abi 



cij3 7 







founded on the Atomic constitution of Fluids. 103 



Supposing the disturbance to 

 be wholly in the direction of the 

 wave motion, let be the origin, 

 a, b, c the positions of thi-ee con- 

 tiguous atoms when the fluid is 

 at rest in the line of the disturb- 

 ance, «, /3, 7 the same atoms 

 after an interval of time t after disturbance. 



Let 



Ob = x, 0^=y 



ab ovbc=2,r,, «/3 = 2r' 



= 2.8^, /37=2r". 



Now (2.S.r)^ being the area of the face of the cube attributed 

 to the atom b, then {2,.hyY will be that to be attributed to the 

 atom /3, with respect to which the elastic forces are to be con- 

 sidered. 



If y and y" are the ordinates of the nearer and further faces 

 of the cube of /3 respectively, we have 



■-y- 



dx 



^■' ^3 + *'°• 



and forming the equation of motion for the particle /3, we have 



d'^y _ pressure on nearer face of atom— pressure on further face 



dt^ mass of an atom 



,- ^ -gKinass of atom ,„ r. .o ^ mass of atom 

 i^-^I/) QJE (3-6?/)- 



8r'3 



8/-"3 



mass of atom 



_ By^.K f 1 _ 1^\ 



_3 d^ 





\dz) 



Neglecting the higher terms of the series, and putting ^ = -^, 



