ON HYDROSTATICS. Q69 



contact with upright walls, without allowing the water to run out, the na- 

 ture of the curve may be determined with tolerable facility,- whether the 

 weight of the bottom itself be considered or not. If the weight be exactly 

 equal to that of the water, the form of a semicircle will agree with the 

 conditions of equilibrium, as Bernoulli has demonstrated, supposing the 

 fixed points at the distance of its diameter; but if the weight of the bottom 

 be neglected, the curvature will be every where proportional to the distance 

 below the surface, the form being the same as that of an elastic rod, bent 

 by two forces in the direction of the surface. The same principles, with a 

 slight difference in the calculations, will serve to determine the forms adapt- 

 ed to the equilibrium of arches, intended for supporting the weight of superin- 

 cumbent fluids, or of such soft materials as approach nearly in their operation 

 to more perfect fluids. (Plate XIX. Fig. 250.) 



\ 



