CONTENTS. XXI 



The construction verified by calculation, art. 438, page 349. The positions of 

 equilibrium determined for a solid, of which the transverse section is in the form 

 of the common parabola, art. 439, pages 349-352. Practical rule for ditto, art. 440, 

 page 352. Example to illustrate ditto, art. 441, page 352. Construction indicating 

 the position of equilibrium, with its verification, art. 442, page 353. The same 

 determinable for the figure in the inclined position, art. 443, pages 353 to 356. 

 Example to illustrate ditto, art. 444, pages 356 and 357. The positions indicated 

 by construction, page 357. The construction verified, page 358. 



CHAPTER XIII. 



OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



Stability of floating bodies, the subject introduced, art. 446, page 359. General 

 remarks concerning ditto, arts. 447, 448, and 449, pages 359 to 362. Definitions, 

 art. 450, pages 362 and 363. A floating body displaces a quantity of fluid equal 

 to its own weight, and in consequence, the specific gravity of the fluid is to that of 

 the solid, as the whole magnitude is to the part immersed, art. 451, pages 363 and 

 364. A floating body is impelled downwards by its own weight, and upwards bj 

 the pressure of the fluid, and these forces act in vertical lines passing through the 

 centre of effort and the centre of buoyancy, art. 452, page 364. When these lines 

 do not coincide, the body revolves upon an axis of motion, ib. If a floating body be 

 deflected from the upright position, the stability is proportional to the length of the 

 equilibrating lever, or to the horizontal distance between the vertical lines, passing 

 through the centre of effort and the centre of buoyancy, art. 453, page 364. When 

 this distance vanishes, the equilibrium is that of indifference, ib. When it falls on 

 the same side of the centre of effort as the depressed parts of the solid, the equili- 

 brium is that of stability, art. 453, pages 364 and 365. When it falls on the same 

 side as the elevated parts, the equilibrium is that of instability, art. 453, page 365. 

 Concluding remarks, ib. A general proposition belonging to the centre of gra- 

 vity, art. 454, page 365. General and subsidiary remarks, ib. 



The stability of floating bodies determined, art. 455, pages 366 to 370. The 

 manner of generalizing the result explained, together with the constituent elements 

 of the equation, art. 456, page 370. Example for illustration, art. 457, pages 370 

 and 371. The steps of calculation illustrated by reference to a diagram, arts. 458, 

 459, 460, 461, 462, 463, and 464, pages 371 to 375. Concluding observations, art. 

 464, page 375. 



The principle of stability applied to ships, art. 465, page 376. The conditions 

 of the data explained, art. 466, pages 376 and 377. The longer and shorter axes, 

 what, art. 467, page 377. In what respects a ship may be considered as a regular 

 body, art. 468, page 377. The principal section of the water, what, art. 468, page 

 377. The circumstances and conditions of calculation explained ,by reference to a 

 diagram, arts. 469, 470, 471, and 472, pages 378 to 382. A numerical example for 

 illustration, art. 473, page 382. Table of the measured ordinates, page 383. 

 Construction of the example explained, pages 384 to 387. Construction continued, 

 art. 474, pages 387 to 389. The contents of the displaced volumes, how obtained, 

 art. 475, page 389. Approximating rules for calculating the areas and solidities, 

 art. 476, page 390. The construction completed, art. 477, page 390. The practical 

 delineation of the vertical and horizontal planes, arts. 478 and 479, pages 391 and 



