in Free Surfaces of Liquids. 137 



This assumption can easily be tested. It follows therefrom 

 that oscillation-period and decrement are independent of the 

 amount of the amplitude. This is not precisely correct ; only 

 the oscillation-period is constant, while the decrements dimi- 

 nish slowly with the magnitude of the amplitudes. I have 

 not pursued the more precise law of this decrease further ; the 

 knowledge of the mean value of the decrements suffices per- 

 fectly for the decision of the question put ; and I have taken 

 care to arrange the experiments so that the decrements corre- 

 spond to average amplitudes. 



If the margin of the plate projects above the free surface, 

 another disturbing circumstance comes in : the surface between 

 the plate and the glass side is perceptibly curved, and in 

 general raised somewhat above the level. During the oscil- 

 lations this elevation is no longer the same on both sides; 

 consequently attractive, and sometimes also repellent forces 

 appear, which lengthen or shorten the oscillation-period. 

 Here, however, with small amplitudes the oscillation-period is 

 independent of their magnitude ; so that the supervening 

 forces must be regarded as proportional to the angle $. The 

 alteration of the oscillation-period is an excellent means of 

 measuring accurately the forces mentioned. I have instituted 

 a series of experiments in this direction, which I intend to 

 communicate in a separate paper. Lastly, if in the surface a 

 thin layer which (according to Marangoni's assumption) is 

 elastic were present, a displacement or bending of it must at 

 all events produce also a resistance, which, in a first approxi- 

 mation, would be proportional to the angle of deviation. 



It follows from these considerations that, when the plate is 

 removed from the interior of the liquid to the surface, in 

 equation (I.) both a and b change. But as the oscillation- 

 period and decrement were always observed, the two varia- 

 tions can be found separately. If we put 



cj> = (l> .e~Tcos(2TrQ, 



then 



«=7jT> 0= ^— (II.) 



Particularly, the approximate measure of the friction is 

 therefore the quantity a, or the ratio of the decrement to the 

 oscillation-period. 



Of course the apparatus suffers also resistance by the air. 

 This was specially observed repeatedly, but was constantly 

 found very little in comparison with the resistance of the liquid 

 to the motion. As the question here is not about absolute, but. 



