1866.] Rev. C. L. DodgsoD on Condensation of Determinants. 155 



We then condense these into the column 



and, supplying from 



the second block of the first series the column 



we obtain 



3 

 1 

 5 2 



as the last two columns of the second block of the new series ; 



and proceeding thus we ultimately obtain the two terms 12, 12. Observing 

 that the y-column has the sign + placed over it, we multiply the first 

 12 by +y, and so form the equation 12y=12, which gives y=l. The 

 values of z, u, and v are similarly found. 



It will be seen that when once the given block has been successfully 

 condensed, and the value of the first unknown obtained, there is no further 

 danger of the operation being interrupted by the occurrence of ciphers. 



+ - + 



_ u -\.2v 4-2 =0 



— M — v —4 =0 

 -2u - V -6 =0 



- u +2v +4 =0 



- + - 



a; — y —2z 

 2x y — z 

 X —2y — z 

 y +2^ 



2x 



■8 =0 



2 

 -1 

 1 



-2 

 -1 



2 

 -1 

 -1 



2 

 -3 



2 

 -4 



-3 -3 -3 

 3 3 3 



-5 -3 -1 

 3 -5 1 



3 -6 



-1 2 



-5 8 



1 -4 



2 

 -1 

 -1 - 



2 



3 

 -1 

 -5 -2 



4 



-2 

 -2 

 6 



2 6 

 -1 -3 

 -1 -1 



3 

 1 -2 



2 

 -1 



5 

 -1 



|2 



-2V: 



4| 



■A...V- 



-2 



'5 



•.3m 



6 6 I 



• G^-^G z- 



6 

 6-6 8-2 



-17 8-4 6 



1 12 12 

 I 18 40 -8 



I 36 - 72 I 

 v_36a;=-72 



12 12 I 

 12y = 12 



r= 2 



5 2 

 3 -1 

 2 3 



- + 



bx +2y 



2»x - y 



2x +3y 



-3 8 

 -2 10 



-2,z 



+ ^ 



1-3 



+ 

 + 3 

 + 7 

 -12 



12 I 

 3^=12 



.11 -7 -15 

 11 5 17 



I -22 22 1 

 .•.22a;=22 .. 



1-7 -14 

 .•.-7y=-14. 



^= 4 

 2 



The Society then adjourned over the Whitsuntide Recess to Thursday, 

 May 31. 



1 



