the Viscosity of Liquids. 453 



Moreover the mass of each of the smaller spheres may be 

 easily estimated, since 



and 



m / v \ - 2 



M " \YJ ' 



The author has been able in this way to determine the mass 

 of a small sphere (and hence its radius) weighing about 

 •003 grm., correct to four significant figures. Having thus 

 determined its dimensions, it may be employed for other 

 liquids than that by which these dimensions were obtained. 



But the important question suggests itself whether /j, is 

 simply inversely proportional to the speed of the falling 

 sphere, or whether, as some maintain, there is a finite coeffi- 

 cient of sliding-friction, and a definite amount of slipping at 

 the surface, which will render the connexion between v and 

 m much more complicated. 



This may be tested in a simple manner by observing the 

 speed V for a small mass, dividing it into two parts, and 

 observing the speeds v^ and v 2 for each part in the same 

 viscous liquid at the same temperature. If there be no 

 sliding-friction, 



VS. JL . 3. 



2=^2+^2. 



If sliding-friction exists the effect will be to render the V 

 calculated in the above equation from v 1 and v 2 greater than 

 the observed speed for the undivided mass, the divergence 

 being most clearly shown when the two parts are as nearly 

 as possible equal to each other. 



For let us assume that the whole is divided into two equal 

 parts, and that the two speeds observed are V and Vi, corre- 

 sponding to the two radii A and a. 



Now A 3 = 2a 3 , and A is therefore = %*a. 

 With sliding-friction, 



/3A + 2//,' 



a, 2 l*26/3a + 3^ 

 - l ' ka • l-26/8a + V 



and 2 fta + Sfj, 



v — feci . -p\ ^ , 



then the speed calculated for the whole mass from the 

 formula 



\2 = v 1 * + Vci 2 =2v 2 



