390 DR THOMAS MUIR ON THE 
the other two terms are expressible in the form 
~(31129+ 54468) + 31246, 
i 
where the binomial and the single term which follows it are both doubly-invariant. 
There is thus finally obtained an expression for the eliminant which shows its property 
of double-invariance, the constituent parts being fourteen single terms and seven 
binomials, viz. 4 
0000 = Ole eece  OAb6 
— 2.50016 £11998 = 24468 
+ 20077’ ey Sta aa 
=2 > 0le7, SILO = 448) 
+ 2.20159 bh Bebe! 
+4. 07'8'9' — 211'88 — >44'99' 
- 0789 PTs ea 7/9! 
+ 0'7'8'9' 
+ 31166 
— 21489 
% S1'4/9'9' ; 
— 1688’ 
= Diese: 
Gy. > Ty et GN ies Gigs Oe 
b, Oy Sy Cy eG; 
Gi bm fh % hy ~ 
As hg + Ue UD Sa 
Dy df i) hy Yo 
Cea OOD Apo ne, 
As he Ce Gs.) Up, als 
bs . dg fy + Cg +. hg Qy 
Cn. SDE Gan eee hs 
4 5 6 4 57 6040 
By transposition of rows and of columns, and by altering its sign, this is readily : 
changeable into a, 
a, b, Cy hy . 9: f Ue 
Dy Oy Cy Iiy  Gy eT 
Og (Us. Bae liga Me SGal yt HS 
hy Oe hy b, Cie I 1 © JQ 
hy As b, Cy 1) Yo 
hg a, b, C, » fe Is 
ca J, % b G hy a 
Io fg Gy Un Cy hy 
93 ig 1dg Uy (ty hy 
