1904 - 5 .] Dr Muir on General Determinants. 
that therefore 
913 
2 P = x 2 DlP+ y 2 D' 2 y P + z^DlP • • • 
+ ^xyD^yP + 2^D a ,D g P + • • ■ • 
and 
p — IT) p P — ID P p - ID P . . . . 
L x~ 2 J - / a: x 5 1 y ~~ 2 LJ y l J z — ’ 
After this the second part of the memoir, consisting of 
geometrical applications, is entered upon. 
Haissen, P. A. (1846, Aug.). 
[Ueber eine allgem eine Auflosung eines beliebigen Systems von 
linearischen Gleichungen. Berichte . ... k. sdehs. Ges. 
d. Wiss. (Leipzig), pp. 333-339.] 
The solution of a set of linear equations is here looked at from 
the point of view of an astronomical computer, and though 
determinants are not used — are, in fact, eschewed — it is interesting 
to note that the hidden identities on which the new process of 
solution depends are 
l a ^ ) 2 i _ 
<h 
+ 
1 1 a 2 
1 kfi i 
a 1 
| a^b 2 | cq 
1 a 4p2 C 3 1 _ 
<h 
+ 
1 «A \' a i 
\ aA c 2 
1 1 ^2^3 1 
1 ®A C 3 1 
a i 
| aqZqc 3 
1 1 a A 1 
| 1 
+ 
a b b x | a 2 
! a 5^1 C 2 
l.l a 2^3 1 , 
1 1 «A 1 
1 a-\b<pod\. | 
a i 
i <( A ! a \ 
1 a A C 3 
I 1 1 a^b^c^ | 
I a^b^c^d^ | | oq&jCg | 
and that these are to be found explicitly stated in Schweins’ 
memoir of the year 1825. 
Cayley (1847). 
[Sur les determinants gauches. Crelle’s Journ ., xxxviii. pp. 
93-96 : or Collected Math. Papers , i. pp. 410-413.] 
As the title implies, the subject of this paper is not general 
determinants. Part of the purpose, however, which the author 
PROC. ROY. SOC. EDIN. — VOL. XXV. 58 
