241] INDUCTION OF CURRENTS. 493 



thus the difference of the two </'s of this sort whose wires it 

 separates. The whole number of q's is now just equal to n, the 

 number of degrees of freedom of the system. The current in any 

 wire is the sum of two or three of the qs with the proper signs, 

 and as the electrokinetic energy is a homogeneous quadratic 

 function of the currents, it becomes one also of the q"s. The 



derivative T . fs >] is the electromotive-force of induction around 

 dt \dq s j 



the circuit s, for 



and every dl r /dq 8 ' is zero except in the case of the currents which 

 bound the circuit, for any of which dl r /dq s ' is either plus or minus 

 unity. The dissipation function, 64, (7) 



becomes also a homogenous quadratic function of the q"s in which 

 the product terms will in general appear. The dissipative force 



will also be represented by ^ ? , for 



which is again the sum of the products El around the circuit. 

 The terms 



dt\ 



*M_ 



are accordingly what we get by adding the equations (i) for all the 

 wires bounding the mesh s. 



Since any charge is equal to plus or minus one of the q's of 

 the second sort, or to the difference between two, W, the electro- 

 static energy, becomes a homogeneous quadratic function of these 



q's. Again = is the electrostatic electromotive-force belong- 

 ing to q s , for 



dq 8 ~ * r de r dq 8 ' 



) while ~ is zer 

 oq s 



lators at the beginning and end of q s , where the derivative has the 



Now by (4), V r) while ~ is zero except for the accumu- 

 oc r oq s 



