HYDROSTATICS. 347 



much doubt, however, remains upon this subject, and he is too rich in 

 honours to render it desirable to increase them by any of uncertain 

 authority. The machines which he constructed for the annoyance of 

 the Roman army, during the siege of Syracuse, astonish even our 

 present proficients in the science ; but as no writings particularly de- 

 scriptive of them have come down to us, we are in a great measure 

 unacquainted with the nature of their powers : and while much of 

 what is invaluable has been lost, much may have been exaggerated by 

 succeeding writers, and little of scientific detail can be relied upon 

 respecting them. No theory of mechanics, with the exception of what 

 little is found in the collection of Pappus, and which is chiefly a 

 repetition of the doctrines of Archimedes, appeared from the time of 

 the latter philosopher, till near the end of the sixteenth century. 



III. HYDROSTATICS. 



We have seen, in the historical chapter prefixed to our treatise on 

 Mechanics, that we are indebted to Archimedes for the first correct 

 theoretical notions of the doctrine of statics ; and it was the same 

 celebrated philosopher who first established the fundamental laws of 

 hydrostatics, or that branch of hydrodynamics which relates to the 

 equilibrium of fluids. 



With regard to the theory of the motion of bodies, whether solid or 

 fluid, or the sciences of dynamics and hydraulics, they have had their 

 birth wholly amongst the moderns ; the former of these we have 

 already noticed in the chapter above alluded to, and the latter will be 

 introduced in its proper place in the present article. 



According to some authors, the work which Archimedes composed Hydrostatics. 

 on Hydrostatics, we owe, as it now exists, to a translation from the Archimedes. 

 Arabic ; while others maintain that we have derived it from an imme- 

 diate translation of the original Greek text. This work is entitled 

 ' De Humido insidentibus,'* and is divided into two books. The basis 

 on which this author founds his theory is this : that every particle of 

 a fluid being supposed equal, and equally heavy, will renjain in the 

 place in which it is found ; or that the whole mass will be in equi- 

 librio when each particular particle is equally pressed in every direction. 

 This equality of pressure, on which the state of equilibrium is made 

 to depend, is demonstrated by experiment. The author afterwards 

 examines the conditions which ought to obtain, in order that a solid 

 homogeneous body, floating on a fluid, may take and preserve the situ- 

 ation of equilibrium : he shows that the centre of gravity of the body, 

 and that of the part immersed, must be situated in the same vertical 

 right line ; that the weight of the body is equal to the portion of fluid 

 displaced by it ; that the body will be entirely immersed when its spe- 

 cific gravity is equal to, or exceeds that of the fluid ; and other princi- 

 ples of the science of hydrostatics, which constitute the basis of the 

 theory of present times. It appears, likewise, from his investigations, 



