244 Mr. W. Williams on the Relation of Dimensions 



irm 







as r^r in the latter. Thus — ~— is of the dimensions 

 MXYT -2 , 



To determine from this the dimensions of 7r we have 



[7mr- 4 0]=MXYT- 2 , 

 [6] =XY~ 1 Z- 1 , 



[n] =MZ(XY)" 1 T" 2 ; 



/. [9r]MZ(XY)- l T- 2 . Y 4 . (XY'^Z-^MXYT- 2 , 



.-. [>]=XY^\ 



Thus it in this case is of the dimensions of a plane angle 

 in the plane XY. 



28. Viscosity. — The viscous resistance between planes moving 



with relative velocity w = — is given by F=J( NwuoL^r- I 



(Olausius). Taking 1 the components of co and L along Z 

 (normal to direction of motion) this becomes dimensionallv 



a tangential force in the plane of motion (XY). The co- 

 efficient of viscosity is 



F irr 2 

 v ^ = xz- 1 T~ 1 - MZ ( YZ ) T 



dz 



= Tangential force per unit area -f- shear per unit time. 



29. Surface Tension. — Tangential force per unit length 



normal to itself. Let Y be the direction of force in the plane 



YZ, and K the surface tension. Then 



MY 2 T -2 

 [K] = MYZ" 1 T- 2 = y Z 



= Energy per unit area. 



Let AOB be a normal section of a cylindrical liquid film. 



