovery in the Emer- 

 son theory, the curve fjr the horizontal extrados, has been 

 omitted. 



M. Berard, professor of mathematics at tlie college of 

 Briancon, has lately published at Paris a work on the equi- 

 libration of arches, entitled Stalic/ne des Fbutes, consisting 

 of five chapters, wiih an appendix on the anse de pnnier, 

 >or false ellipse, a curve much used by French architects. 

 Mr. Mylne adopted it at Blackfriars Bridge, in its simplest 

 conslructif>n. As this tract is of greater extent than anv 

 yet published, a summary of the content? mav be accepta- 

 ble, ^fhe first chapter is occupied in determining, from a 

 given intrados, the extrados ; and under certain circum- 

 stances to find the intrados. He deduces a simple n:ode 

 of determining the extrados to a semicircular arch, which 

 is as folk)W3 : 



Let AJJ, &c. (fiff. 8) he a semicircular arch ; c the centre.; 

 Vc vertical, and VB the thickness at the veriex: draw Vu 

 and ob horizontal. Through any point d, draw the radius 

 C'a, inlerseeting Va and hl< in a and b. On aC as a dia- 

 meter 



