30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



If the horizontal motion is uniform then 



whence 



whence 



*?> = and dv y = 

 dt dt 



P x = +2w sin X v cos a 



(6) 



Py = — 2 co sin X v sin a 



P = 2 co v sin X 



where P is the whole pressure exerted in a horizontal direction. 



If we substitute in equation (6) successively all values of a between 

 a = and a = 2 71 we soon perceive that the pressure P is 

 always perpendicular to the path of the moving mass and if X is 

 positive the pressure is always directed to the quadrant on the 

 right-hand side of the direction of motion. 



If the motion is uniform along the axis of % only, then for positive / 

 the direction of the pressure P will still be always toward the right- 

 hand of the direction of progress of the mass so long as the value 

 of a lies between and n, i. e., so long as the progress is in a direc- 

 tion between east and south and west. 



But if the motion is uniform along the axis of y only, then for posi- 

 tive X the pressure of P will be directed toward the right of the direc- 

 tion of progress for any value of this latter direction that lies be- 

 tween a = it and a = 2z. 



If the motion is not uniform along the axis of x or the axis of y 

 then the direction of the pressure P may be either toward the left 

 or the right of the direction of motion depending on the current 



dv x dv 



values of — r~ and -7- to an extent and manner easilv determined from 

 dt dt 



equation (5). 



