the Motion of Spheres through Liquids. Ibl 



if the liquid is contained in a cylinder of circular cross- 

 section of radius li, and ot length L, the simple formula 

 should be modified to read 



H 1 +*" 4 sX 1+3 ' 1 e) 



Using this corrected form he examined the viscosity of 

 Venice turpentine, using a series of steel spheres, and 

 obtained the value 1343, whereas the value found by the 

 capillary tube method at the same temperature was 1325. 

 This seems to have been the first direct comparison of these 

 two methods, and their agreement to within 1*3 per cent, 

 shows the validity of the corrected formula in the case of 

 liquids of very high viscosity. As Laden berg points out, 

 this boundary effect may account for the results obtained by 

 0. Jones*, who nsed spheres of mercury in glycerine, and 

 found viscositv values so high as to cast considerable doubt 

 on the validity of Stokes's law. 



Experiments with liquids of low viscosities were carried 

 out by Allen -f, using air bubbles, and spheres of amber and 

 paraffine, in water and in aniline. His results vary widely 

 among themselves, but in general seem to confirm the simple 

 formula. With the air bubbles in aniline, however, the 

 velocities observed were uniformly higher than those com- 

 puted. This is more striking when we consider that the 

 formula should give the maximum terminal velocity (pro- 

 vided there is no surface slip). If, instead of the value of n> 

 used by Allen, we substitute the more probable one obtained 

 by extrapolating from Wijkander'sJ tables to the tempera- 

 ture 9°'8 at which Allen worked, we find his values for the 

 observed velocities to be from 10 per cent, to 30 per cent, 

 higher than those calculated, a departure not easily attributable 

 to experimental errors. 



Allen also investigated the effect of increase of size upon 

 the terminal velocities, but as most of his observations were 



* O. Jones, Phil. Mag-, xxxvii. p. 451 (1894). Cf. also K. Schottner, 

 Beibl. iii. p. 60. 



Note : I have repeated these experiments using- solid spheres, and have 

 obtained the following- values for the viscosit}^ of glycerine : — - 



Temperature -9 c -8 — o°-2 2°*7 6°-0 20°-0 22°'0 30°-0 



Viscosity 188 105 42-2 27'6 137 7-61 3'43 



That these values are on the whole a little lower than Schottner's may 

 be due to impurities in the glycerine, as no precautions were taken to 

 guard against' traces of water. 



t Phil. Mag. 1. p. 323 (1900). 



X Beibl. vii. p. 11 (1879). 



