234 Dr. J. A. Fleming on the Distribution of 



The first minor of the leading element of d n is rf tt _ 



3 



-1 







-I 











-1 



3 



._1 



















-1 



3 











-1 



-1 











3 



-1 



















-1 



3 



-1 











-1 







-1 



3 



The value of this last is 320. 



Hence the resistance of the network between the points A 

 and B is 



±t ~d„- 1 ~~320~5' 



We can easily verify this result in the above symmetrical case, 

 for the hexagonal framework in fig. 8 is traversed symme- 

 trically by the current flowing through it ; and hence no 

 disturbance of the distribution of currents will take place by 

 separating it, as in fig. 9. We break the connection between 

 the semidiagonal conductors a, b and the mean diagonal A B, 

 whilst keeping them in contact with each other, the resistance 

 of each branch still remaining unity. It is then easily seen 

 that the hexagon so arranged must offer exactly the same 

 resistance between the points A and B as in its original form. 

 Now the combined resistance of a, b, and /, each equal to 

 unity, between the points C, D is §, and the combined resist- 

 ance of this with e and g in series is 2§ ; and hence the total 

 resistance of the whole network between A and B is equal to 

 that of three conductors in multiple arc whose resistances are 

 respectively 2§, 2, and 2§, which is equal to 



1 4 



2f + 2 + 2f 



the same result as obtained above. 



These numerical examples show conclusively that, in cases 

 in which the resistance of a network can be obtained by simple 

 direct methods, the results coincide, as should be the case, 

 with those obtained by the employment of the general method ; 

 but at the same time the general method is capable of con- 

 ducting easily to a solution in the most unsymmetrical cases. 

 The general rule will, for instance, just as easily give the 

 determinants when the selected points between which the 

 resistance is required are not symmetrically placed, but are, 



