27 
[104 
105] 27 
igations to Mr Sylvester in' 
re to him—intermutant and 
it, and the names date from 
)ir in the Cambridge Philo- 
Yansformations, [13, 14]. It 
coefficients of a biquadratic 
e — 2222, and forming the 
ction ace + 2bed - ad 2 — b 2 e — c 3 
as brought into notice by 
105. 
r ere represented by symbols 
could be expressed in the 
nse, is explained by me in 
6, [69] ; see the paragraph 
in as follows : “ On obtient 
les d’un determinant défini 
ni. Car en exprimant &c.,” 
Some time in the present 
nt remark, that as one of a 
CORRECTION OF THE POSTSCRIPT TO THE PAPER ON 
PERMUTANTS. 
[From the Cambridge and Dublin Mathematical Journal, vol. vn. (1852), pp. 97—98.] 
âidering 00 = a, 01 = 10 = b, 
Mr Sylvester has represented to me that the paragraph relating to his com 
munications conveys an erroneous idea of the nature, purport, and extent of such 
communications; I have, in fact, in the paragraph in question, singled out what imme 
diately suggested to me the expression of the function Qabcd + 35 2 c 2 — 4ac 3 — 4b 3 d — a 2 d 2 
id to my notice, I found 
as a partial commutant or intermutant, but I agree that a fuller reference ought to 
have been made to Mr Sylvester’s results, and that the paragraph in question would 
more properly have stood as follows: 
;ant, and I was thence led 
given in the memoir on 
rstood between Mr Sylvester 
ct Mr Sylvester’s right to 
part as may belong to him 
“Under these circumstances Mr Sylvester communicated to me a series of formal statements, 
not only oral but in writing, to the effect that he had discovered a permutation method of obtaining 
as many invariants—viz. commutantive invariants—by direct inspection from a function of any degree 
of any number of letters as the index of the degree contains even factors; one of these commu 
tantive invariants being in fact the function ace + 2bcd - ae 2 - bd 2 - c 3 , expressible, according to Mr 
/ ccl) 
Sylvester’s notation, by ( 2 ’ ^ \ ; and, according to the notation of my memoir in the Carnb. 
00 
Phil. Trans., supposing 00 = a, 01 = 10 = 6, 02 = 11 = 20 = c, &c. by 11 
22 
Mr Sylvester and I shall, 1 have no doubt, be able to agree to a joint statement 
of any further correction or explanation which may be required. 
4—2