J. DOUGLAS HAMILTON DICKSON ON A CLASS OF DETERMINANTS. 

that is, a3, = | b, 9 b, = —_ 
ay ? ae) ’ ay ’ Asi Oa ) ae) ’ Anti 
b, , b, by ’ On5 | b, 5) by 5) Ones 




Advancing in equations (2) each letter, @, b, a, B 
Gy ? Cn 
by ? b, ? Bn+s 
Cy ? 
Boyn =) haar 
Cy 5) Cnt 
which becomes, by one application of equations (A), 









627 
b,, Op, ; he) 

, to the next, 
an Boy n es Cy ; Cn == ey | Be : C1, Cy 
b, ) b, ) Ont b, ’ by , Ons 
Oa ) ae) 5) | ay ’ as 2 ay D) On+.9 | aa 5) Ay ) 3 p) Q,+9 
b,, b bh, bs b, ’ On+2 bh, Orn 203 Baro 
and by a second application 
2 — | = —— a a a 
a Bon aa | Gy, Az} ,| Ms, G41 = WD Vy eosei 
b, ’ by b, ry ieee . b, 5) by ? Onas 
| . b, 5) b, 5) re b, y) ’ b, 3 Ona 
| uy 5 My, (sz ? An+2 aa > Ay o) 5) as 2 Gn+2 
| b, D bs 5) bs ? Ono b, ? by i) ’ b; p) Orns 

or, subtracting the second top line from the third top line, and adding the 
second column from the left hand to the third column from the left hand, 
2 — i 
. aA BY n =— | Oe Os Ca | 
. b, 
. 5 6 b, ’ Dee Os 
, de, An+4 . 
(3) 
b, i) b, , Ons 
by 
ay ’ ly ) Ue) ’ Cs ’ An +2 
b,, by , by , by, (Dane | 
My, Az, UW, Ante 
bh, bs , bs , On.9 

In like manner the evaluation of 6, may be deduced from y, ; thus 
b, ? b, ’ Da 
(1, Co, Cn4i 
hb, bo , bs, On +9 
Cy, Cy, C3, Ch+9 
Boon = ° 

