Prof. Potter on Hydrodynamics. 311 



and substituting tlie value vp^ , we have 



«^ /Vfe 



2 =-1/7 



= C-/Cl0g(5)j 



and V becomes v' when s becomes B,, 



Substituting the vahie of w from this expression in that forjo, 



we have 



Ko'v'R 

 p= -^ 



vs 



Kp'v'R 



s(v'^+2Klog—j . 



To find the position of the minimum pressure and density, we 

 have 



ds ' 

 which gives 



In order to compare the results of experiment with these for- 

 mulae, we require to know the values of k and v' ; and since ^' 

 at the edge is the pressure of the atmosphere, we have 



p' = Kp'—gp'Yi.; 



if H is the height of the homogeneous atmosphere, 



.-. K=gM; 

 also 



' \p, a / 



= v<^ + 2k\os(^), 



which gives t;' when p, the density of the air at passing the edge 

 of the pipe is known. 



Ar we have considered the air to diverge from the centre of 

 the disc, the pipe in experiments should be small compared with 

 the size of the disc, in order to have the results of theory and 

 experinient nearly agreeing ; and unfortunately Messrs. Hopkins 

 and lloberts used a pipe with an aperture 2f inches diameter, 



P2 



