1886.] On Tliichiess and Surface-tension in Liquid Films. 441 



dark tachylytic belt formed between it and the clear basalt- 

 glass, x 120. 



6. Portion of the same preparation, showing the sharp division of 

 the tachylytic belt from the clear basalt-glass, x 120. 



IV. " On the Relation between the Thickness and the Surface- 

 tension of Liquid Films." By A. W. Reinold, M.A., F.R.S., 

 Professor of Physics in the Royal Naval College, Green- 

 wich, and A. W. Rucker, M.A., F.R.S. Received May 15, 

 1886. 



(Abstract.) 



Plateau, Liidtge, and van der Mensbrugghe have investigated 

 experimentally the relation between the thickness and surface-tension 

 of thin films. None of these observers, however, have used films thin 

 enough to show the black of the first order of Newton's colours. The 

 authors have therefore made a careful comparison of the surface- 

 tension of black films with that of coloured films, the thickness of 

 which was from 10 to 100 times greater. The principle of their method 

 is the same as that utilised in Liidtge's experiments. The interiors of 

 the films to be compared are connected, and the relation between 

 their surface-tensions is deduced from measurements by which their 

 curvature is determined. In the authors' experiments a cylindrical 

 film was thus balanced against another, which, though sometimes 

 cylindrical and sometimes spherical, was initially of the same 

 curvature as itself. The necessity for this arrangement arises from 

 the fact that the authors' previous observations have shown that a 

 film thins to the black of the first order more readily if it is cylindrical 

 than if it is of any other form. The fact that small changes in the 

 forms of cylindrical and spherical films, attached to two circular rings, 

 convert them into unduloids or nodoids, renders the mathematical 

 theory somewhat complicated, but other considerations have been 

 made to give way to the necessity of obtaining films which readily 

 yield the black. 



The sensitiveness of the methods employed by the authors and by 

 previous experimenters is investigated. All these methods depend 

 upon the measurement of a length, such as the change in the diameter 

 of a cylinder, or in the sagitta of a spherical segment (Liidtge and 

 van der Mensbrugghe), or the displacement of the liquid in a mano- 

 meter tube (Plateau). 



Let an increment dT in the surface-tension T produce an alteration 

 dL in this length. The fraction T dL/dT is taken as a measure of the 

 sensitiveness of the experiment. If dL and dT are infinitely small, this 



