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"VII. On the Determination of the Coefficient of Normal 

 Viscosity of Metals. By Kotaro Honda and Seibei 

 Konno *. 



[Plates III. -VI.] 



1. TF i; be the velocity of a fluid moving in the direction 

 J- of at, and z an axis perpendicular to x, then the 

 tangential or ordinary viscosity per unit area is given by 



j. dv 



where y is the coefficient of tangential viscosity. In the 

 same way, if the velocity of the fluid varies in the direction 

 •of a, we may define the normal viscosity per unit area by 



dv 

 Jn *.dx 9 



where f is the coefficient of normal viscosity. According 

 to the dynamical theory, the normal viscosity of a fluid is 

 numerically related to the tangential viscosity. 



2. In the case of solid substances, we may also conceive 

 these two kinds of viscosity, as already done by Professor 

 W. Voigt |. The tangential and normal viscosities correspond 

 in elasticity to the moduli of rigidity and elasticity respec- 

 tively ; they are independent of each other. 



Let a wire be fixed at its upper end and loaded with a 

 horizontal disk at its lower end. By letting the system 

 oscillate in vacuum, the motion is gradually damped o wing- 

 to the internal viscosity of the wire. The equation of motion 

 of the suspended disk at any time t is given by 



where 6 is the angle of twist, I the moment of inertia of the 

 disk, p and q are two constants depending on the dimensions 

 and the nature of the suspended wire. If I and R be the 

 length and the radius of the wire respectively, and n its 

 rigidity, we have a well-known relation 



TTTlR 4 



In a former paper, one of the present writers has shown 



* Communicated by the Authors. 

 t Wied. Ann. xlvii. p. 671. 

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