ELEMENTARY ELECTRICITY AND MAGNETISM. 29 



Applying the second principle in a similar manner to the mesh 



2-3-6 gives: 



^6-^2 + ^=0 (vi) 



Applying the second principle in a similar manner to the mesh 

 465 gives : 



-rtl- r #* + r h=- e ( V ") 



Applying the second principle in a similar manner to the mesh 

 1-3-5 gives : 



rA + r J* + r h = - e (viii) 



For convenience let us call the equations (i), (ii), (iii) and (iv), 

 which refer to branch points, point equations ; and the equations 

 (v), (vi), (vii) and (viii) which re- 

 fer to meshes, mesh equations. 

 In problems of this kind there is 

 always one superfluous point 

 equation and one superfluous 



f r > "^6 ohms 



mesh equation, and any one of % 



the point equations together with 



any one of the mesh equations are to be dropped, thus leaving 



as many independent equations as there are unknown quantities 



*v *v h> * * and V 



Example. A iio-volt battery is connected to two branch 



points a and b, Fig. 14, between which are two branches (2 and 

 3). Branch 2 has 10 ohms resistance and contains a 25-volt 

 battery as shown in Fig. 14. Branch 3 has a resistance of 6 

 ohms. It is required to find the currents i v i 2 and t y 

 Considering the point a we have the equation : 



h -h~h = (0 



Considering the mesh 1-2 we have the equation : 



50^ + io/ 2 = 1 10 25 (ii) 



Considering the mesh 1-3 we have the equation : 



50/1 + 6/ 3 = 1 10 ' (iii) 



