Electric Currents in Networks of Conductors. 227 



(3) If every constituent in any row or column be multiplied 

 by the same factor, then the determinant is multiplied by that 

 factor. 



(4) A determinant is not altered if we add to each consti- 

 tuent of any row or column the corresponding constituents of 

 any other row or column multiplied respectively by an iden- 

 tical factor, positive or negative. 



For example, suppose that the solution of a series of network 

 equations with numerical coefficients of resistance yield the 

 determinant 



5 



3 



1 



6 



7 



8 



9 



2 



2 



1 



4 



3 



10 



7 



5 



7 



we proceed to operate on this as follows : — Subtract the 

 second column from the first and write the remainder. As a 

 new first column we get 



2 3 1 



-18 9 



1 1 4 



3 7 5 



Subtract the third row from the first and put the remainder 

 as a new first row. Also add the third row to the second for 

 a new second row, and we get 



12-3 



9 13 



114 



3 7 5 



Again, subtract the first row from the third for a new third, 

 and subtract three times the first row from the fourth row for 

 a new fourth row, and we have 



12-33 

 9 13 5 

 0-170 

 1 14 -2 

 which is equivalent to the third order determinant 



9 13 5 



-1 7 



1 14 -2 



6 



2 

 3 



7 



3 



5 

 3 



7 



