1888.] Determination of the Viscosity of Water. 129 



latter greater than it would otherwise be.* As far as could be 

 observed there was no trace of eddies with axes parallel to that of the 

 cylinders. The proportion between the two terms depends on the 

 ratio between the length of the cylinders and the breadth of the 

 annulus, the square term becoming smaller and smaller compared to 

 the other as the ratio increases. 



It was found that when the temperature of the fluid was altered 

 the coefficient of the term varying as the velocity changed, but that 

 the coefficient of the square term remained unaffected. 



The value of the viscosity constant deduced from these experiments 

 agrees closely with that obtained from the experiments of Poiseuille 

 on the flow of liquids through capillary tubes. 



I now proceed to give the method and the numerical data which 

 were employed in the computation. 



Let r T = radius of cylinder B = 4'636 



r 2 = A = 5-017 



li depth of immersed surface ofB . . . . =11*07 

 v = linear velocity of surface of A, 



6 = torsional angle through which B is turned by the action 

 of the water ; 



F = K = K (Av + Bv 2 ) = whole tangential force ; 

 I* = coefficient of viscosity ; 



the units being the gram, centimetre, and second. 



If instead of being in an annulus the water was contained between 

 two parallel planes of infinite extent, the distortion caused by 

 the motion of one of these planes parallel to the other would be 

 uniform throughout the whole mass of enclosed fluid. But in the case 

 of the liquid enclosed between two cylinders, although the distor- 

 tion is uniform over each cylindrical surface in the fluid coaxial with 

 the enclosing cylinders, yet it changes in passing from one such 

 surface to another, increasing as the radius decreases. In fact, since 

 the total moment transmitted by each surface is constant,f the rate of 

 distortion necessary to produce this moment must be inversely as the 

 area of the surface and radius of the cylinder at which it occurs ; 

 that is, the rate of distortion at radius r is proportional to 1/r 3 , hence 

 the value of dv/dr at r is 



* Professor J. Thomson has pointed out that a circulation having a very similar 

 origin must take place in a stream when flowing round a bend. 



f [A correction has been introduced here, and in the equations (1), (2), (3). 



It was originally stated that the force transmitted was constant, but the error 

 was pointed out to me by Lord Rayleigh. In consequence of this error the 

 numerical val ues of p subsequently given must be multiplied by 1'08. January 1, 

 1889.] 



