via

preferred to Gregory’s simple deduction. JohnBernouilli, in his 81st epist. to Leibnitz, says ofLa Hire, “ La Hirius affinitatem inter forniceset catenarias suboluisse videtur ; nec tamen remsatis assequi potuit, nostro calculo destitutus.Vidit aliquid; quid autem viderit ipse non intel-ligit.”

The other theory which Emerson has givenin Prob. 20. of his Doctrine of Fluctions, hasrelation to the “ nature of the curve boundingthe top of the wall supported by a given arch ;by the pressure or weight of which wall all theparts of an arch are kept in equilibrio withoutfalling.” In the last century there have beenabout thirty writers upon this subject, and mostof them eminent for their mathematical know-ledge. *

Formulae to determine the height of the keyof an arch with relation to the materials used,and the weight to be sustained, illustrated by atable of practical utility, and by reference tosome of the principal bridges in Europe, aregiven in the second Tract, and methods to findboth geometrically and numerically the batter-

* An account of the works of the principal writers on thetheories which have been from time to time advanced sinceGalileo thought of the funicular curve, will be found in thePhilosophical Magazine, Dec. 1811, and Jan. 1812, and inChap. IV. of Gauthey’s Traite de la Construction des Ponts;and illustrated in respect to a cast iron arch of 600 feet span,in Rep. Sel. Com. Port of London, 1801.