The theory of determinants in the historical order of development, by Sir Thomas Muir.

470 HISTORY OF THE THEORY OF DETERMINANTS
both results. The three of the other set are less general, namely,.12
21
31 32
11

12 1
23 1
I1. 1221-l1223,
1.

where the I's cover 3 and 6 terms respectively;

21
31
41
1

12 13 14 1
23 24 1
32. 34 1 12 2334 - E123443
42 43. 1
11 1.

- 122331,

where the L's cover 24, 12, 8, terms respectively;

12 13 14 15
21. 23 24 25
31 32. 34 35
41 42 43. 45
51 52 53 54
1 1 1 1 1

1
1
1
I
1

- E 12 23 34 45
-= j+ 1223. 4554
+E _122331. 45

-E1221. 3443
+ 12 23 3441

where the I's cover 120, 15, 60, 30, 40 terms respectively. Here
again no generalisation is attempted.
(E) CENSUS OF TERMS IN SPECIAL DETERMINANTS.
The first instance of the finding of the number of terms in
the final development of a determinant of special form has
already been drawn attention to, the investigator being Scherk,
and the date 1825.
During the period now occupying us, the earliest suggestion
on the subject occurs in 1844 in Crelle's Journ., xxviii. pp.
191-192, the determinant being of the 8th order, and the