► Prof. W. H. Bragg on the u Elastic Medium " 



Obviously the charge, Q, on the sphere (0 in fig. 5) 



Fig. 5. 



will force in the boundary of the plate on the side nearer 0. 

 As the plate is connected to earth this will cause no bulge on 

 the other side of the plate, the excess of aether will run away. 

 Suppose now a negative charge, numerically equal to Q, is 

 placed at 0', the image of 0, in the nearer surface of the plate. 

 The plate being supposed for the moment exceedingly thin, 

 this new charge will draw in the dielectric, and the amount of 

 the drawing in at any point on one side of the plate is exactly 

 equal to the encroachment on the other side of it. 



In fact, if the charges at and 0' both existed, the dis- 

 placement of dielectric would be everywhere the same as if 

 the plate were " unearthed," or, in fact, if it did not exist — it 

 is exceedingly thin, it must be remembered. 



Thus the displacement at P, when there is a charge Q at 

 and an infinite non-insulated conducting plate, is the same as 

 if there were charges Q at and — Q at 0' and no plate at all. 



From the latter hypothesis we see the charge at P must be 

 of the density 



Q.OB 



2tt.OP 3 ' 



11. Next consider the case of a charged sphere placed near 

 the plane boundary between two dielectrics of different elas- 

 ticities ; the radius of the sphere being small compared with 

 its distance from the plane. 



Our method is well adapted for such a problem, as the 

 physical significance of every step is clear. 



