the Motion of Spheres through Liquids. 



7G7 



Table III. summarizes these results, giving the viscosities, 

 the computed values of r, the radii r x at which the inertia 

 terms become apparent, and the ratio of: these last two, which 

 gives the upper limit of applicability of the formula in terms 

 of the critical radius. Through the range of viscosities 

 covered, this upppr limit seems to be independent of the 

 coefficient of viscosity. 



Table III. 





Viscosity. 



Critical 



Radius 



r. 



n- 



rjr. 





•695 

 •535 

 •070 

 •019 



•0G6 

 •054 

 •06S 

 •02 G 



•042 

 •040 

 •043 

 •016 



•64 



•74 

 •63 

 •62 



Linseed oil 



Transformer oil 



Alcohol and water ... 



Surface Slip. 



In no case was there any tendency for the value of fi 

 computed from the motion of the spheres to fall below that 

 obtained by Poiseuille's method. This means that even for 

 the smallest spheres used the factor 



1 + 



P 



er + 2p 



does not differ from unity by more than the errors of obser- 

 vation. In the case of colza oil, where the smallest radius 

 used was *0065 cm., if we assume that a deviation of 2 per 

 cent, due to slip could have been detected we see that /3 must 

 be greater than 5000. 



Of the several observers who have obtained values for /3, 

 Petroff * has assigned to it the largest, namely 700. With 

 this value the smallest sphere used in colza oil should have 

 given /jl about 10 per cent, less than the actual value, a 

 deviation which could not have escaped detection. The 

 evidence that the value of j3 is higher than that ob- 

 tained by Petroff is not as conclusive as could be desired, 

 for it is conceivable that the roughness of the surface of 

 the spheres may have influenced the results. But as the 

 surfaces appeared fairly smooth under the microscope, and 

 especially as after the most careful polishing there must 



* Fortschr. dcr Pfa/s. vol. i. 1897, p. 391. 

 3E2 



