1899-1900.] Dr Muir on the Theory of Skew Determinants. 203 
De la, en ecrivant 
11 - 13'.ll| 12 = ir-23', 
22 := 13'-22', 
on obtient 
12 | 12 - 11-22 + ( 12 ) 2 , 
= ll / .{22 , -(13') 2 +ll'.(23') 2 }, 
c’est a dire 
12 | 12 = ll'« 123 | 123'- 
On a de merne 
1234 | 1234' = 1 T-22'-(34') 2 + 1 1'-33'-(24') 2 + 22'-33'-(14') 2 + (1234') 2 , 
et dela, en ecrivant 
11 = 14'.11', 
22 = 14'-22', 
33 - 14'-33', 
on obtient 
123 | 123 - 11-22-33 + ll-(23) 2 + 22-(31) 2 + 33-(12) 2 , 
= ll'-14' ( 22'-33'-(14') 2 + (1234') 2 
t # + 1 T 22 '-( 34') 2 + 1 r 33 '( 24') 2 
c’est a dire 
123 | 123 - ll'-14'-1234 | 1234'.” 
The remainder is devoted to the next two cases, the verification 
of which, of course, occupies still more space. The theorem thus 
dealt with may be roughly described as giving the transformation 
of a skeio determinant , having one zero element in its main diagonal , 
into a skew determinant of the next lower order ; and in a nota- 
tion which needs no explanation and which was perfectly familiar 
to Cayley at the time, the four examples may be written thus : — 
12 =± ir-24', 23 = 1234', 
13 = IT-34', 
