20 Trans. Acad. Sci. of St. Louis. 



In 1894 the writer made an attempt to verify Newton's 

 formula by rotating a Pitot tube around the shaft of a steam 

 engine. A pipe about six feet in length was clamped to the 

 rim of the driving wheel. The outer ends terminated in i s 

 which faced in the direction of motion. A T tube at the 

 axis was joined by a flexible connection with a light drum in 

 a water joint, so that the axial pressure could be transmitted 

 to and measured with a water gauge. It was of course ex- 

 pected that the axial pressure would be less than J S'v'^ on 

 account of the rotation. It was however found that the 

 axial pressure was less than that of the atmosphere. The 

 decrease of pressure at the axis, due to rotation was appar- 

 ently greater than the increase due to the wind blowing into 

 the mouths of the Pitot tubes. It was also found that part 

 of this was due to a vortex motion set up in the air by the 

 engine wheel. 



A discussion of the theory of this experiment was then 

 begun and has been continued at intervals up to the present 

 time. 



Suppose the tube to be closed at the ends and at the axis, 

 thus imprisoning a column of air whose length measured 

 from the axis of rotation is r. The pressure b and tempera- 

 ture T may be assumed to be that of the atmosphere. By 

 the law of sases 



S3' 



B'T 



(7 = 2.88 X 10«. 



If the tube be rotated with an angular velocity &> := 2 7r?i, 

 the pressure will no longer be constant throughout the tube. 

 For constant values of 7i we may suppose the temperature to 

 become constant throuofhout. At anv distance r from the 



axis, the density is 



S' 



S = j(b + P) 



An element of gas in a column of unit cross section at any 



distance r is 



8' 

 . din = 8clr z= ^ {h -\- P) dr. 



