98 PHYSICAL SCIENCES IN ANCIENT GREECE. 



assumed to represent the first. Now this arbitrary and capricious 

 evasion of the question we consider as opposed to the introduction of 

 the distinct and proper idea of Pressure, by means of which the true 

 principles of this subject can be apprehended. 



We have already seen that Aristotle was in the number of those 

 who thus evaded the difficulties of the problem of the lever, and con- 

 sequently lost the reward of success. He failed, as has before been 

 stated, in consequence of his seeking his principles in notions, either 

 vague and loose, as the distinction of natural and unnatural motions, or 

 else inappropriate, as the circle which the weight would describe, the 

 velocity which it would have if it moved ; circumstances which are 

 not part of the fact under consideration. The influence of such modes 

 of speculation was the main hindrance to the prosecution of the true 

 Archimedean form of the science of Mechanics. 



The mechanical doctrine of Equilibrium, is Statics. It is to be dis- 

 tinguished from the mechanical doctrine of Motion, which is termed 



O ' 



Dynamics, and which was not successfully treated till the time of 

 Galileo. 



Sect. 2. Hydrostatics. 



ARCHIMEDES not only laid the foundations of the Statics of solid 

 bodies, but also solved the principal problem of Hydrostatics, or the 

 Statics of Fluids ; namely, the conditions of the floating of bodies. 

 This is the more remarkable, since not only did the principles which 

 Archimedes established on this subject remain unpursued till the revi- 

 val of science in modern times, but, when they were again put forward, 

 the main proposition was so far from obvious that it was termed, and 

 is to this day called, the hydrostatic paradox. The true doctrine of 

 Hydrostatics, however, assuming the Idea of Pressure, which it in- 

 volves, in common with the Mechanics of solid bodies, requires also a 

 distinct Idea of a Fluid, as a body of which the parts are perfectly mov- 

 able among each other by the slightest partial pressure, and in which 

 all pressure exerted on one part is transferred to all other parts. From 

 this idea of Fluidity, necessarily follows that multiplication of pressure 

 which constitutes the hydrostatic paradox ; and the notion being seen 

 to be verified in nature, the consequences were also realized as facts. 

 This notion of Fluidity is expressed in the postulate which stands at the 

 head of Archimedes' " Treatise on Floating Bodies." And from this 

 principle are deduced the solutions, not only of the simple problems 

 of the science, but of some problems of considerable complexity. 



