EQUATIONS OF MOTION OF A PERFECT LIQUID 

 AND A VISCOUS LIQUID, WHEN REFERRED 

 TO CYLINDRICAL AND POLAR CO- 

 ORDINATES. 



BY P. E. DOLDNA,* A. M. 



(Continued from Vol. VII, p. 48.) 



Equations of a Perfect Liqiid. 



CijliiidricdlCo-onlinaU's: The etiuations of motion of 

 a perfect tliiid when referred to cylindrical coordinates may 

 be derived from those already obtained for rectangular co- 

 ordinates by transformation. The following, however, is a 

 more satisfactory method in so much as it gives a definite 

 interpretation to each term appearing in the resulting equa- 

 tions. Moreover, the method to be applied in the derivation 

 of the equations when referred to cylindrical coordinates and 

 polar coordinates forms th^ basis of several important prin- 

 ciples involved in the derivation of the ecpiations of motion 

 of a viscous fluid referred to the same systems of coordinates. 



The velocities u, i\ iv, and the impressed forces X, Y, Z 

 have the directions of ?•, (K and z, respectively; v is angular 

 velocity. 



X.p r do dz (/r= impressed force in the direction of r 



* Died at Colorado Spring.^, January G, 1900. 



