162 Dr. W. F. Magie on the 



exactly the same, whether the successive displacement in the 

 polarity of the magnetization through the common core of 

 the armature be accomplished by mechanically rotating it, or 

 by electrically shifting the polarity of the surrounding field- 

 magnet in a rotatory fashion. With equal weights of copper 

 in the primary and secondary coils of the armature part, the 

 effect of mutual induction will here also be approximately to 

 double the internal resistance and to neutralize the self- 

 induction of the secondary winding. 



XIX. The Contact- Angle of Liquids and Solids. 

 By W. F. Magie, Ph.D.* 



Introduction. 



GAUSS, in his discussion of the theory of Capillarity, 

 demonstrates that the surface of any liquid in contact 

 with a solid will make with the solid a definite angle at the 

 line of contactf . The assumptions at the foundation of his 

 theory are the same as those made by Laplace — that the force 

 between two molecules diminishes very rapidly as the distance 

 between them increases, and that, nevertheless, the radius of 

 molecular force is such as to include within it a large number 

 of molecules. The expression for the contact-angle A (that 

 is, the angle between the normal to the solid surface and the 

 normal to the liquid surface at the line of contact, or, more 

 strictly, at a distance from the solid equal to the radius of 



2/3 2 — a 2 

 molecular force) is cos A= ^ — . The quantities a 2 and /3 2 



are constants for each liquid and solid, depending respectively 

 upon the forces between the elements of the liquid and those 

 between the elements of the liquid and the solid. Upon the 

 hypothesis that the laws of these forces as functions of the 

 distance between the elements are the same, or that the ratio 

 of the functions/^') and F(V) representing them is indepen- 

 dent of the value of x, these constants a 2 and /3 2 are propor- 

 tional to the forces upon which they depend. Upon this 

 hypothesis, then, there will be an obtuse contact-angle when 

 the force between two liquid elements is greater than twice 

 that between a liquid and a solid element. When the force 

 between two liquid elements is less than twice and more 

 than once the force between a liquid and a solid element there 

 will be an acute contact-angle, which is not zero. Such an 



* Communicated by the Author. 



t Gauss, Fig. Fluid., Werke, vol. v. p. 69. 



