208 Prof. Potter on Hydrodynamics. 



tion of s, so thatj stopping at the first terms of the expansion of 

 ip + Bp), we have 



fy=±(2Bs), 



and 



4^jP..Ss^~ = 4,f'-^^ ^'" 



ds^^^'^SB^ 



_ dp 

 ~Jd's' 

 and the equation becomes 



then for elastic fluids, 



and supposing when s=0, that j9=jo,, and the velocity =V, we 

 have, putting v= -j-. 



+ «log(^)-l(i;2-V2) = 0. 



9^ 



-\p, 



For the case of liquids we must iise the law of density /3/=/3 

 (1 — cjo), and the equation is 



or, taking the limits as before. 



If we take c=0, these equations coincide with those from the 

 old theory for elastic and non-elastic fluids respectively. 



Proposition. To apply the general equation to the theory of 

 sound. 



We have now R = 0, and the pressure is a function of the or- 

 dinate of the displaced atom. 



Let s be the ordinate of the atom at rest, and S that when 

 displaced, at the time t : let ^>^ and pi be the pressure and density 

 before the disturbance, p and p their values at the time t. Then, 

 as in the paper on Sound in the last Number, 



_ K mass of an atom 



