a Spherical Conducting Shell on. Dielectric Induction. 155 



mitted in this manner on land through distances of four or five 

 miles. 



It has been suggested that the same plan could be employed 

 to communicate with lightships. The primary is laid on the 

 sea-bottom round the area over which the lightship swings, 

 the ends of the cable being brought to land; the secondary 

 is coiled round the lightship. I have been informed by 

 Mr. S. Evershed that successful experiments were carried out 

 by these means last summer in Dover harbour, the depth of 

 the sea being about 1000 centitns. To be able to judge 

 whether a similar experiment will succeed in a greater depth of 

 water, we must calculate the induction through the secondary 

 circuit; sea-water being a conductor the investigation is 

 somewhat complex, the final result, however, comes out in a 

 simple form. 



(2) The two following cases are considered : — 



Case I. 



A circular circuit carrying an alternating current is placed 

 in the dielectric inside a spherical conducting shell, the axis 

 of the circuit passing through the centre of the shell: to find 

 the normal magnetic induction at any point in the dielectric 

 outside the shell. 



Case II. 



The circular circuit is placed on one side of an infinite 

 conducting plate, the plane of the circuit being parallel to 

 the plate : to find the normal magnetic induction at any point 

 on the other side of the plate. 



In both cases the following result is arrived at : — 



where v is the maximum value of the normal magnetic 

 induction at any point outside, u the maximum value of the 

 normal magnetic induction due to the current in the primary, 

 supposing the conducting shell or plate absent, at the same 

 point, 7] is the thickness of the shell or plate, 



fj, is the permeability of the conducting shell or plate, a its 

 specific resistance, p = 2ir times the frequency. 



Let the frequency be 300, which makes /> = 1885; <x for 

 sea- water =2.10 10 C.G.S. units, n=l. 



If 97 = 2000 centims., which is about the depth of the sea 



M2 



