194 M. K. Zoppritz on some Hydrodynamic Problems 



so that the stratum preserves the constant depth A, and if we 

 further put 11=^=0 and 



lop_ 



consequently 



p = N + fig. v. 



N denotes then the pressure for ^=0, consequently (if the 

 origin of coordinates is transferred to the upper boundary 

 plane) the pressure, taken as constant, exerted by the conti- 

 guous medium upon the surface. Hereby becomes 



oz oy 



Since moreover the first of the differential equations is iden- 

 tically satisfied, there remains, for the determination of w, only 

 the third, 



dw __Jc p\o 



dt ~~ fi o% 2 



because the fourth merely expresses that w is independent of 

 z, and thereby causes the second differential quotient according 

 to z to be omitted in the present equation. 



In the condition-equation which must subsist for #=0, 

 P now signifies the pressure-component exerted, parallel to 

 the Z-axis, upon an element of the surface perpendicular to 

 the X-axis. According to F. Neuman and Kirchhoff 's nota- 

 tion, 



therefore here 



• T=-/*g=\(«> 1 -«>)- 



In the most general case, w 1 = <f>(t) is a given function of 

 the time. 



The application is not limited to cases in which only low 

 velocities occur, the squares of which can be neglected against 

 the first power : for since 



but here 



dw "dw "dw , ow "dw 



dt G t ox cy oz 



OZ 



