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

318 HISTORY OF THE THEORY OF DETERMINANTS

the eliminant found being a power of
ia b c
b cd
c de.
Possible extensions of the problem are indicated.
WHITWORTII, W. A. (1865): ZEIPEL, V. v. (1865).
[Of recurring series. Oxford, Cambr. and Dubl. Messenger of Math.,
iii. pp. 11 7-121; or Math. from Educ. Times, iii. P. 1 00.1
[Determinanter, livars elementer liro binomialkoefficienter. Lunds
Univ..Arsskrift, ii. pp. 1-68.]
Whitwortli's paper is summed up in one proposition, namely,
if CO +cIx+C2 X2 +.. be any convergent recurring series of the r"'
order of recurrence whose first 2r terms are given, its scale of relation
will bep

cr1 el,
and its sum
0 slxrco cl
cl c),
cl-, c1.

-1 Xr2 1
Cr+I... C)I
to infinity will be
2 r-2...S
c3... r
cr+i... c91..1
-II

co
el
cr_1

c1 c2
c2 C 3
cr cl'.+i

c1r -i
I
cr

-I
-1

cr1 ci,

terms.

where s,,, denotes the sum of the first m of the given
The 'scale of relation' being of the form
1+~1X+f22X +... 3. I

there are r equations'
C10,7 + c2,3r..1 +
cr-1/3. + c?437- +,. +c2+. = 0. r1= 0
+C-1= 0