hersey: viscosimeters 525 



PHYSICS. — The theory of the torsion and the rolling ball viscos- 

 imeters, and their use in measuring the effect of pressure on 

 viscosity. 1 M. D. Hersey, Bureau of Standards. (Com- 

 municated by S. W. Stratton.) 



Theory of the torsion viscosimeter . By dimensional reasoning, 

 the torque exerted on the suspended inner cylinder, by the uni- 

 formly rotating outer cylinder of liquid, is found to be 



T = fJL nr*f(—,—, shaped (1) 



\g v / 



in which p denotes viscosity, n revolutions in unit time, r radius 

 of inner cylinder, g gravity, and v kinematic viscosity n/p, where 

 p is the density. The unknown function / may be determined 

 empirically by varying the arguments shown, and this may be 

 done without altering r. Three interesting cases are, first, that 

 in which turbulence and the drag on the bottom are negligible, 

 while the inner cylinder projects above the free surface. In this 

 case we may calculate, approximately, the proportions for which 

 the concavity in the free surface, due to centrifugal force, will 

 serve to secure compensation against speed fluctuations, thus 

 dispensing with the use of either a speed governor or a stop 

 watch. It turns out that a large sample of the liquid will be 

 required. The second special case is that in which the torque 

 is not independent of the density of the sample, owing to spiral 

 flow across the bottom or to turbulent end effects, but in which 

 the free surface is level, so that the argument containing g in 

 (1) drops out. In this case the instrument is self-calibrating; 

 by observing with a single liquid what function of speed the 

 deflection is, we can at once infer what function it is of the 

 viscosity. Finally, a third case is that of a completely immersed 

 cylinder, so slender that the end effects are small, and run- 

 ning so slowly that the final deflection is independent of the 

 density. For this case we may integrate the equations, and 



1 This work was done at the Jefferson Physical Laboratory, Harvard Univer- 

 sity. It will later be published in detail, as a part of a more general paper on 

 lubrication. 



