The theory of determinants in the historical order of development, by Sir Thomas Muir.

COMPOUND I)ETERMINANTS (SYLVESTER, 1851) 195
and
/ (~'n-l)(m -2)... (nO-r) 5
1.2...
In reference to this one must remark at the outset on the
inappropriateness of the notation
q01 q02.. I '0rn
for the qtlI combination of 1' integers taken' fromt 1, 2,..., m.
Manifestly
though equally awkward, would have.been less misleading.
Indeed, as there is one clear misprint in the enunciation, namely,
" less than n " for " less than mn"; and as Sylvester is known to
have been inaccurate in the correction of proofs, we might
suspect 0m to be a misprint for 0r, were it not that Om occurs
four times in the short passage and 01. not once.* For q0, it
would have been much more convenient to write pq, which
would thus have stood for "the pth integer of the qth combination";
and Sylvester's theorem.might then have been written
a,, "~21.. ari am-i-i Ctrn4. am~n "12 (t22 c... ain2i,,,+ 2 a.2... an+n
b1i b2l - bri bin+, b11+2.,. bm+n b12 b2... bl-2 b111~1 bn+2... bmn+n
a,,, a2,1... a- C m+ Ctrnmil. 2. a,21,,,+
bjE~, b2CL.' bj-L E bin+, bm+2 bm~.nS~n
= am+ am+2... amnn a, a2... a
bm+l bm bbb... brn+nn b, b2 bm+71
Ax being used as before for C T,,. To help towards clearness let
us illustrate by means of the case where mn = 4, n = 3, r = 2. We
then have A = 6; each set of O's equal to a binary combination of
the first four integers, that is to say,
101102, 2012 02, 301302, 630 0602
equal to
12, 13, 14, 23, 24, 34;
* Om was actually a misprint. Sylvester himself had to draw attention to it a
year later in the Cambridge anid Dub. Math. Joqrn., viii. p. 61.