666 Dr. G. Green on some Probl 



ems 



The coordinates of any point referred to point at each 

 instant we shall denote by (x, y, z) and the coordinates of the 

 same point referred to the three parallel axes through 0' are 

 then (#, y, z4-R), where R denotes the radius of the earth 

 approximately. For our present purpose we may treat the 

 earth as a perfect sphere. The three axes which we have 

 chosen through 0' are at each instant rotating axes. We 

 shall accordingly represent by 



co x : — the angular velocity of rotation of axes O'Y and 

 O'Z about axis O'X', 



with G) y and co z as corresponding quantities for the other 

 axes respectively. The corresponding rates of change of 

 these quantities are then denoted by co x , coy, co z respectively, 

 and the components of the velocity of the fluid relative to 

 the moving axes specified above, at each instant of time t, 

 are denoted by u, v, w respectively. 



Any possible motion of the fluid must now satisfy the 

 following system of equations : — 



(a) The equations of motion : 



^-2 &x w + 2a> z u - <M> + R) + *V* - (»,' + co x 2 )y = - ~ |^ > (A) 



dw 9n 1 "dp 



-£ — ItoyU + 2co x r — w y x + m x y — (a/ + co/) = — g — ■- g^ j 



where -=- = ^- + u^- + v^~ + w^- . 



<u 0^ O^' 03/ O^ 



(6) The equation of continuity of the fluid : 



l + KS + l + S)=°- " • • (B) 



(c) The equation determining the physical nature of the 

 iluid :— 



p = kp for an isothermal atmosphere, 



pz=kp y for an atmosphere in convective equilibrium, 

 where 7 denotes the ratio of the specific heat of 

 air pressure constant to the specific heat volume 

 constant. 



