On the Equilibriicm of Arches. lot 



Again, as tang. l" co. ar. 1.75808 



is to 10 tons - 1. 00000 



fo is tang. 30° - - 9.76144 



The whole weight upon 30° = 330.77 tons - 2.5195a 

 Double this will be the whole weight of the bridge. 



la. It was fhown (3.) that the comprefling force of any 

 leg in a fyfteni of angles was as thefecant of the angle which 

 that leg formed with the horizontal line. The leg at any 

 point of a curve will coincide with the tangent at the fame 

 point, and therefore the compreffing force at any point of the 

 arch of a circle is as the fecant of the arch between that 

 point and the vertex (8.) Thus the comprefling force at 30° 

 from the crown, is as the fecant of 30°; and this is the force 

 exerted upon the abutment in direction of the tangent to the 

 arch there. The compreffing force at %° from the crown is 

 as the fecant of 2", and at the crown (10.) as the fecant of 

 o degrees. 



* Thus, as the tang, of 1° - co. ar. 1.75808 



is to 10 tons - 1.00000 



fo is fecant of 0° - - 10.00000 



The compreffing force at the>v _______ 



crown = the horizontal {^^^ ^^ . ^ „ -.^o^o 



force, or thruft, or puft, p72.90 tons - 3.75808 



againft the abutment -^ 



Again, as the tang, of i^ - co. ar. 1.7580S 



is to 10 tons - 1. 00000 



fo is fecant of 30' * - 10.06247 



The compreffing force exerted -j 



aoraind the abutment in di- I ^^^ ^^ . ,,„ „ o^^.-- 



'^t-L- f .u . .. .1, > 061. <'? tons 2.02055 



reilion of the tangent to the "^-^ ^^ 



arch at that point 



13. This fecms to be all that is requifite to be known of 

 the theory of the equilibrium of arches of a circle, fo far as 

 it relates to pra6lice : the builder will naturally defire to con- 

 Itrui^l his bridge with the feweil materials confiftent with 

 ftabiliiy, and will probably firfl determine the dimenfions and 

 wci<>-ht of thofe ,at the crown, which he will fix at a mini- 

 nmm, and from that, by the rules juft given, the weight 



• To fome of thofc who may not have a logaritlimic table of fecants it 

 ,iT»;»y be ufcful to fay, that the loijarithniic fecant of an angle may be had 

 by fubtr;ic\intj the co-finc of tlie anele from io.ocooo. 



G 3 over 



