626 J. DOUGLAS HAMILTON DICKSON ON A CLASS OF DETERMINANTS. 







Wize 
Gh =) Gael | = da, — 6, and, 2 = 2° or upwards, a, =| @,, @,4 
b, 2 1 ’ b, > b, | 
a a 
6 = By oe ee ag eee oe 
Bava = ee and, i= 2. or pwardss io Betsy On, wee 
Gy ? if Gq ? Cn 
_ & _ Bs _ Bos 
d, — B ’ 2 Bo SARe! Oy Marae (ey, 4; Ses tal Ke d,, a Bo 
Then in like manner from the sets (c, d) two new sets 
€@1, 2, 3, - + 
TR Ja oo 
by means of the auxiliary quantities 
Yo> Y2> Y3 » opm. oe ce 
f 5p 5) 5. ? 53 oe he 
Wize. 
y =| G; 1 l]G4—@, and, 7 = 2 or upwards, >. = | Glas 
d, ? 1 | d, ? d,, 
a _% __ ett 
Ta ROP gnaneer sca ee a Cia oe 
> =|\4@,,1\=¢é,—4, and,” — Dior upwards, 0. —s\"0..ae, 
Ay 5) 1 @ 5] En 
Oo 63 ae bn41 
j= Sy a Sor @ incites P seae a 35 
and so on indefinitely. 
(III.) A few particular cases will present the question more clearly. 
We have 
On, = | UM, A . ° : ‘ 
nea 
Also 
Ve. "Oi eee 
| A, Cn | 
or by equations (A), 
a8, — | bh, oe 
O25 Ant 


