202 SCIENCE PROGRESS 



sufficient to produce a tornado of such violence as actually 

 occurs in nature, his argument being as follows : 



where p is the pressure at height h 



g is the acceleration due to gravity 

 A is the vertical acceleration of the air 

 D is its density 



is an equation which is true within the core of a tornado, as 

 well as in the outside air. At the ground-level there is a dif- 

 ference of pressure between the core and the outside air, which 

 decreases to zero at that height where the rotational move- 

 ment comes to an end. It follows that the mean value of -£ 



ah 



must be less inside the core than without. Now, the accelera- 



db 



tion A would increase numerically the value of — given by 



equation (i) if it were directed upwards, but, on the other 



hand, there cannot be an appreciable downward acceleration 



if the tornado is to persist for any length of time. 



dp 

 Taking, then, -£ = — gD . . . (2) simply, and using the 



equation p = R D T 



where R is Charles' constant for air 

 and T is the temperature at any point 



we get dp — g 



pdh '''' RT 



and therefore log -p = -^ . . . (3) 



where B = barometric pressure at the ground 

 P = barometric pressure at the top 

 H = height of the tornado 

 M = harmonic mean of T. 



Outside the tornado the same equations apply, and the follow- 

 ing relationship is arrived at : 



TV 



10^) 



log© 



C\ M 



