Il6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5 1 



whence 



dt 

 If the particle start from the center, 



and we obtain 



JO 



B — and = — Jo, 

 dt 



4:R 4:R 



r = (1 — cos % at) = (1 — cos 6). 



The particle therefore describes a cardioid, but if there is damping 

 the motion will come to be along the circle r = ^R/a 2 . 



The time to reach the circle is 7i/a, or about 8 hours for latitude 



5°°- 



These times are not large meteorologically, and we may there- 

 fore expect the relation between air velocity and pressure gradient 

 to be that corresponding to steady motion so long as there are no 

 irregularities to produce turbulent motion. 



For application to wind velocities in the upper air we require to 

 know the upper-air isobars. If we have air in which the horizontal 

 laj^ers are isothermal, then from the equations 



dp= - gp dz, p = gkpT, 



it follows that 



P. Jo kT 



We have, therefore, if p and p + dp are surface isobars and 

 p z and p z + dp z the corresponding upper isobars, 



*-^ f so that **•-*£. 



Pz Po Pz Po To 



Therefore the velocity calculated from the surface isobars will 

 apply to the upper air, except for the factor, TJT . For z =iooo 

 meters the effect of this factor is to diminish the velocity by about 

 2 per cent. 



If the conditions are not isothermal, but such that the isotherms 

 and isobars intersect at an angle (/>, the upper isobars will have a 

 different direction from the surface isobars, and the value of the 

 upper gradient will also be changed (see fig. 4). 



