hersey: viscosimeters 527 



parts permits its performance to be predicted mathematically, 

 are the advantages of this modification over those recently used 

 by McMichael, and by Hayes and Lewis. 



The torsion viscosimeter was used to determine the viscosities 

 of a series of liquids, ranging from water to castor oil, subse- 

 quently needed in calibrating the rolling ball viscosimeter. 



Theory of the rolling ball viscosimeter. The time required for a 

 ball to roll down a slanted tube, filled with the liquid, has been 

 proposed and used by Flowers, who resorts to a fine bore to 

 make roll time proportional to viscosity. In adapting this type 

 of viscosimeter to observations under pressure, the writer has 

 avoided the difficulties of technique accompanying small tubes, 

 by using a large tube, fo^ which the roll time is not proportional 

 to the viscosity, and then determining its characteristics by 

 dimensional reasoning. 



Assuming no surface friction, some relation must subsist be- 

 tween the roll time t, the kinematic viscosity v, density p, ball 

 density p , gravity g, tube diameter D, ball diameter d, tube 

 length I, angle with horizontal a, and roughness r. If so, the 

 relation can be completely mapped out, for any one series of 

 geometrically similar arrangements, by varying experimentally 



the three arguments tt„> -^tj and — Or, without stopping to 



U~ L) p 



establish the complete relation, we can at once determine rela- 

 tive viscosities by comparing observations taken under dynami- 

 cally similar circumstances; for, as long as the above arguments 

 are kept constant, 



n = W = \dJ 



Finally, by observing the transit time r per unit length, between 

 two points for which the speed is sensibly constant, the three 

 arguments above may be coalesced into two, leaving 



F (x, y) = (5) 



in which .t denotes r \Dgl Po -l J and y denotes v \D 3 g( ° -lj. 



