234 SMITHSONIAN MISCELLANEOUS COLLECTIONS [VOL. 51 



§35. Influence of the movement of the system of wind 



In the preceding example we have considered the movement of 

 a system of wind under the hypothesis that the system keeps its 

 form unaltered while moving. But this hypothesis is not correct. 

 A moving cyclone does not transport its system of isobars in the 

 same way that a system of circles is geometrically transported. 

 We shall consider the general case in which the cyclone is movable 

 as to location and variable as to the pressure at the center. We can, 

 therefore, by. the aid of the following equations determine directly 

 the variations of the pressure d and d that we have already deduced 

 less precisely in another way in §§30 and 32. 



Exterior portion 



Consider a horizontal current; the equations of motion (see §19) 

 assume the form 



1 dp . n . du du du ... 



. — — -2w sin .v — k u — — — u — — v — . . (1) 

 p dx dt dx dy 



\ dp . dv dv dv . 



-.— = 2wsino.« - k v — — — u — — v— . . . (2) 

 p dy dt dx dy 



Let £ and 17 be the coordinates of the moving origin and assume 

 that the velocities u and v are expressible in the form 



r 2 



v _ M(y - v ) - N(x - fl 

 r 2 

 where 



r 2 = (x - £) 2 + (y - T)) 2 



(4) 



Here M and N like £ and 9 are functions of the time /, and we 

 designate their derivatives with respect to t by M' N ,' £' and rf 

 We easily see that the condition 



d 2 p d 2 p 



dy dx dx dy 



will be satisfied when we have 



du _ dv 

 dy dx 



