1904-5.] Dr Muir on the Theory of Continuants. 
651 
and his problem is to obtain for any one of the said series an 
expression involving no others of the series except the first two, 
the multipliers u Y , u 2 , . ... y and the addends tt 1 , 7t 3 , . . . . 
He does not draw attention, as he might well have done, to 
the fact that if the 7 r’s had been absent, the equations would 
have been of the familiar type which gives rise to continued 
fractions. Taking the case of seven equations he says the result 
of solution is 
1 
u 
2 
1 
-1 . 
“a - 1 • 
1 »4 - 1 
. 1 u 5 -1 . 
1 u 6 - 1 
1 U>] 
u ifii + A) 
-£l + *l 
^3 
and viewing the last column as the sum of the three columns 
u \Pi Po 
~ Pi • 7r 1 
^5 
he thence readily obtains 
u i 
1 
P8~ 
- 1 
u 2 
1 
-1 . 
Uo - 1 
1 - 1 . 
1 1 * 5-1 . 
• . 1 -1 
1 Uyj 
Pi 
U 2 1 
1 Uo ~ 1 . 
• 1 f* 4 - l . 
. . 1 -1 
1 U Q 
1 
^1 
Uh 
-1 . . 
M, - 1 . 
i « 4 -i . . 
1 2* 5 - 1 
1 u 6 - 1 
1 u 7 
