377 
1905 - 6 .] Dr Muir on the Theory of Alternants. 
and as it also means that 
a 6 +i? 2 a 4 - ... ] 
b 6 -p Y b b +jp 2 & 4 ~ • • • + P& = ® I 
f 5 - Pif + Ptf - ■ ■ ■ + p«=° 
from which we have 
a 6 
a 4 
a 2 
°1 
1 
a 5 
a 4 
a % 
a 2 
“1 
1 
\ 
h 
h 
A 
1 
h 
\ 
h 
\ 
1 
A 
A 
A 
A 
A 
1 
A 
ft 
A 
A 
A 
1 
a 5 
a Q 
a 3 
°2 
a 1 
1 
a 6 
«4 
a 3 
«2 
a i 
1 
h 
\ 
^3 
h 
1 
4 - 
h 
h 
h 
1 
h 
A 
A 
ft 
A 
1 
A 
A 
A 
ft 
fl 
1 
it follows that in later notation 
j a°b l c 2 d z e A f 6 | h- | a°b^c 2 d z ef b \ = 'Za , 
j a°b l c 2 d z e b f 6 | - | a°b l c 2 d^e 4 f 5 \ =%ab, 
| aLb~ { c 2 d^e b f b | -4- | a°b l c 2 d z e 4: f 5 | =%abc , 
with similar results when the alternants are of any other order. 
Scheibner (1856). 
[Ueber die Auflosung eines gewissen Gleichungsystems. 
Berichte . . . Ges. d. Wiss. zu Leipzig , viii. pp. 65-76.] 
Joa.chimsthal (1856, Sept.). 
[De aequationibus quarti et sexti gradus quae in theoria 
linearum et superficierum secundi gradus occurrunt. 
Crelle’s Journ., liii. pp. 149-172.] 
The problem of finding the normals drawn from an external 
point (£, rj , £) to the surface 
£ + £+£-i 
a b c 
9- 
