136 Dr. A. Obcrbeck on the Friction 



plates could be inserted in the vessel, parallel to the first, so 

 as to permit observations to be made with the side plates at 

 different distances. This arrangement was found necessary 

 for the following reasons. If the brass strip turns round a 

 vertical axis in the interior of a laterally unlimited liquid, it 

 first and immediately puts in oscillatory motion that quantity 

 of liquid which fills a cylinder whose diameter and height are 

 determined by the length and height of the strip. It is self- 

 evident that, in consequence of friction, the adjacent liquid 

 also partakes of the motion, although at all events with rapidly 

 diminishing strength. If the upper edge of the strip lies in 

 the free surface of the liquid, a moving disk, of the dimensions 

 indicated, will to a certain extent be separated, which will be 

 chiefly although not exclusively set in motion. Friction in 

 the surface will take place principally at the margin of this 

 disk, where moving and nearly still layers border on one 

 another. Hence it was to be feared that herewith the surface- 

 viscosity that might be present would exercise but little influ- 

 ence. It is different when the liquid is inclosed by two not 

 widely distant plates, to which it adheres. The action of fric- 

 tion, and especially of augmented friction at the surface, must 

 then become evident. Plateau himself, in his experiments 

 cited above, intensified in a similar way the action of the fric- 

 tion. I will subsequently communicate a series of experiments 

 in proof of the correctness of the whole of these speculations. 



4. The motion of the liquid under the influence of the oscil- 

 lating plate is in any case tolerably complicated ; and for the 

 moment it seems to me impossible to calculate it from the 

 general hydrodynamic equations. Even its reaction upon the 

 oscillating system probably takes place not according to a law 

 which could be simply rendered by a mathematical expression. 

 I am therefore far from regarding the diminution of the oscil- 

 lations at once as a measure of the friction-coefficient. But 

 if two experiments be made, differing only in this, that in one 

 of them the immersed plates cut the free surface with their 

 upper margins, while in the other they are sunk a fraction of 

 a millimetre deeper, then the resistances to the motion cannot 

 be different unless the surface-layers exert a special influence. 



As in all the experiments I confined myself to oscillations of 

 small amplitude, it might readily be supposed that the liquid 

 would chiefly produce a resistance proportional to the angular 

 velocity of the apparatus, so that also for the oscillation of the 

 system when the plate was immersed the simple equation 



3:+*i+M-° • • • • W 



would hold good. 



