﻿1014 Prof. S. Timoshenko on the Distribution of 



Is correct ; e. g., a tungsten wire coated with graphite (from 

 the process of wire-drawing) gave the same results as a 

 clean wire. 



In all the experiments described so far the liquids used 

 have been true liquids. But in such processes as enamelling 

 • or painting the liquids are usually suspensions. The varia- 

 tion of the viscosity of suspensions with their solid contents 

 and with the size of the suspended particles has been 

 investigated by several authors *. We have repeated some 

 of this work on liquids in which we were particularly 

 interested, and have confirmed many of their results. But 

 the question arises whether the viscosity of a suspension 

 measured by shearing it between parallel plates is the same 

 as that which determines the amount of liquid adhering to 

 a solid drawn out of it. We have made many observations 

 in this matter. It appears, as might be expected, that the 

 two viscosities are the same so long as the diameter of the 

 suspended particles is not larger than the thickness of the 

 'liquid layer drawn out. If the diameter exceeds that 

 thickness the liquid behaves in drawing as if it had a 

 viscosity much less than that measured by shearing. But n 

 consideration of fig. 1 shows that such large particles cannot 

 be expected to enter the layer of liquid on the solid 

 surface ; they are squeezed out from it. Accordingly 

 the failure of formula (10) for these large particles is 

 simply due to the fact that the liquid which is being drawn 

 is that from which the large particles have been removed 

 and of which the viscosity is correspondingly lower. 



XCI. On the Distribution of Stresses in a Circular Ring 

 compressed by Two Forces acting along a Diameter. By 

 S. Timoshenko f. 



CONSIDERING the problem as a two-dimensional one, we 

 can obtain a solution in the case represented in fig. 1 

 by combining the known solutions of the problem of com- 

 pression of a disk \ (fig. 2) and that of a ring § (fig. 3) . 



If we take the normal and the tangential tensions acting 

 on the inner rim of the ring (fig. 8) as equal and opposite to 

 the tensions acting on the cylindrical surface of the radius 

 r in a disk (fig. 2), the stress-distribution in the case of 



* E. C. Bingham, Bar. Stand. Bull. no. 278 (1916). B. Humphrey 

 and E. Hatschek, Phys. Soc. Proc. xxviii. p. 274 (1916). 



f Communicated by Prof. E. G. Coker, F.R S. 



% See A. E. H. Love, ' Treatise on the Theory of Elasticity/ p. 21o, 

 ,1920. 



§ A. Timpe, Z.f. Math. u. Phys. lii. p. 348 (1905). 



, 



