MECHANICS. 151 



232. In an elliptic arch, or one of which the in- 

 trados is a semi-ellipsis, if 2 a be the span of the 

 arch, or the longer axis of the ellipsis, and b the 

 height of the arch, or the semi-conjugate axis of 

 the ellipsis ; then, if from any point in the curve, 

 a perpendicular w be let fall on the longer axis, 

 the weight of the key-stone is to the weight of the 

 voussoir which has its middle at the point from 

 which the perpendicular is let fall, as a s to 



Hence, if W is the weight of the key-stone, and V 

 that of the voussoir, 



V = _ ft5 x W. 



This is the same with the theorem given by BOSSUT, 

 (RechercliessurTEquilibre des Voutes, 14.), though 

 the expression is somewhat changed, with a view to 

 facilitate the numerical calculation. 



233. If the weights of the voussoirs are all equal, 

 the arch of equilibration is a catenarian curve, the 

 same that a chain or cord of uniform thickness 

 would assume if hanging freely, the horizontal 

 distance of the points of suspension, being equal 

 to the span of the arch, and the depth of the low- 

 est point of the chain being equal to the greatest 

 height of the arch. 



a. It 



