154 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



By introducing a mean value of the density and by expressing 

 the distance r in degrees of the meridian, we can write 



a a' 



G = - + - (8) 



r r v 



in which a and a' are constants. Then the increase d b of the pres- 

 sure in millimeters is equal to G d r and we shall find 



a r a' / 1 1 \ 



6 - 6 °=m 1o s-7 -2(7>~v) (9) 



The equations that we have developed demand that the altitude 

 of the current of air remains constant since we assume its horizon- 

 tality. We can then, therefore, only apply the equations to the 

 exterior parts of a whirl about a barometric depression, for in the 

 interior of the whirlwind the currents have an ascending movement 

 so rapid that we cannot neglect it. 



Applications 



(1) Whirlwind having a great velocity (see fig. 9). 

 Let the latitude = 20°, 



k = 0.00002, 

 r = 20°, 



= 0.001006 (for a mean pressure of 753 mm ) 



t; = 50 m , 

 r = 0°.3. 



Expressing r in degrees of the meridian we have 



0.8 2.014 r 1.007 



G =— +— ;&-6 = 1.842 log- + 11.19- — 



<p =328 T °; a =68° 5.8' 



r = 0°.3 0.°4 0°.5 



7/ = 50 m 37. 5 m 30 m 



G =77. 3 mm 33.5 mm 17.7 mm 

 6-6 o = mm 5.1 mm 7.6 mm 



-y>=0° 41° 73° 99° 140° 172* 340° 



