Viscosity of Hydrogen, Nitrogen, and Oxygen. 



583 



heretofore accepted tables of viscosities contained in the 

 existing physico-chemical tables. 



The Theory. 



The method employed here consists in causing one 

 cylinder to revolve with a constant 

 angular velocity about another which 

 is suspended by a torsion thread. If 

 a be the radius of the cylinder which 

 is revolving with an angular velocity 

 iv, and b the radius o£ the suspended 

 by/ / cylinder which has turned through 

 an angle 6 away from its position 

 when the outer cylinder is at rest, 

 the equation for the viscosity can be 



derived in the following manner * : — 



The tangential force F acting on any cylindrical surface 



at a distance r is 



F = 27rrlrjdv/dr, 



where I is the length of the suspended cylinder, 97 the 



coefficient of viscosity, and dvldr the velocity gradient at r 



due to the slipping of one cylinder over another. 



Since 



v = rw, 



dvldr = rdw/dr + wdr/dr. 



As the term wdr/dr enters only when we have a rigid 

 body, we have here simply 



dv/dr = r dwjdr. 



F = 27rr 2 l v dwjdr, 



or the moment of shear 



Fr = "lirrHr) dwjdr 

 or Yrdrjr* — 2irlr)dw. 



and for summation we have 



— C a * i x>r 



Fr 1 drfr z = 2irly 1 dw, 



J 6 Jo 



since Fr does not depend upon r. 

 We then have 



Yr = 4c7rlr)[a 2 b 2 /(a 2 — b 2 )]w. 



* This particular form of derivation is taken from unpublished 

 lecture notes of Professor Millikan. 



2 S 2 



Therefore 



