232 



Dr. J. A. Fleming on the Distribution of 



determinant easily into 







ri — r 



r 2 —r 2 



r 3 

 which is equal to 



The first minor of the leading term of the network deter- 

 minant is 



ri + r* ~ r 2 

 — r 2 r 2 + r B 

 which is equal to 



and hence the resistance of the network between A and B is 



ssdn-l, 





t y t 2 t z 



r 1 r 2 + r 2 r z + r 2t r 1 



which is a known result. In these simple cases the above 

 general rule is, of course, a less easy method of finding the 

 combined resistance than the direct application of Kirchhoff 's 

 corollaries of Ohm's law ; but whereas the general method is 

 alike applicable to the most complicated as well as to the most 

 simple cases, the simple direct method requires twice as many 

 equations, and does not determine the direction as well as 

 magnitude of the current in each branch. 



§ 8. As a simple numerical example we may take the case 

 of a crossed square of wires. Let 12 conductors join 9 points 

 (fig. 7) so as to form a square divided into four squares, or a 

 four-mesh network of conductors. Let the resistance of each 

 branch, as a&, be unity. It is required to find the combined 

 resistance between A and B. Number the meshes 1, 2, 3, 

 4, 5 ; V being the added mesh formed by joining A B by a 

 dotted line, making an additional fifth mesh, the resistance of 

 this additional ideal conductor being zero. Then the network 

 determinant is 



4 

 -1 

 -2 

 ■1 



=d 



-1 



-2 



-1 







4 



-1 







-1 



-1 



4 



-1 











-1 



4 



-1 



-1 







-1 



4 





