CONTENTS. XIX 



tion, art. 361, page 285. Transformation of the equations, art. 362, pages 285 and 

 286. Concluding remarks, art. 362, page 286. The change in the aerometer cor- 

 responding to any small variation in the density of the fluid, art. 363, page 286. 

 Practical rule for ditto, art. 364, pages 286 and 287. Example for illustration, art. 

 365, page 287. Remarks, ib. The sensibility of the instrument increased by 

 decreasing the diameter of the stem, and otherwise, art. 366, pages 287 and 288. 

 Practical rule for ditto, art. 367, page 288. Example for illustration and remarks 

 on ditto, art. 368, pages 288 and 289. Hydrostatic Balance introduced and de- 

 scribed, art. 369, pages 289 and 290. The specific gravity of a solid body determined 

 by the balance, that of distilled water being given, art. 370, page 291. Practical 

 rule for ditto, art. 371, page 291. Example for illustration, art. 372, page 291 . 



CHAPTER XII. 



OF THE POSITIONS OF EQUILIBRIUM. 



The positions of equilibrium of a triangular prism determined, art. 373, pages 

 292, 293, and 294. Remarks on the form of the resulting equation, art. 374, pages 

 294 and 295. Geometrical construction effected by means of two hyperbolas, art. 

 374, page 295. Example for illustrating the reduction of the formula, art. 375, 

 pages 295 and 296. Construction and calculation of the figure and its parts, arts. 

 376, 377, and 378, pages 296, 297, and 298. More positions of equilibrium exhi- 

 bited by the equation, and remarks on ditto, art. 379, page 299. The positions 

 determined when the section of the prism is isosceles, art. 380, pages 299 and 300. 

 Practical rule for ditto, art. 381, page 300. Example for illustration, art. 382, 

 pages 300 and 301. Other positions determined, art. 383, page 301. Remarks on 

 the resulting equation, art. 383, page 302. Practical rules for reducing ditto, art. 

 384, pages 302 and 303. Limits to the positions of equilibrium, art. 385, page 303. 

 Example for illustration, art. 386, pages 303 and 304. Remarks on ditto, art. 

 386, page 304. The positions delineated, art. 387, page 304. The same demon- 

 strated, pages 305 and 306. Remarks, art. 388, page 306. The positions of equi- 

 librium dependent upon the specific gravity, art. 389, pages 307 and 308. The 

 true positions delineated according to the conditions of the problem, art. 390, page 

 308. The positions of equilibrium determined when the section of the body is in 

 the form of an equilateral triangle, art. 391, pages 308 and 309. The positions 

 calculated, art. 392, pages 309 and 310. The positions delineated according to this 

 determination, page 310. Other positions determined, art. 393, pages 310 and 311. 

 The same positions delineated by construction, art. 393, page 31 1. The positions 

 of equilibrium determined for a triangular prism, when two of its edges fall below 

 the plane of floatation, art. 394, pages 311, 312, 313, 314, and 315.- The method of 

 reducing the general equation described, art. 395, page 315. Example to show the 

 method of reduction, art. 396, pages 315, 316, and 317. The position delineated 

 and verified, art. 397, page 317. Another condition of equilibrium, what, art. 398, 

 page 317. The same verified, page 318. Other positions of equilibrium determin- 

 able, the determination left for exercise to the reader, art. 399, page 318. The 

 same determined when the section of the figure is in the form of an isosceles 

 triangle, art. 400, page 318. The equation reduced, art. 401, page 319. Practical 

 rule for reducing the equation, art. 402, page 319. Example for illustration, art. 



or THE A 

 UNIVERSITY 3 



