CONTENTS. XV 



form of a right angled triangle, and first when the fluid presses on the perpendi- 

 cular, art. 219, page 203. Practical rule and example for this case, art. 220, page 

 203. The same determined when the fluid presses on the hypothenuse, art. 221, 

 pages 203 and 204. Practical rule and example for this case, art. 222, page 204. 

 The construction exhibited, art. 223, pages 204 and 205. Concluding remarks, 

 art. 223, page 205. The thickness of the dyke determined when it yields to the 

 pressure by sliding on its base, art. 224, pages 205 and 206. The resistances of 

 adhesion and friction compared with the weight of the dyke, art. 225, page 206. 

 Example for illustrating the resulting formula, art. 226, page 207. The breadth of 

 the dyke at the top determined, art. 226, page 207. The breadth of the dyke at 

 the bottom determined, when the side on which the water presses is perpendicular 

 to the horizon, art. 227, page 207. The same determined when the opposite side is 

 perpendicular, ib. The same when both sides are perpendicular, ib. The same 

 determined when the section of the wall is triangular, having the side next the 

 fluid perpendicular, and the remote slope equal to the breadth, art. 228, page 207. 

 The same takes place when the remote side is perpendicular, and the slope on 

 which the water presses is equal to the breadth, art. 228, page 208. Concluding 

 remarks, ib. 



The dimensions of the dyke determined when it is constructed of loose materials, 

 art. 229, pages 208, 209, and 210. Example for illustration of ditto, art. 230, page 

 210. The conditions necessary for preventing the dyke from sliding on its base 

 determined, art. 231, page 210. When the water presses against the vertical side 

 of a wall, the curve bounding the other side so that the strength may be every 

 where proportional to the pressure, is a cubic parabola, ib. Introductory remarks 

 to Chapter IX, art. 232, page 211. 



CHAPTER IX. 



OF FLOATATION, AND THE DETERMINATION OF THE SPECIFIC 

 GRAVITIES OF BODIES IMMERSED IN FLUIDS. 



The buoyant force equivalent to the weight of the displaced fluid, art. 233, pages 

 212, 213, and 214. The pressure downwards equal to the buoyant force, art. 233, 

 corol. page 214. The height determined to which a fluid rises in a cylindrical 

 vessel, in consequence of the immersion of a given sphere of less specific gravity, 

 art. 234, pages 214 and 215. Practical rule for ditto, art. 235, page 216. Example 

 for illustrating ditto, art. 236, page 216. The same determined when the sphere 

 and the fluid are of equal specific gravity, art. 237, page 216; Practical rule for 

 ditto, ib. Example for illustrating ditto, art. 238, pages 216 and 217. The height 

 determined to which the fluid rises in a paraboloidal vessel, in consequence of the 

 immersion of a sphere of less specific gravity, art. 239, pages 217, 218, and 219. 



Practical rule for ditto, art. 240, page 219. Example for illustrating ditto, art. 

 241, pages 219 and 220. The same determined when the sphere and the fluid are 

 of equal specific gravity, art. 242, page 220. Practical rule for ditto, art. 243, 

 page 220. Example for illustrating ditto, art. 244, pages 220 and 221. Remarks 

 on ditto, art. 244, corol. page 221. A homogeneous body placed in a fluid of the 

 same density as itself, remains at rest in all places and in all positions, art. 245, 

 pages 221 and 222. The upward pressure against the base of a body immersed in 



