240, 241] INDUCTION ,OF CURRENTS. 491 



241. General Theory of Electrical Oscillations. We 



shall now consider the question of electrical oscillations in the 



,-, FIG. 95. 



most general case of a network of linear conductors, conducted 

 with any number of conductors K which may carry electrostatic 

 charges. These may be grouped in pairs to form condensers, as 

 in the last section, or they may be entirely independent of one 

 another. Of the linear conductors, any one may form a closed 

 circuit unconnected with the others, and affected only by current 

 induction, or may end at points of embranchment with other 

 conductors, or upon any of the conductors K. For brevity we 

 shall call the linear conductors wires, and the conductors K 

 accumulators. We shall suppose that the net contains p points 

 of embranchment, k of which are connected with accumulators, 

 for all wires which end on the same accumulator are to be 

 considered as meeting in an embranchment. Let the number of 

 wires be I. Then if all the wires form a part of the same net, 

 the number of independent meshes is I p + 1, for we see at once 

 that the smallest number of lines that can join p points to form 

 a closed net is p, giving one mesh, and that after the first mesh 

 every additional line adds a mesh*. 



For every wire r between points a and 6 we have an equation 



where E ab is the impressed electromotive-force from a to b and V a 

 and V b are the potentials of the points a and 6. There are I 

 equations of this sort. 



* By independent meshes we mean such that circulation about any one is not 

 the resultant of circulation about any number of others. For instance the outer 

 boundary of a plane net is not independent of its meshes. 



