144 Dr. A. Oberbeck on the Friction 



horizontal direction, but also downward and upward. In 

 close proximity to the free surface giving way in the last 

 direction is impossible, or at least more difficult; for in this 

 case the liquid particles would have to overstep the upper 

 horizontal boundary plane ; and with that both gravity and 

 the capillary forces would counteract their motion. It is 

 moreover possible that, in consequence of the evaporation 

 taking place at the free surface, its temperature is some- 

 what below the mean temperature of the liquid, so that the 

 friction, quickly changing with the temperature, is there 

 somewhat greater than in the deeper layers. By this is pro- 

 bably to be explained especially the striking behaviour of sul- 

 phide of carbon, the resistance of which at greater depths is 

 much less than those of alcohol and water, while in close 

 proximity to the surface (h= +05) it considerably exceeds 

 them. In spite of the precautions which were taken, with 

 sulphide of carbon the evaporation was so considerable that 

 its temperature had fallen during the experiments some 

 degrees below that of the enclosure. At all events, in these 

 and similar experiments it is necessary to take into account 

 the behaviour of the free surface, and therefore to bear in 

 mind that, under some circumstances, it opposes an increased 

 resistance to a motion taking place close beneath it. 



7. To come now to the chief object of the investigation, the 

 behaviour of the free surface, it follows unequivocally from 

 the experiments above given that in water the resistance sud- 

 denly increases very considerably as soon as the upper edge 

 of the plate comes into the free surface. In consequence 

 of the entire arrangement of the experiments it appears to 

 me beyond question that this is caused by increased friction 

 in the surface layer. The aqueous salt-solutions studied 

 behave very similarly to distilled water. The increase of the 

 resistance on passing from the last position of the plate within 

 the liquid to its entrance into the surface amounts : — 



Per cent. 

 In distilled water .... to 60*9 

 In solution of KN0 3 . . . „ 75'1 

 „ Na 2 S0 4 . . „ 73-7 

 „ K 2 C0 3 . . . „ 61-0 

 „ „ CaCl 2 . . . „ 54-1 



These numbers are, on the whole, of the same order of mag- 

 nitude. The resistance in the free surface might, of course, 

 be compared also with that at greater depths. The differ- 

 ences are then considerably greater still. The correctness of 

 the facts, under the conditions of the experiments, surely 

 cannot after this be doubted. It is true that the question 

 is not thereby yet decided whether we have here to do with 



