to the received Principles of Hydrodynamics. 249 



With respect to the case I have proposed regarding the piston 

 and the weight, of which Professor Challis has treated, he ap- 

 pears to have failed in catching the point of my objection. Ad- 

 mitting for the moment that the piston would begin to descend 



with the accelerating force ,. , with what accelerating force 

 ° M + m 



will the stratum of air begin to descend according to the ordinary 



theory ? 



At the beginning of the motion the pressure on the upper 



side of the stratum would be My, and that on the under side 



would equally be My. Hence, while at the beginning of the 



motion the piston, according to the received theory, would have 



a tendency to move represented by the accelerating force ^-~ — , 



the stratum in immediate contact with the piston at the same 

 epoch would have no tendency to move whatever, a state of cir- 

 cumstances which I maintain to involve a contradiction. If the 

 introduction of the second weight does not produce in the stra- 

 tum under consideration a tendency to move, what other circum- 

 stance can occur which would produce in the stratum such a ten- 

 dency ? If it be answered that this will happen when the piston 

 has descended through an indefinitely small space, I reply that 

 the piston cannot descend through an indefinitely small space 

 without the underlying stratum of air descending through a 

 corresponding space, and that it is impossible that a stratum 

 which has no tendency to move can descend through even an in- 

 definitely small space. 



I am afraid that I cannot agree with Professor Challis as to 

 the bearing upon Boyle's law in the case of motion of the cases 

 I have suggested where the density varies per saltum. If on one 

 side of a given plane we have a density 21), and on the opposite 

 side a density D, then without waiting or attempting to decide 

 what the motion would be under such circumstances, it appears 

 to me that I cannot err in saying that, according to the received 

 theory, the pressure of the first portion of the fluid on the second 

 is double that of the second on the first, and that therefore to 

 assert that Boyle's law and the law of the equality of action and 

 reaction hold in this case is simply to maintain a contradiction 

 in terms. 



If the views I have endeavoured to unfold are correct^ it will 

 follow that the true function of experiment in determining the 

 motion we have been considering is to determine the initial 

 values of the pressure, density, and velocity. These being known, 

 the values of the arbitrary functions </>, ijr lf ^ 2 can be ascertained, 

 and the motion will be completely represented by the equations (2) . 



P.S. — It may be remarked that, if it be intended that we shall 



