24 Dr. W. N. Shaw. On the General [May 16, 



flow of air must diverge from strict parallelism with the isobar towards 

 the region of higher pressure, and vice versa. The angle of divergence 

 at any point would be, however, too small to affect the considerations 

 put forward in this paper. 



Neglecting the effect of frictional resistance, the condition of persistent 

 motion along parallel isobars is that the force due to the distribution 

 of pressure, i.e., the pressure gradient, shall supply the acceleration 

 which is necessary to keep a particle of air in its path; this condition is 

 expressed by the relation between the pressure gradient 7, expressed in 

 inches of mercury per degree (60 nautical miles), and the velocity V of 

 the moving air in statute miles per hour, as follows : 



7 = D (V 2 cot ,ox 0-000016 + V sin Xx 0-033), 



where X is the latitude, p the angular radius of the small circle oscu- 

 lating the path, and D the density of the moving air in pounds per cubic 

 foot. 



Of these two terms, that containing p depends upon the curvature of 

 the path and, from the magnitude of the numerical coefficient, it is 

 clearly insignificant unless the velocity of the wind is very great or 

 the radius of curvature of the path very small. It becomes very 

 important in the case of revolving storms of small diameter. The 

 other term is that depending upon the rotation of the earth, and repre- 

 sents 2o> V sin X,* where w is the angular velocity of the earth's 

 rotation. Omitting the first term we get for the condition of steady 



motion 



7 = DV sin X x 0-0330 inches per degree of 60 nautical miles. 



On fig. 2 the gradient is already indicated by the separation of 

 the isobars, the pressures being noted on the diagram in millimetres ; 

 the wind velocity which is necessary for steady motion, assuming' 

 for the purpose of computing D, a fixed vertical temperature gradient, 

 and neglecting the effect of the divergence or convergence of the 

 isobars, is given in figures in various parts of the diagram. The 

 velocities here indicated refer to the air at the 4000 metre level, but 

 it may be noticed that since the pressure gradient for a given velocity 

 is proportional to the air density, and the pressure is due to the weight 

 of the superincumbent air, steady motion along parallel isobaric lines 

 with the same velocity at all altitudes would result, if the run of the 

 isobanc lines were the same at every altitude. That condition would 

 be satisfied if at each altitude the isobars were also isothermal lines. 



The wind velocity near the surface is diminished by surface friction, 



t follows from this relation between gradient and velocity that 



) range of appreciable surface friction the velocity does not 



* See Uann, ' Meteorologie,' p. 421. 



