On the Friction in Free Surfaces of Liquids. 133 



essentially different from the friction in the interior of a liquid*. 

 Here also a similar view might be taken — namely, that the 

 friction-coefficient in the interior of the first liquid has a con- 

 stant value, rapidly changes on approaching nearer to the 

 boundary surface, and on the other side again assumes that 

 value which belongs to it for the second liquid. 



These considerations show that the superficial viscosity is 

 absolutely incompatible with the notions we have hitherto 

 entertained of the nature of liquids. Whether it actually 

 exists, and therefore whether it is justifiable to assume a dif- 

 ferent value of the coefficient of friction at the surface from 

 that in the interior, can of course only be decided by expe- 

 riment. 



2. Plateau's fundamental experiments on surface-viscosity 

 consisted in observing the time taken by a magnetic needle to 

 fall back from a deflection of 90° to the magnetic meridian. 

 For this different times were necessary, according as the 

 motion of the needle took place in the free surface or in the 

 interior of the liquid. If the time in the first case was greater 

 than in the second, Plateau inferred a greater — if the contrary, 

 a less viscosity in the surface. Thus, according to Plateau, 

 water, aqueous salt-solutions, glycerine, and especially solu- 

 tions of albumen and saponine in water are liquids in which 

 the friction at the free surface is greater than in the interior. 

 Conversely, with alcohol, oil of turpentine, ether, bisulphide 

 of carbon the internal viscosity is greater than the external. 

 Finally, by mixing water and alcohol a liquid could be pro- 

 duced in which the two observed times are equal. Plateau 

 has also endeavoured in a somewhat different manner to ascer- 

 tain numerical values for the difference between the friction 

 in the interior and at the surface. He observed the angle to 

 which the needle, in falling back to the meridian, moved 

 beyond its original position of equilibrium. From this, on 

 the assumption that the resistance of the liquid is proportional 

 to the square of the velocity, numerical values for the differ- 

 ences of viscosity in different cases can be calculated. Plateau 

 himself, however, admits f that they can make no claim to pre- 

 cision. 



After the publication of these experiments the surface- 

 viscosity was investigated by Luvini % and Marangoni § ; and 

 the result arrived at by the latter was, that a distinction 

 between internal and superficial viscosity is not justified. He 



* Cf. 0. E. Meyer, Pogg. Ann. cxiii. pp. 68, 441 (1861). 

 t Mem. de V Acad, de Belg. xxxviii. p. 76 (1868). 

 X Phil. Mag. [4] xl. pp. ±90-197 (1870). 



§ Nuovo Cimento. [2] v.-vi. pp. 239-273 (1872), [3] iii. pp. 50-68, 97- 

 115, 192-212 (1879). ^ U ^ 



