XX CONTENTS. 



403, pages 319 and 320. The position delineated by construction, art. 404, page 

 320. Other two positions of equilibrium determinable, art. 405, pages 320, 321, 

 and 322. 



Limits to the specific gravity defined when the body floats with two of its angles 

 immersed, art. 405, page 321. Expression for the arithmetical mean between the 

 limits, equation (247), page 321. Expressions for the extant sides of the triangular 

 section, (equations 248 and 249), pages 321 and 322. Remarks on ditto, art. 405, 

 page 322. Example for illustration, art. 406, page 322. Construction indicating 

 the positions, art. 407, page 322. The construction verified by calculation, art. 407, 

 page 323, and art. 408, page 324. The positions of equilibrium determined when 

 the triangular section is equilateral, art. 409, pages 324 and 325. Remarks on 

 ditto, art. 409, page 325. Example for illustration, art. 410, page 325. Construc- 

 tion indicating the positions, art. 410, page 325. The same verified by calculation, 

 art. 410, page 326. Two other positions assignable, ib. The limits of the specific 

 gravity defined, art. 411, pages 326 and 327. Positions of equilibrium determined, 

 art. 411, page 327. Construction indicating the positions, art. 412, page 327. 

 The same verified by calculation, arts. 412 and 413, pages 327 and 328. Con- 

 cluding remarks on ditto, art. 414, pages 328 and 329. The positions of equilibrium 

 determined for a rectangular prism with one of its edges immersed, art. 415, pages 

 329 to 331. General remarks on ditto, art. 416, page 332. The positions deter- 

 mined when the ends of the prism are squares, art. 417, page 332. General 

 inference from ditto, art. 417, page 333. Practical rule for ditto, art. 418, page 

 333. Example for illustration, art. 419, page 333. Construction indicating the 

 position, arts. 419 and 420, page 333. Condition establishing the equilibrium, 

 art. 421, page 334. The maximum limit of the specific gravity defined, art. 422, 

 page 334. Two other positions determined, as they depend upon the limit of the 

 specific gravity, art. 423, page 334. Conditions that limit the specific gravity, 

 art. 424, page 334. Positions determined according to the limits, and repre- 

 sented by diagrams, art. 425, pages 334 and 335. Positions determined from 

 the arithmetical mean of the limits, and represented by diagrams, pages 335 and 

 336. The positions determined when three edges of the prism are immersed, 

 art. 426, page 336. The positions determined when two edges are immersed, art. 

 427, page 336. Remarks on the superior difficulty of this case, page 337. Pre- 

 paratory construction, ib. The conditions necessary for a state of equilibrium, 

 page 338. The first condition established, equation (265), page 339. The second 

 condition determinable by a separate construction, page 339. The investigation 

 pursued, pages 340, 341, and 342. The positions determined, art. 429, pages 342, 

 343, and 344. The same determined when the section is a square, art. 430, page 

 344. When the specific gravity of the prism is half the specific gravity of the 

 fluid, the body sinks to half its depth, art. 431, page 344. This position repre- 

 sented by a diagram, ib. The positions which the body would assume in the course 

 of revolution assigned, page 345. Two other positions assignable, dependent on 

 the limits of the specific gravity, page 345, equations (273 and 274). Construction 

 indicating the position according to the limits, art. 432, page 346. The maximum 

 limit of the specific gravity determined, art. 433, page 346. Remarks, accompanied 

 by diagrams to indicate the positions, art. 434, pages 346 and 347. The arith- 

 metical mean between the limits assigned, art. 435, page 347. The positions 

 assigned numerically, art. 436, pages 347 and 348. The same indicated by con- 

 struction, art. 436, page 348. The reverse positions exhibited, art. 437, page 348. 



