1887 .] Dr T. Muir on the Theory of Determinants. 
469 
be 
x 2 = As ± + Bs 2 + Csg + Ds 4 ] 
x 2 — Es 4 + Es 2 + Gs 3 + Hs 4 I 
x B — Is 4 + Iv6‘ 2 "1" Esg + Ms 4 | 
% 4 = NSj + 0^2 -r P^ 3 + Q$ 4 J , 
then the solution of the set 
m + ^3 + n y± = v i' 
fyi +fy 2 +^n + °y± = v 2 > 
cyi +yy 2 + l Vs +py±= v 3 \ 
dy 1 + liy 2 + my B + qy± = v 4 j , 
which has the same coefficients differently disposed, will be 
y 1 - A^ + Ewg +1% + Nv 4 ' 
y 2 = Bv 1 + Fv 2 + K«? 3 4- Ov 4 
y B — Oy 4 + + D^3 + P^4 | 
y 4 = Dv 1 + Ht7 2 + Mv 3 + Q«J 4 J ; . . . (xxvi.) 
and hence, that the solution of a set having the special form 
ax x + bx 2 + ex 3 + dx A = s 4 ] 
bx 1 + ex 2 +fx 3 + ya* 4 = s 2 I 
CMJj +/o? 2 + ^ tx s + ^4 = % | 
<fe 4 + gx 2 + ix B +jx± — s 4 J 
will itself take the same form, viz. 
A$ 4 + B§2 + C§ 3 + Ds 4 — a? 4 ] 
Bs 4 + Es 2 + Es 2 •+• Gs 4 = x 2 I 
0 4 + Fs 2 + Hs 3 + Is 4 = x B 
Ds 4 + G§2 P 1% + Js 4 = x^ 
(xxvi. 2.) 
GAUSS (1801). 
\Disquisitiones Arithmetics. Auctore D. Carolo Friderico Gauss. 
167 pp. Lips.] 
The connection of Gauss with our theory was very similar to 
that of Lagrange, and doubtless was due to the fact that Lagrange 
had preceded him. The fifth chapter of his famous work, which is 
the only chapter we are concerned with, bears the title “ De formis 
squat ionihusque indeterminatis secundi gradusf and its subject may 
be described in exactly the same words as Lagrange used in regard 
