The Travelling Cyclone. 421 



revolving uniformly in the plane xy with angular velocity g>*, 

 u and v are the components of relative velocity of the fluid 

 in the directions of the revolving axes, that is the components 

 of wind. We have now to define the motion for which we 

 wish to determine the balancing pressures. 



We contemplate a motion (relatively to the ground) of 

 rotation about a centre 0, fig. 1, situated on the axis of x. 



the successive rings P at distance R from C revolving with 

 an angular velocity f, which may be a function of R. And 

 upon this is to be superposed a uniform velocity of transla- 

 tion U, parallel to x and carrying everything forward. If 

 initially be at 0, the fixed origin, its distance from along 

 Ox at time t will be Vt. Thus 



tt=U-{fc v=.r(,,-TJt), .... (4) 



f being a known function of R, where 



W=y*+(x-my=y* + X\ ... (5) 



These equations give u and v in terms of the coordinates and 

 of the time, and the values are to be introduced into (1) and 

 (2). From the manner in which x and t enter (representing 

 a uniform translation of the entire system) it is evident that 

 djdt =—JJ d/dx. We ha ve 



du £Zy 



dx~ R ""' 



du 

 dy~ 



& R 



dv rx 2 



dx~^ + R ' 



dv 

 dy ~ 



R ' 



* In the application to a part of the earth's atmosphere, wis the 

 earth's angular velocity multiplied by the sine of the latitude. 



