1902-3.] Dr Muir on Axisymmetric Determinants. 
565 
Qua in formula, expressio 
i $n $22 * • • 
, . , n(n - 1) • • • (n — m+ 1) 
designat summam — —L v ' expressionum, 
D2 . . . m 
quae e 
^ j — ®11 ®22 • • • 
proveniunt, si in 
$11 *^22 ■ " ' 
loco indicum priorum simul ac posteriorum 1, 2, . . . , m 
scribimus omnibus . modis, quibus fieri potest, m alios e 
numeris 1, 2, 3, . . . , n.” 
There are, however, two minor instances in which it is the 
special determinant that is alone concerned. The first occurs 
after proving (p. 13 , footnote) the theorem (see Rothe’s paper of 
1800 ) that if the solution of 
a l} x 1 + $ 2^2 + • • • + a n \X n ' — UK (X = 1 , 2 , . . . , n) 
be 
X K ±$ n $22 • • ' a nn = b K \U\ + 5/c,2$2 + • ■ • + b Kn U n (k = 1 , 2 , . . . , n) 
then the solution of 
$Al£/i + $A 2^/2 + * ‘ * + aKnVn = vk (X= 1, 2 , .... n) 
must be 
y K it $11 $22 • • • — b\ K v\ + &2k^2 • * • + b nK v n (/c — 1 , 2 , . . . . %) 
when he adds the corollary that if a K K = $a« then also b K K = 5 a* . 
The second occurs quite similarly when, having pointed out 
(p. 20) that the coefficients b K K in either solution are expressible 
as differential coefficients of 2 ± $ n $ 22 . . . a nn , he adds the 
sentence, “ Quoties a K \ = $a* differentials semisse tantum sumi 
debet si k et X diversi sunt.” 
Jacobi (1834). 
[Dato systemate n aequationum linearium inter n incognitas, 
valores incognitarum per integralia definita (n - l)tuplicia 
exhibentur. Crelle’s Journ ., xiv. pp. 51-55.] 
