236 



Dr. J. A. Fleming on the Distribution of 



this determinant being derived from the one in the equation 

 for x by adding the second and third columns for a new third 

 column. 



This last determinant equation writes out into 



(Q + S + D) 



T, 

 P, 



r 

 R 



+ D 



T, 8 

 P, Q 



=o. 



Hence the condition that the current in the galvanometer- 

 branch shall be zero is that both determinants in this expression 

 shall be simultaneously zero, or 



that is, 



T, r 

 P, R 



= 0, and 



T, S 

 P, Q 





T r S 

 P~R~Q 



■• 



= 0; 



Hence this condition expresses the relation which must hold 

 good between the magnitudes of the resistances T, P, Q, S, r, 

 R, in order that the galvanometer-branch G may be conjugate 

 to the battery-branch B. 



The above example shows well the symmetry of the method 

 when dealing with a case of distribution of currents in a net- 

 work. 



§ 11. As a final illustration, let us consider the case of a 

 circular wire APBQ, with a diametral wire P Q across it. 



Take any two points A, B, at the extremities of a diameter 

 not coinciding with P Q ? but separated by an angular distance 

 from it, and let us obtain the resistance of the circular wire 

 so crossed between the points A and B. 



Join the points A, B by a dotted line of zero resistance. 

 Call the three meshes so formed os } y, and z ; let r be the 

 radius of the circle ; and let p be the electrical resistance of 

 the wire per unit of length. Then the 



Resistance of branch PQ = 2pr, 

 AF = pr0, 

 „ „ AQ=pr(7r-0), 



and 



Resistance of branch BQ = resistance of AP, 



PB_ 



Then the network determinant d n is 



-pr(ir— 6), 

 pr(»+2), 



AQ. 



prir, 

 -pr{*-6), 



-e, 



-pr2, 



-e 



-pr2 

 pr(7r- 



•2) 



