Pressure in Fluids. 



121 



If o) 1 = C ] and (o 2 = Q 2 be the respective integrals of the equa- 

 tions 



2p 2 ^' 



(8 a) 



we shall have in a^, &> 2 /wo values for/, since they obviously 

 satisfy (7) and also, being free from x, ij, and t } satisfy (8). 



Again, we have for the integration of (8) the following auxi- 

 liary equations, viz. 



= dx 



2D 



= dp, 

 0=dv. 

 Hence we shall have the two following additional values for/, viz. 



^'L*- 2D M ' 



/=<£ 



(9) 



P- C T, T+ <v +')4 



where </> is arbitrary, provided these values satisfy also equa- 

 tion (7). 



But if (9) satisfies (7), the latter will be satisfied by 



/=*{*- X 



+ VV 2 + 4Rp s 



2D 



■-}■ 



in order to which we must have 

 d 



0== ^( V + ^V 2 + 4V) 



^//3 



+ 



V+,v/V 2 i-4V 

 2p 2 



G^ 



(V+ •V 2 + 4V);j 



> (io) 



or, which is the same thing, 



= ( V + V 'V 2 + 4 V) ^ ( V + v/ V 2 + 4 V) 



> . (10 a) 



