On the unsymmetrical Six-valued Function of six Letters. 369 
escape of the air will cease in ?’. In fact it would suffice to 
Yepeat, mutatis mutandis, the reasoning in (8) to see that the 
escape must necessarily last more than ¢". : 
P.S. In my note on the Inductive Spark, which was inserted in 
the December Number of this Journal, the expression point of light 
should have been streak of light. 
et 
LVI. Note on the Historical Origin of the unsymmetrical Siz- 
valued Function of six Letters. By J. J. Sytvuster, Professor 
of Mathematics at the Royal Military Academy, Woolwich*. 
iene discovery and first announcement of the existence of the 
& celebrated function of six letters having six values, and not 
symmetrical in respect to all the letters, is usually assigned to 
my illustrious friend M. Hermite, to whom M. Cauchy expressly 
ascribes it in a memoir inserted in the Comptes Rendus of the 
Institut for December 8, 1845, p. 1247, and again, January 5, 
1846, p. 30. | 
M. Cauchy adds that the conversation he held with M. Her- 
mite on this subject excited in himself a lively desire to sound to 
its depths the question of permutations, and to develope the 
consequences to be deduced from the application of the princi- 
ples relative thereto, which he had himself long previously laid 
down. | 
I was not at that date in the habit of consulting the Comptes 
Rendus, or I should at once have made the reclamation of priority 
which I now do, not from any unworthy motive of self-love in so 
small a matter, but out of regard to historic truth. It isa year or 
two since I first learnt that the origin of this function was 
usually referred to M. Cauchy or M. Hermite; but although 
aware that its existence was known to myself long previous to 
the dates quoted, I did not recollect that I had ever communi- 
cated it to the world through the medium of the press, and I 
therefore kept silence on the subject. 
Turning over, a few days ago, for another purpose, the pages 
of a back volume of this Magazine, my eye chanced to alight on 
a footnote to a paper of my own inserted therein, under date of 
April 1844, “On the Principles of Combinatorial Aggregation,” 
which I will take the liberty of quoting at length, as it proves 
incontestably the priority which I lay claim to. 
“When the modulus is four, there is only one synthematic 
arrangement possible, and there is no indeterminateness of an 
kind; from this we can infer, @ priori, the reducibility of a bi- 
* Communicated by the Author. 
Phil. Mag. 8. 4. Vol. 21. No, 141. May 1861. 2B 
