on the Received Principle* of Hydrodynamics. 449 



variation of pressure taking place per saltwn. Of course if we 

 admit the equation p = a 9 p, variation per saltum of density and 

 variation per saltum of pressure necessarily go together ; but in 

 a discussion as to the truth of that equation it is evident that 

 its validity cannot be assumed. 



But though believing variation of pressure per saltum to be 

 impossible, I see no more difficulty in supposing a variation of 

 density per saltum to occur in a fluid than in supposing two 

 fluids of different densities to be in contact, or that two solids of 

 different densities may be pressed together. Till, therefore, 

 Professor Challis has shown variation of density per saltum to 

 be impossible in a fluid, I shall consider myself entitled to insist 

 on all the consequences which, according to the received theory, 

 would flow from its occurrence. 



As to the second case, where a weight is suddenly placed 

 upon a piston supported by a vertical column of air, Professor 

 Challis admits that the dilemma I have suggested "is fairly in- 

 ferred and demands explanation." If it be true that the di- 

 lemma is fairly inferred, I think that most persons will regard 

 it as incapable of explanation, and as necessarily involving a 

 modification of the existing theory. 



Professor Challis' s explanation consists in supposing that "as 

 soon as the weight is added, there will be a tendency to an excess 

 of pressure on the upper side [of the stratum immediately under- 

 neath the piston] due to the disturbance of pressure in the solid 

 piston." 



If the words in italics mean any thing, they mean that there 

 will be an increased pressure of the piston on the air, at the 

 same time that, according to the received theory of pressure in 

 elastic fluids, no increase can have taken place in the pressure of 

 the air upon the piston ; which is manifestly a contradiction of 

 the law of the equality of action and reaction. Whatever dis- 

 turbance of pressure may exist in the other parts of the solid 

 piston, none such can occur at its base consistently with the rela- 

 tion p = a?p } until the lapse of an interval of time after the depo- 

 sition of the additional weight upon the piston. 



At the same time I think that a true and complete theory of 



early struggles in connexion with the subject, did have recourse to the 

 assumption of the truth of this law ; but, so far is it from being an adequate 

 foundation for a general theory of fluid motion, its retention is simple 

 strangulation to the theory, and accounts for the limited and unpromising 

 progeny which trace their origin to it. The true foundation of the theory 

 of fluid motion is the principle of continuity (continuity of motion, that is, 

 as well as continuity of mass), from which it results, as can readily be 

 shown, that any element of the fluid mass will comport itself exactly in the 

 same manner as an element of a rigid body would do under the same cir- 

 cumstances, and may therefore be dealt with accordingly. 



Phil. Mag. S. 4. Vol. 46. No. 308. Dec. 1873. 2 II 



