( 535 ) 
Mi ANP +PA+Q=09, |) 
ME Ne Pago | 
which give, according to the method of Brzour, the following resultant: 
(7) 
(MN) (MP') (MQ) 
| 
| (MP') (MO) (NP) * WD ISA . . ®) 
| (4Q) (NQ) (PQ) 
5. From this is evident that the form of the final equation is 
found, but it is a very intricate one, as is proved from the values 
of the coefficients, given here: 
i508 5 Bache Lt BB bebt tr Bb BB; 
Na OB Bea), Al Bebe ANB + 2, A 2. SB set 
PB BN be ALB eb ANB Sa, Be Oh. ARB = 
END he ARBs Da Br Bb Bi 
Om A; B, : 
Pb A Aa B Asa A Bra, A, BO brt 
an pele, od B, GT Bett ope: dB 
DAANEN AB Beb AA Br 
At 2 
3 A, 155 3 
a, 
Qa A, A. a, Ay a, A, A; — a, es —a,, A, A, —a,,A,A3. 
M' =>... B, B, + },, B, B, + 6,, Bs — ba B, B, — bs By —b,, B, B,; 
IN! Sá BB; 4 ay A, B, + 6,, A, B, + a, B, B, + 6,, A, B, + 
bs A, B, + a, B;? + 26,, A, B, — as B, B, — bs pi B, — 
bis A, B, — as B,? — 2b,, A, B, — a, En B, — b,, A, B, — 
ne Al Tey 
BE by AA eA, Biel a. AB, + bis AAS Aras, Ay By 
2a 4, B, + 2a,, A, B, + bs As — b,, A, A, — 4,, 4 Ee Ei 
Z = 2 Z Z == A 
a,, B, 4, — 2a,, A, B, — b,, A,’ — bo, A, A; as. B, — 
APEN: 
fi ae 2 
Opal AR ANS ar AA tran oA? ee fale al, ee val IS ha 
6. With the aid of these expressions the equation of the locus 
of the axes can be determined for each separate case, which was 
the purpose of this paper; we shall conclude by giving a few 
observations. 
a. Even in the general case abridgement is possible in the operation. 
If we assume that the axes of coordinates coincide with the principal 
axes of one of the surfaces, e.g. of B—O, then 6,,=0, b,, — 0, 
