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XXXVII. Theory and Experiments relating to the Establish- 

 ment of Turbulent Flow in Pipes and Channels. By 

 Louis Vessot King, M.A.(Cantab.), T).Sc.(McGill), As- 

 sociate Professor of Physics, McGill University, Montreal* '. 



Index to Sections. 



Part I. — The Mathematical Theory of "Viscosity and its 

 Experimental Verification. 



(1) Historical Survey of the Theoretical Development. 



(2) Steady Motion between Parallel Planes. 



(3) Steady Motion in a Pipe of Circular Cross-Section. 



(4) Shearing Motion between Parallel Planes. 



Part II. — On the Stability of Laminar Flow in Pipes 

 and Channels. 

 (o) Historical and Critical Survey of the Theoretical 



Development. 

 (6) Discussion of Experimental Results in the Flow of 

 Fluids. (i.) Liquids. (ii.) Gases. 



Part I. 



The Mathematical Theory of Viscosity and its 

 Experimental Verification. 



Section 1. Historical Survey of the Theoretical Development. 



AS the fundamental problem of fluid-resistance in both 

 laminar and turbulent flow is intimately connected 

 with the mechanism of shearing stresses across adjacent 

 layers of a fluid in relative motion, it may not be out of 

 place in the present paper to undertake a critical survey of 

 the theory of viscosity and of its experimental verification. 

 The fundamental hypothesis of viscosity asserts that when 

 layers of a viscous fluid are in motion relatively to each other, 

 the mutual tangential stress per unit area is proportional to 

 their relative velocity divided by the distance between them. 

 To be more precise, suppose the fluid to be flowing in layers 

 parallel to the plane xy with velocity U in the direction of 

 the /c-axis. If the gradient of velocity in the direction of the 

 sr-axis be dXJ/dz, the shearing stress per unit area of the plane 

 xy in the direction of flow is given by 



F ~"*« W 



jjl being a constant depending only on the physical properties 

 of the fluid and called the " coefficient of viscosity." 



The insertion of the fundamental hypothesis (1) in the 



* Communicated by the Author. 



