Travelling Atmospheric Disturbances. 3 



Further simplification is not possible without some know- 

 ledge of the size of the quantities involved. If it be assumed, 

 as is usually correct in these latitudes, that the pressure 

 gradients and wind velocities are small enough for their 

 squares to be neglected in a first approximation, we have 

 nearly 



poy ) 



which gives the so-called " Geostrophic relation." If the 

 isobars are concentric circles we have as a second approxi- 

 mation, the density being assumed constant, the equation 



l 2 +2(oV= i^ (5) 



r p or y 



where V is the resultant velocity and r the distance from 

 the common centre, which is the usual form of the equation 

 giving the wind in terms of the pressure gradient. It is 

 often assumed to be correct even when the pressure distri- 

 bution is changing with the time ; but this involves the 

 assumption that the air is not accelerated along its path, 



which means that —r- is neglected while ~~ is retained. 

 at ° ot 



This is a very uncertain hypothesis, for in general these 

 two quantities would be expected to be of the same order of 

 magnitude. 



When the pressure distribution is varying, the problem 

 becomes much more complex. A cyclone in most cases 

 moves fairly steadily in one direction, the isobars remaining 

 approximately concentric. Sometimes the depression in the 

 centre deepens as it moves, more often it becomes shallower and 

 spreads out, but frequently it travels for thousands of miles 

 practically unchanged. Now if it were merely a wave free 

 to spread out, it would, as was said before, do so With a 

 velocity comparable with that of sound, and would therefore 

 disappear in a few hours. On the other hand, the motion 

 of the depression is not itself of the character of the pro- 

 pagation of a wave, for it only takes place at the rate of 

 some feet per second. Thus the moving depression, like the 

 stationary one, requires peculiar conditions for its main- 

 tenance, and it is intended to indicate some of these in the 

 present paper. The method adopted is that of successive 

 approximation according to powers of the pressure gradient. 



B2 



