1890.] Slipping at the Boundary of a Liquid in Motion. 229 



greater, obviously owing to irregularities in the tubes, but never 

 less. 



The surfaces of the tubes were then modified in various ways : by 

 cleaning with acids and alkalis, by polishing with emery powder, by 

 coating with a film of oil, and by amalgamating with mercury. In 

 no case, however, could any deviation from Poiseuille's laws be 

 detected. Girard gives no account of the method he employed for 

 determining the diameters, and this may explain his results ; any 

 constant error would of course be more important in smaller tubes 

 than in larger ones, and produce the same result as a slipping coeffi- 

 cient. The tubes I used were some of them smaller than those of 

 Girard, and any slipping would have produced an even greater effect. 



IV. At the beginning of Helmholtz and Piotrowski's paper, the 

 latter claims to have shown by experiments on a glass flask, plain and 

 silvered, that the friction exerted on it when oscillating by the con- 

 tained water depended on the nature of the surface. These experi- 

 ments were repeated, care being taken to make corrections for tem- 

 perature, and to prevent alterations in the bi filar suspension, which 

 were very apt to occur. Both of these precautions were neglected by 

 Piotrowski, who only took two observations of the logarithmic decre- 

 ment and the time of swing for each state of the flask, but deduced a 

 4 per cent, difference in the frictions. 



The results of my observations are 



Silvered surface, time of swing . . 8'806 sec. log. dec. O142335 

 Unsilvered surface .. 8779 0'142217 



By the theoretical part of Helmholtz's paper, this makes the ratio 

 of tbe friction on glass to the friction on silver 



1-0022 : 1. 



The change, if any, is less than 0'3 per cent., and the ratio is unity 

 within the limits of experimental error. 



The figures given above are the means of twelve observations for 

 the silver, and of twenty-three observations for the glass, some being- 

 taken before, and some after, those for the silver. 



V. A modification of Piotrowski's experiment was then tried. 

 Instead of filling the oscillating flask with water, it was filled with 

 sand, and oscillated as a rigid body in a beaker of water. The ordi- 

 nary investigation for such cases was then applicable, and it is easily 

 shown that if k and Tc are the frictions, X and V the log. decrements, 

 and T and T' the times of swing for the two cases, 



k XT 



