Mr Molin, An examination of SearWs method, etc. 23 



An examination of Searle's method for determining the viscosity 

 of very viscous liquids. By Kurt Molin, Filosofie Licentiat, 

 Physical Institute, Technical College, Trondhjem. (Communicated 

 by Dr G. F. C. Searle.) 



{Read 9 February 1920.] 



§ 1. The determination of the coefficient of internal friction in 

 very viscous liquids has been the object of measurements by many 

 different methods. A review of these will be found in Reiger*. 

 A number of more recent methods are given by Kohlrauschf, and 

 among them is a method of Searle'sJ. An examination of this 

 method is the object of the present paper. 



In his paper, "A simple viscometer for very viscous liquids," 

 Dr SearleJ gives an account of a viscometer he has constructed. 

 The method consists in causing a vertical cylinder to rotate within 

 a coaxal cylinder containing liquid, and in determining the angular 

 velocity of the inner cylinder for a known value of the driving 

 couple. The couple is produced by the weights of two loads acting 

 on a drum by two threads. The time, T seconds, of one revolution 

 of the cylinder is found, and the length, I cm., of the inner cylinder 

 immersed in the liquid is observed. 



Newton's statement is that 



f--^Tn' <1) 



where/ is the force per unit area which acts against the direction 

 of motion and at right angles to the normal, n, to the surface, 

 dV/dn is the velocity gradient, and rj is the coefficient of viscosity. 

 In this statement the motion of the liquid is supposed to take place 

 parallel to a fixed plane. Treating the liquid as incompressible, 

 and modifying (1), by substituting the rate of shearing for dV/dn, 

 so as to suit the case of rotation, we obtain the following formula: 



gD (a2 _ 62) fMT\ ^ (MT\ 



Here D is the effective diameter of the drum, a and h are the radii 

 of the cylinders, and M is the mass of each of the two loads, which 

 are required to move the inner cylinder with the constant angular 

 velocity Q, such that 2ttJQ. = T. 



* R. Reiger, Ann. d. Phys., 19, p. 985, 1906. 



t F. Kohlrausch, Lehrbuch d. praktischen Physik, xii. Aufl., p. 268. 



% G. F. C. Searle, Proc. Cambridge Phil. Soc, 16, p. 600, 1912. 



