26 Trans. Acad. Sci. of St. Louis. 



It is of course understood that (3) is not the real solution 

 of (2) and that no closed solution of (2) is possible. Never- 

 theless in this range of velocity from to 1406 miles per 

 hour, the greatest differences between the planimeter deter- 

 minations of (2) and the values computed from (3) are not 

 greater than the errors in the planimeter values. It is also 

 evident that by (3) the value of h-\- P' will become zero, 

 when V =&)?• = 00 , which seems to be a reasonable result. In 

 order to test equation (3) for a wider range of temperature, 

 a planimeter determination of ( 2 ) was made for a temperature 

 t = lOO^C or T= 373. The case where n = 100 and r = 100 



b + P' 

 was selected. The value of was found to be 0.4612. 



b 

 The value computed from (3) is 0.4580, giving a difference 

 of -I- 0.0032. 



If an oj)ening be made in the tube at the axis of rotation, 

 the pressure there will rise from b -\- P' to b. The pressure 

 at the outer end distant r from the axis may then be deter- 

 mined from (1) by making P' = in that equation. 



The pressure at the end caps in excess of the pressure b, 

 is when P' = 0, 



P TUT , W 



This value may be represented by the following series : — 



b^2CT^ 2.4C''^T2'^ ¥n.6..n {OT)l A. \ 



For all values of v less than 5000 cm. per sec. (110 miles 



per hour) the second and succeeding terms of (5) are small. 



Assuming T= 293% and v = 5000, the value of the first term 



is, for air, 0.014, while the second is 0.000110. For such 



velocities as occur in ordinary storms, Eq. (5) therefore 



becomes 



b 8 



•^ ~ 2 CT ^ ~2 

 This is identical with Newton's equation applied to the 



