SHORr MEMOIRS ON METEOROLOGICAL SUBJECTS. 4dd 



lu the case of a cyclone ou the earth's surface of comparatively slight 

 extension, and for which therefore the curvature of the earth's surface 

 can be neglected, we have a phenomenon quite similar to the preceding. 

 In addition to the rotatory movement of a cyclone relative to the earth's 

 surface there is also to be considered the proper motion of the latter, 

 one component of which corresponds to the turning of a disk about a 

 center. In the elementary text-books of physics, in connection with the 

 explanation of Foucault's pendulum experiments, it is demonstrated 

 that the magnitude of this horizontal component of the daily rotation is 

 expressed by n sin <p for the latitude ^, where n is the angular velocity 

 of the earth's rotation. We have therefore in the above expression to 

 substitute n sin ^ for w in order to find the magnitude of the centrifugal 

 force effective in a cyclone. The term n^ sin^ ^ must be omitted as 

 before, because we refer the difference of pressure or the barometric 

 gradient to the elliptical surface of the earth and uot to the surface that 

 would be if there were no rotation about an axis. 

 Let 



h — b' be the difference of pressure, expressed by the height of a 

 column of mercury, for a unit of distance in the horizontal direc- 

 tion along the normal to an isobar upon the earth's surface or a 

 surface parallel thereto, and let 



<T be the specific gravity of mercury, 

 then will the pressure of the unit volume of air in the direction of the 

 normal and toward the side of lower pressure be equal to (b — h') a. 

 The pressure in the opposite direction of the unit of volume resulting 

 from the centrifugal force of the rotating air is, according to an element- 

 ary proposition in mechanics, expressed by 



= -r io^ . 



org 

 where 



S is the specific gravity of the unit volume of air, 



g the acceleration of gravity, 



V the linear velocity of the air in its path, 



CO the angular velocity of the air in its path, 



r the radius vector of the air in its path. 



In our case, 



r w^ is (2 n sin 9? + ii) v. 



If, therefore, the air neither approaches nor recedes from the axis of 

 rotation, the following equation must obtain : 



{h — I') (T = - (2 n sin y + u) v. 



If further we designate by 



Ji> the "gradient" or the barometric difference for a definite dis- 

 tance I (the Loudon Meteorological Office assumes I = 50 nautical 

 or geographical miles = 92.7G kilometers), 



28 s 



