Prof. J. Perry on Liquid Friction. 457 



The following numbers show the sort of error introduced, 

 taking R=10 ? and 1 the greatest value of x. 



Values of x. 



Values of v. 



Correct. 



Approximate. 



On the assump- 

 tion of motion 

 in plane layers. 



1 







1 



1 



•2 



•7914 



•7914 



•8 



•5 



•4875 



•4872 



•5 



•7 



•2895 



•2892 



•3 



10 















The solution of (11) for vibratory motion is easy enough; 

 but we found it still difficult to calculate fjt, from our observa- 

 tions. Even w T hen we assume that the motion is in plane 

 layers, so that the solution used by Maxwell is employed, we 



find that our — is too great for a logarithmic decrement to 



exist with such amplitudes and times of oscillation as we had 

 employed in the experiments, and it was impossible for us to 

 repeat the experiments under the same conditions again at 

 slower velocities, because the apparatus had been taken to 

 pieces and could not be fitted up again in exactly the same 

 way. When we say that a logarithmic decrement did not 

 exist, we mean that it was not constant, but varied with the 

 amount of the oscillation. For the tractive force to be pro- 

 portional to the velocity of the cylinder it is necessary for yt.jp 

 and the periodic time to be so great that the velocities of the 

 fluid at all places shall be in the same proportion as if the 

 motion were steady. 



After this paper was written we asked Mr. J. B. Knight, 

 of the Chemical Department of the Finsbury Technical College, 

 to make measurements of the specific gravity of sperm-oil at 

 different temperatures. His results give a very striking con- 

 firmation of the views expressed in the paper as to a discon- 

 tinuity of some kind due to rise of temperature. As all the 

 authorities whom we have consulted seemed to see no possible 

 reason for a discontinuity in the rate of change of y. with 

 temperature in sperm-oil at about 40° C, it is possible that 

 these results may be of importance. 



