688 /<£/./. sysTn.\r technical jourxal 



resistance and capacity in series in mesh j and let Ljk, Rjk, Qk denote 

 the correspondini; mutual elements between circuit j and k. Now 

 write down Kirchhoff's equation for any circuit or mesh, say mesh 1; 

 it is 



Corresponding equations hold for each and every one of the w 

 meshes of the network. Writing them all down, we have the system 

 of equations 





(1) 



The system of simultaneous differential equations (1) constitute 

 the canonical equations of electric circuit theory. The interpreta- 

 tion and solutiiiii of these equations constitute the subject of Electric 

 Circuit The(ir\ , and it is in connection with their solution that we 

 find the most direct and loiiical introduction to the Operation d Cal- 

 culus. 



As an example of the apiirojiriate mode of setting up the cirniit 

 equations, consider the two mesh network shown in sketch 1. Writ- 

 ing down Kirschhoff's Law for meshes 1 and 2, respecti\"eh', we lia\e 



In this case the self and iiiutu,il rdelTicients are t;i\en hv 



The conventions adopted for the positive directions of currents and 

 voltages are indicated b\ the arrows. The sign of the muiual in- 

 ductance iU will depend on the relative mode of winding of the two 

 coils. 



