408 



Messrs. Stables and Wilson on the 



This operation was repeated a number of times and the mean 

 taken. The logarithmic decrement was calculated from the 

 readings obtained from the graduated scale. 



The plate was suspended by each of the three rods in turn 

 immersed to a depth exceeding 1 centim., and the logarithmic 

 decrement and mean time of oscillation determined for each. 

 The following table shows the results obtained with the 

 saponine solution and with water: — 



Table I. 



Water. 



Saponine. 



Eod. 



Time of 

 oscillation. 



Log. dec. 



Time of 

 oscillation. 



Log. dec. 



1 



sec. 

 519 



5-20 



5-22 



0477 

 0479 

 •0483 



sec. 

 524 



526 



5-26 



•0785 

 •1424 

 •2045 



2 



3 





The great difference between the surface-properties of 

 saponine and those of water is here made very evident. The 

 alterations in the dimensions of the rod which produced a 

 slight effect only in the case of water increased the logarithmic 

 decrement in the case of saponine two and a half times, a result 

 which could only have been due to the increase of the section 

 in contact with the surface. 



If we assume that the disk oscillated under the influence 

 of two forces, one of which (that of torsion) is proportional to 

 the angular displacement from the position of rest, while the 

 other, due to the viscosity of the liquid, is proportional to the 

 velocity, the latter is measured by MX/T, where M is the 

 moment of inertia, X the logarithmic decrement, and T the 

 time of an oscillation. If, as in the case of a saponine 

 solution, the surface resistance be so great that the friction 

 between the surface layer and the interior may be neglected 

 with regard to it, MX/T would be approximately of the form 

 a + br 2 y where r is the radius of the rod and a and b are con- 

 stants. 



The values of these, determined from the above equations by 

 the method of least squares, are a = 8*42, 6=191*6. 



Using these coefficients to calculate the value of M\/T 

 from the observations on the saponine solution, we obtain the 

 following results : — • 



