3l6 PHILOSOPHICAL TRANSACTIONS. [ANNO I7Q8. 



of sail, without danger or inconvenience, is reckoned among their most essential 

 properties ; though the wind may, in one sense be said to constitute the power by 

 which ships are moved forward in the sea, yet, if it acts on a vessel deficient in 

 stability, the effect will be to incline the ship from the upright, rather than to 

 propel it forward : stability is therefore not less necessary than the impulses of the 

 wind are, to the progressive motion of vessels. This power has also a considerable 

 influence in regulating the alternate oscillations of a ship in rolling and pitching ; 

 which will be smooth and equable, or sudden and irregular, in a great measure, 

 according as the stability is greater or less at the several angles of inclination from 

 the upright. From constantly observing that the performance of vessels at sea 

 depends materially on their stability, both navigators and naval architects must, at 

 all times, be desirous of discovering in what particular circumstances of construc- 

 tion this property consists, and according to what laws the stability is affected by 

 any varieties that may given to their forms, dimensions, and disposition of contents; 

 which are determined partly according to the skill and judgment of the constructor, 

 and partly by adjustments after the vessel has been set afloat. 



When a ship, or other floating body, is deflected from its quiescent position, the 

 force of the fluid's pressure operates to restore the floating body to the situation 

 from which it has been inclined. This force is distinctly described, in a treatise 

 written by the most celebrated geometrician of ancient times, who uses the follow- 

 ing argument for demonstrating the position in which a parabolic conoid will 

 float permanently in given circumstances. To show that this solid will float with 

 the axis inclined to the fluid's surface at a certain stated angle, depending on the 

 specific gravity and dimensions of the solid, he demonstrates *, that if the angle 

 should be greater than that which he has assigned, the fluid's pressure will diminish 

 it ; and that, if the angle should be less, the fluid's pressure will operate to increase 

 it, by causing the solid to revolve round an axis which is parallel to the horizon. 

 It is an evident consequence, that the solid cannot float quiescent with the axis 

 inclined to the fluid's surface, at any angle except that which is stated. The force 

 which is shown in this proposition, to turn the solid, so as to alter the inclination 

 of the axis to the horizon, is the same with the force of stability ; the quantity or 

 measure of which, Archimedes does not estimate ; nor was it necessary to his pur- 

 pose, since the alteration of inclination required to establish the quiescent position, 

 may be produced either in a greater or less time, without affecting his argument. 

 It does not appear, that this method of determining the floating positions of bodies 

 was afterwards extended to infer similar conclusions in respect to solids of any other 

 forms, nor to determine any thing concerning the inclination or equilibrium of 

 ships at sea, which require the demonstration, not only that a force exists, in given 

 circumstances, to turn the vessel round an axis, but also the magnitude or precise 

 measure of that force. M. Bouguer, in his treatise intitled " Traite du Navire-f-," 

 has investigated a theorem for estimating the exact measure of the stability of 



* Archimedes de iis quae in humido Yehuntur.— Orig. f Livr. 2, sect. 2, chap. 8.— Orig* 



