1892.] as affected ly Stresses in Excited Dielectrics. 57 



opinion as to whether a medium transmitting stress in this way could 

 be imagined, let us suppose the dielectric divided into thin layers, 

 like those of an onion, by much thinner conducting sheets, which 

 coincide with the equipotential surfaces. The potential will not 

 thereby be altered ; if we run a tube of force across the dielectric, 

 equal and opposite charges will reside on the portions of the two 

 faces of each sheet intercepted by it. The layers of dielectric will be 

 electrically independent of each other, being separated by conducting 

 layers. Each dielectric layer will, therefore, form a condenser, and 

 the energy of its electrification per unit surface will be K(V) 2 /87r, or 

 KF 2 /8?r, where t is the thickness at the point, and <$V the difference 

 of potential between the faces ; that is, there will be a distribution of 

 energy KF 2 /87r per unit volume. The resultant traction on both 

 the equal and opposite charges, each a per unit area, on the two faces 

 of a layer of dielectric, will be normal to the layer, and equal to 

 ^ff(dF/dn)8n per unit surface; now, by Green's form of Laplace's 



/7TT /i i \ 



equation, = ^( 1 ) where K l? B 2 are the radii of prin- 



dn \R>i B 3 / 



cipal curvature of the sheet; thus the traction is -'( 1 ). By 



8 TT \R, l R 2 / 



the theorem of surface tension, this normal traction will produce and 

 be balanced by a uniform surface tension along the sheet, of intensity 

 F^M/STT, or F 8 /87r per unit thickness. In this laminated medium, 

 owing to the attraction across the layers of very small thickness, we 

 have thus set up a tension KF 2 /8?r along the lines of force, which 

 by reaction on the medium produces a pressure uniform in all direc- 

 tions round the lines of force, of the same numerical value. Or, 

 again, we might, following Maxwell, postulate that the stress system 

 in the medium must be symmetrical round the lines of force, and 

 deduce, by the condition of internal equilibrium, that the tension and 

 pressure of which it must thus consist are equal. A spherical system 

 will form a simple illustration, capable of elementary treatment. 



The fact that the surface of a dielectric liquid like petroleum is 

 raised up by attraction, towards an electrified body brought near it, 

 also affords evidence that this tension must exist. Consider two 

 horizontal condenser plates, one inside the petroleum and the other 

 over its surface in air. When the condenser is charged, the surface 

 of the fluid rises between the two plates. There must, therefore, be 

 some traction acting on it upwards to sustain it against gravity. 

 The intensity of this traction is, in fact, according to Maxwell's law, 



"P2 17" /~C1 'i\ ~C12 / -i \ 



[== i, that is, (1 - ] where F is the electric force in the 



87T 87T\K/ 87T\ K/ 



air; being positive, it acts upwards, in accordance with the actual 

 phenomenon. Without the assistance of a traction of this kind, the 

 fact would be unexplained, unless by assuming, with Helmholtz, 



