SECT. I. THE PROJECTS OF BRIDGES, &C. 1

crease from the middle towards the ends; but if higher atthe ends than the middle, which can seldom happen, theymay then increase towards the ends. A choice of the mostconvenient arches is to be made from some of the followingpropositions, where their several properties and effects aredemonstrated and pointed out: Among these, the elliptic,cycloidal, and equilibrate arch, will generally claim the pre-ference, as well on account of the strength, and beauty, ascheapness or saving in materials and labour: Other particu-lars also concerning them may be seen under the word Archjm the Dictionary in the last section.

Next find what thickness at the keystone or top will benecessary for the arches. For which see the word Keyston ein the Dictionary in the 5th section.—Having thus obtainedall the parts of the arches, with the height of the piers, thenecessary thickness of the piers themselves are next to becomputed. This done, the chief and material requisites arefound; the elevation and plans of the design can then bedrawn, and the calculations of the expense thence made, in-cluding the foundations, with such ornamental or accidentalappendages as shall be thought fit; which, being no part ofthe plan of this undertaking, is left to the fancy of theArchitect and Builder, together with the practical methods ofcarrying the design into execution. I shall however, in theDictionary, in the last section, not only describe the terms,parts, machines, &c, but also speak of their dimensions, pro-perties, and any thing else material belonging to them; andto which therefore I from hence refer for more explicit in-formation in each particular article, as well as to these im-mediately following propositions, in which the theory of thearches, piers, &c, are fully and strictly demonstrated.