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SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



must be added to the exterior forces. This vertical force includes 

 also the force of gravity. 



FIG. 166 



§19. Equations of motion 



In order to study the general motion of the air we take three rect- 

 angular axes of which the axes X and Y are horizontal and the 

 axis Z vertical and ascending. Denoting by u, v and w the com- 

 ponents of the velocity parallel to the axes and by x, y and z the 

 components of the forces referred to the unit of mass and by p the 

 density, the equations of hydrodynamics are written 



p dz 



dt 



(1) 



