J. DOUGLAS HAMILTON DICKSON ON A CLASS OF DETERMINANTS. 629 
or, as before, 
GqoryiO = GO og wll om Lah Oui O, dys) Gan 
Ors Ox, Os 5, Oars 
Diy 
G1, Az, Az, M3, As, Ants 
se Oe On penO rena nn (DUN Oda 
Dine). ee 
QM, Ay, Ar, As, Az, M&, ls y Qn+4 
b, oe bs, b5,, 39 by, Dee Ore 
SUG Ns oe Ci ete Ga, Ciects : f s (6) 
Dix, Ora, Os 5) O05 
i dx 5 On ON Oe cs 
Oia Os (Om OO ets 
Gia en) Ons (Ue, Onn pce, 
Ui 80a, O85. Ugo nOea” Oy ck 

The method of reduction of determinants of the proposed forms is now 
apparent. I have, however, calculated ¢,. Repeating the foregoing equa- 
tions, (1) to (5), and adding the equation (6) for @,, the series of the six 
equations is 


C= nitty, Gale is ; : Z : ; . (1) 
b, ? b, 
a8, =— bi sab (2) 
aT > Ay ? An+1 
by ? b, ) Baar 
aBoYn = Dy ~ My, Gy, Us : é 3 , : 5 (3) 
i by ? b, ? Oras 
Oa ’ A, ? a: ? An+2 
b,, bs , bs , On+2 
Foye ne toe A ee! A) 
A, A, Az, Ure 
UR nec 
Gy, Az, As, UW, Un+3 
; by 5) bs ? b, ? b y) Gras 
VOL. XXVIII. PART II. SA 


