114 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



the motion were steady, the air would in general move tangentially 

 to the isobars, and its velocity would agree with that calculated from 

 the equation given above. 



The question, however, arises as to whether the pressure is likely 

 to continue steady long enough for a condition to supervene in which 

 the equation is applicable. We can get an idea of the time that 

 would elapse before air, starting from rest, would reach a state of 

 steady motion, by considering the motion of a particle on the earth's 

 surface (1) under a constant force in a constant direction, corre- 

 sponding to straight isobars; (2) under a constant radial force corre- 

 sponding to cyclonic and anticyclonic conditions. The particle 

 would begin to move at right angles to the isobars in the direction 

 of the force, but as its velocity increased it would be deflected by the 

 effect of the earth's rotation until it moved perpendicularly to the 

 force. 



The equations of motion of a particle, referred to axes fixed rela- 

 tively to the earth and having an origin on the surface in latitude 

 X, are 



dH dz .dy v 



■ — — 2co cos X — - 2w sin i ~ = X , 

 dt 2 dt dt 



d 2 y _ . , dx - T 



—L + 2uj sin X — = Y, 

 dt 2 dt 



d 2 z dx 



— + 2u> cos k — — Z, 



dt dt 



where the axis of z is vertical and the axes of x and y are west and 

 south respectively. 



If there is no vertical motion we may write the first two equations 



d 2 x dy ,. d 2 y , dx * , 



— — a — = X , — + a — = Y, 



dt 2 dt dt 2 dt 



and the form of the equations and the value of a are unaltered by 

 changing to other axes in the same plane. Let us take the y axis 

 to be in the direction of the constant force b. Then 



whence 



