240 Prof. Challis on the Principles of Hydrodynamics. 



the equation (11.) are the coordinates of the position of the ele- 



d1 

 meut for a given value of -^. By substituting these values in 



the expressions for u and v, it will appear that the velocity of a 

 given element in each position is a function of arbitrary quan- 

 tities. Hence this is a case of constrained motion, the law of the 

 action of the parts of the fluid on each other not coming imder 

 consideration. The fluid may be conceived to be compelled to 

 move between two vertical cylindrical siii-faces indefinitely near 

 each other, the equations of which ai*e a?/ = c^ and .ry:=(c-f 8c)^, 

 the impressions at the vertical boundaries of the flviid being given. 

 Or, it may be conceived to move between a series of such sur- 

 faces ; in which case, if the pressures at opposite points of the 

 separating surfaces be made equal by properly adjusting the 

 disturbances, the surfaces may be removed without afiecting the 

 motion ; and we shall thus have the case of a mass of fluid, im- 

 pressed in a known manner so that the resulting motion at any 

 point is given by the equations u=^mx, v:= — my. 



In the next communication I propose to apply to compressible 

 fluids considerations analogous to those which have here been 



■ given to incompressible. ;,;(■! jliiifi--. i; 



Cambridge Obsen-atory, ' ' ... - -'i. ri) (d .bioit 



'!' ^-- Januaiy 13, 1851. A ; ,(\>n vrxn^t jih v noxJfifs'i oxt 



[To be continued.] ,, ( 



The Article by Professor Stokes m the last Number of the 

 Philosophical Magazine requires from me a few words of no- 

 tice. I am quite willing to enter upon a discussion of any of 

 the new principles or propositions in hydi-odynamics of which I 

 am the author, and I approve of the course which Professor Stokes 

 proposes to adopt, viz. to notice one important point only at a 

 time, and to discontinue the discussion if it be found impossible 

 to agree on a question of vital importance. 



Before proceeding to the consideration of the two arguments 

 directed against my second axiom, I must correct a misappre- 

 hension into which Professor Stokes has fallen, probably from 

 want of explicitness on my part, with respect to the remark I 

 made after enunciating the axiom. The remark is unimportant, 

 and fomis no part of my argument. I meant to say, that a col- 

 lection of indefinitely small discrete atoms may move so that the 

 lines of motion at a given point of space may intersect each other 

 at finite angles of inclination, and at the same time the equation 

 of constancy of mass be satisfied, but that the condition expressed 

 by the axiom excludes such motion. It was not my intention to 

 assert, that in cases to which the axiom did not apply, the mo- 

 tion could only belong to a set of discrete atoms. 



