1887 .] Dr T. Muir on the Theory of Determinants. 
475 
HIESCH (1809). 
[Sammlung von Aufgaben aus cler Theorie der algebraischen Gleich- 
ungen, von Meier Hirsch. pp. 103-107. Berlin, 1809.] 
The 4th Chapter Von der Elimination u. s. w., contains five pages 
on the subject of the solution of simultaneous linear equations. 
These embrace nothing more noteworthy than a statement, without 
proof, of Cramer’s rule, separated into three parts (iv., iii. 2, v.), 
and carefully worded. 
BINET (May 1811). 
[Memoire sur la theorie des axes conjugues et des momens d’inertie 
des corps. Journ. de VEcole Polytechnique , ix. (pp. 41-67), 
pp. 45, 46.]* 
In this well-known memoir, in which the conception of the 
moment of inertia of a body with respect to a plane was first made 
known, there repeatedly occur expressions, which at the present 
day would appear in the notation of determinants. There is only 
one paragraph, however, containing anything new in regard to these 
functions. It stands as follows : — 
“Le moment d’inertie minimum pris par rapport au plan 
(C), a pour valeur 
1,ink 2 =/ 2 x 
ABC - AF 2 - BE 2 - CD 2 + 2DEF 
r’(BC - F 2 ) + AC - E 2 ) + i 2 (AB - D 2 ) + 2gh(EF - CD) + 2gi(DF - BE) + 2hi(DE - AF) • 
Si, dans le numerateur, 
ABC - AF 2 - BE 2 - CD 2 + 2 DEE 
on remplace A, B, C, &c. par 2mx 2 , 21 my 2 , &c. que ces lettres 
represented, on a 
^mx^my^mz 2 - '$mx 2 (’%myz) 2 - %my 2 {%nxz) 2 
- 2 mz 2 {%mxy ) 2 + T%mxy'%mxz%myz , 
et l’on peut s’assurer que cette expression est identique a 
%mm'm"(xy'z” + yz'x" + zx'y" - xzy" - yx'z" - zy'x") 2 ; 
par une transformation analogue, on peut ramener la quantite 
* An abstract of this is given in the Nouv. Bull, des Sciences par la Societe 
Pkilomatique, ii. pp. 312-316. 
