r 23 



r. 



'-.I! 



F 3I> 



Add the first column multiplied by r, 2 to the fourth ; add the first multiplied by 

 ?* 13 to the fifth ; and subtract the first multiplied by r., 3 from the sixth, the determinant 

 will reduce to the minor of the first row and column. Continuing this process twice 

 more, we ultimately deduce 





o-?o|o-f K 6 



J*1IJ ~~" -"12 -"13 



-tvl2) -t*-22j ~~ 



-*-M3 -"23> ~" 



in" 



We will now proceed to calculate such of the minors of A as will give us results 

 beyond those obtained for two correlated organs.* 



We require the correlation of cr, and r., 3 , and of r n and r, :j . 



Taking a- l and r 2 s we must strike out in (xxxii.), as we have taken only three 

 organs, the 4th, 7th, 9th, and 10th rows and columns straight oflf, and for the required 

 minor the 1st row and the 8th column. We have then for the minor M (or,, r 23 ), 



To reduce this expression take the third row multiplied by r, 2 from the first, and 

 -the fifth row multiplied by r, 3 from the first. Then take the fourth row multiplied 

 by 7*13 from the second, and the fifth row multiplied by r 23 from the second, then 

 remembering that 



As a matter of fact all the minors were worked out and the results of (xv.) to (xviii.) thus verified. 



