Travelling Atmospheric Disturba?ices. r i 



Motion of the depression in one definite direction cannot 

 therefore occur, though it may change its form subject to 

 the condition that it must remain symmetrical with respect 

 to these axes. Hence a cyclone cannot travel if it is 

 symmetrical with respect to two axes ; if it is to do so it 

 must be definitely ovoid in form. A case of motion produced 

 by asymmetry is afforded by the ordinary cyclone. This 

 forms at the edge of a region of low pressure, so we shall 

 take the general distribution of pressure to be decreasing in 

 the direction of x increasing. In such a system a depression 

 forms, the lowest pressure being near its centre. It seems, 

 however, that the distribution does not consist of a sym- 

 metrical distribution on which a uniform increase in one 

 direction is superposed. For if it were so, we should have 



P = -B<r + R, 



where R is a function of x 2 + y 2 only, and B is a constant. 

 Then 



a( Vi , P,P) =B 3Vi s R 



~d\oc,y) by ' 



and the rate of variation of P is given by 



BP = gKB 3Vi 2 R 

 ~dt 8ft> 8 /? "dy 



Now if the disturbance is travelling unaltered we must 

 have 



| +U |_ + v|-=0, 



bt bx by 



where U and V are the components of the velocity of trans- 

 lation, and the object of the operation is any of the physical 

 quantities of the system. But the density does not depend 

 on t or ?/, and therefore this operation on it shows that U is 

 zero. Next applying it to P we find 



by 8co*p Q by 



First, consider the order of magnitude of the velocity of 

 translation thus indicated. Let the horizontal dimensions 

 of the cyclone be of order a ; then Vi 2 R is comparable with 



R/cr, and V is of order — -J^ *. 



Q(oy a J 



Now ~B/2cop is the geostrophic wind corresponding to the 

 general pressure gradient ; and gH/iw 2 is the square of the 

 distance sound would travel in an interval comparable with 

 12 hours, which is itself much greater than the linear 



