Dr Muir on General Determinants. 
681 
1907-8.] 
ausdriicken lassen.” We are prepared, therefore, to find his ground already 
pretty well covered by Joachimthal’s paper of November 1849. The latter 
established the result 
0C = 9A 0B '_3A 0B + + 9A 3B 
dc K x da 0 K ’ ba lK ' da nK bb nk ’ 
and said others could be found : Hesse established one of these others, 
namely, 
02q _ i 3 2 A S 2 B 
bc K ^c /xv 1 • 2 bdp^dciq^ bbp\dbq V 
and said that the next would be 
8 3 C = X 1 03A 3 3 B 
bc K xbCfjn/dCpcj- 1 • 2 • 3 dap K da qi jda r p obp\db qv db r(r 
where p, q, . . . . have the values 0, 1, 2, . . . , n. 
We can only remark that the second and third results are not so simple 
as they ought to have been: for Hesse does not point out that (1) when p 
and q are identical the term vanishes ; (2) putting p, q — a, (3 gives the same 
term as putting p, q = /3, a ; and (3) therefore the second result should be 
02 0 ^ 3 2 A 3 2 B 
bCicxdc^p ^,|J bdp^Clq^ bbp\dt)q v 
where p has any of the values 0, 1, 2, . . . , n — 1, and q any of the values 
1, 2, . . . , n, subject to the condition that p<q. It would then agree with 
the extended multiplication-theorem of Binet and Cauchy, and especially 
with the latter’s form of it. 
Ohio, F. (1853, June). 
[Memoire sur les fonctions connues sous le nom de resultantes ou de 
determinants. 32 pp. Turin.] 
The title here is not sufficiently descriptive, almost the whole of the 
thirty-two pages being occupied with the consideration of determinants 
whose elements are binQmial. Beginning with the “ tableau ” 
«o + m o 
a Y + m Y . . 
. . + m i _ 1 
\ + n 0 
h + n \ . 
. . + 
^0 "t ^0 
h + h 
Ohio seeks, of course, to express its determinant as a sum of determinants 
with monomial elements, and thereafter applies his result to particular cases. 
