139 
1906-7.] Dr Muir on Axisymmetric Determinants. 
removes from it the factors 2, 6, 6, 2. A verificatory proof, unsatisfactory 
to himself, is given, the determinant being as a preliminary again altered 
into a multiple (by 1296) of 
a 2 
ab 
2b 2 -ac 
36c- 
2 ad 
ab 
iac - J6 2 
§6c + l ad 
2c 2 - 
- bd 
2 b 2 - ac 
§ be + \ad 
ibd-ic 2 
cd 
3bc - 2 ad 
2c 2 - bd 
cd 
d 2 
d 2 
ab 
ac - 3 r ad -{- 9 q 
ba 
b 2 + 2r 
be — q bd - 3p 
ca - 3r 
cb - q 
c 2 + 2p 
cd 
da + 9 q 
db-3p 
dc 
d 2 
j 
where 
p = |(^-c 2 ), q = \{bc — ad) , r = f(ac-6 2 ), 
the last change being probably due to the fact that it was known that 
V = 9 (pr-q 2 ) 
and that verification would thus be easier. 
Sylvester (1850, Aug.). 
[On the intersections, contacts and other correlations of two conics 
expressed by indeterminate co-ordinates. Cambridge and Dublin 
Math. Journ., v. pp. 262-282 : or Collected Math . Papers , i. pp. 
119-137.] 
In this paper an important property of axisymmetric determinants is 
incidentally brought to notice; but, unfortunately, the author’s intended 
statement is almost hidden through want of care. He says (p. 270) that 
the determinant 
where 
A 
C' B' 
l 
C' 
B A' 
m 
B' 
A’ C 
n 
l 
in n 
0 
A = 
be- a' 2 , 
B 
— ca - b' 2 , 
1 
<5 
e 
O 
A' = 
- b'e + ad, 
B' 
= - cd + bb\ 
C' = - ab' + cc 
is “ the product of the determinant 
a c V 
c b a 
b' a c 
