Maxwell. 301 



curvature of lines of force in electrostatic fields, had noticed 

 an apparent tendency of adjacent lines to repel each other, as 

 if each tube of force were inherently disposed to distend 

 laterally ; and that in addition to this repellent or diverging 

 force in the transverse direction, he supposed an attractive or 

 contractile force to be exerted at right angles to it, that is to 

 say, in the direction of the lines of force. 



Of the existence of these pressures and tensions Maxwell 

 was fully persuaded ; and he determined analytical expressions 

 suitable to represent them. The tension along the lines of 

 force must be supposed to maintain the ponderomotive force 

 which acts on the conductor on which the lines of force 

 terminate ; and it may therefore be measured by the force 

 which is exerted on unit area of the conductor, i.e., *E 2 /87rc 2 or 

 iDE. The pressure at right angles to the lines of force must 

 then be determined so as to satisfy the condition that the aether 

 is to be in equilibrium. 



For this purpose, consider a thin shell of aether included 

 between two equipotential surfaces. The equilibrium of the, 

 portion of this shell which is intercepted by a tube of force- 

 requires (as in the theory of the equilibrium of liquid films), 

 that the resultant force per unit area due to the above- 

 mentioned normal tensions on its two faces shall have the- 

 value T(l/pi + l//o 2 ), where pi and p z denote the principal radii 

 of curvature of the shell at the place, and where T denotes, 

 the lateral stress across unit length of the surface of the shell,, 

 T being analogous to the surface-tension of a liquid film. 



Now, if t denote the thickness of the shell, the area inter- 

 cepted on the second face by the tube of force bears to the 

 area intercepted on the first face the ratio (pi + t) (p z + t)/p!p 2 > 

 and by the fundamental property of tubes of force, D and E 

 vary inversely as the cross-section of the tube, so the total force 

 on the second face will bear to that on the first face the ratio 



piptKpi + 1} (p z + 1), 



or approximately 



