Prof. Challis on the Principles of Hydrodynamics. 27 



It will be necessaiy for the complete exhibition of the com'se 

 of the reasoning, to begin by a consideration of the fundamental 

 principles of the mathematical treatment of the equilibrium and 

 motion of fluids. 



Definition I. The parts of a fluid press against each other, 

 and "against the surface of any soUd with which they are in 

 contact. 



Definition II. The parts of a fluid of perfect fluidity may be 

 separated by an uifinitely thin solid bounded by plane faces, 

 Avithout the a])plication of any assignable force. 



The fii-st of these two definitions is the statement of a general 

 property of fluids knowTi by common experience. The other is 

 equally" di-awn from experience, being suggested by the facility 

 with which the parts of a fluid may be separated. As all knowrf 

 fluids possess some degree of cohesiveness, none answer strictly 

 to this definition. The hypothesis of perfect fluidity is made 

 the basis of exact mathematical reasoning applied to the equili- 

 brium and motion of fluids, in the same way that the hjT)othesis 

 of perfect rigidity is the basis of exact mathematical reasoning 

 applied to the mechanics'of solids. 



These two properties suffice to define fluids generally, and 

 may be employed in the investigation of a certain law of pressure, 

 which is common to all perfect fluids, however they may be spe- 

 cifically distingviished. The law of pressure is found as follows, 

 the fluid being supposed to be at rest. 



Proposition I. The pressure at any point in the interior of 

 fluid at rest on an imaginaiy plane passing through that point, 

 is the same whatever be the position of the plane. 



Suppose an indefinitely small .element of the fluid to be sepa- 

 rated from the rest by indefinitely thin solid plates, and let the 

 form of the element be that of a prism, the transverse section of 

 which is a right-angled triangle. By Definition II. the pressui-e 

 is in no respect altered by insulating the element in this manner, 

 it being done without the application of any assignable force. 

 Also by Definition I. the element presses against the solid plates 

 with which it is in contact ; and these pressm-es, it is clear, must 

 be counteracted by equal pressures of the plates against the ele- 

 ment. But the plates are incapable of pressing in any other 

 directions than those of normals to their surfaces. Hence the 

 directions of these mutual pressures are perpendicular to the 

 plane faces of the element. Conceive the plates removed : the 

 pressures will remain the same. Consequently the element is 

 held in equilibrium by the pressm-es of the surrounding fluid 

 perpendicular to its surfaces, and by the impressed accclerative 



Now let ft be the length of the i)rism, a, /3, 7 the sides of the 



