151 
This theory of many-valued functions, or what is exactly 
the same thing, this theory of groups, is, after all, though 
perplexing enough at first sight, merely a trifle compared 
with the theory of the polyedra, the subject of competition 
for the grand prize of the Academy for the years 1861, 1863, 
1864, &c. This was also proposed early in 1858 thus : 
Perfectionner en quelque point important la theorie geometrique 
des poly hires. The null results of the competitions of 1861 
and 1 863 may be read in the Comptcs Rendus. Although I 
have had the honour to present to the Royal Society a 
complete discussion of this vast theory (which was first 
written in French, and intended for the contest of 1861), and 
which has already so far appeared in their Proceedings and 
in the Philosophical Transactions as to secure my humble 
claims, it is a fortunate thing for the competitors for the 
medal of 1861, that the most difficult part of the investi- 
gation has yet to be brought to light. As it is not a subject 
that many persons are anxious to read, I hope that the Royal 
Society will be in no hurry to anticipate the efforts of our 
French friends, and thus to spoil the interest of their contests. 
The remarks of the distinguished Rapporteur (Comptes 
Rendus, Mars, 1861) on the competition of 1860, brief as 
they are, are to me the most tempting subject in the world 
for criticism, chiefly in their reference to the efforts of my two 
learned competitors. But, even if this were the place for 
such criticism, my sincere respect for the illustrious Academy, 
in whose name and authority those remarks are permitted to 
appear, would command me to forbear. Some will of course 
suspect that I have said too much already: many know full 
well how much I have refrained from saying. One security 
I have ; that no man, who can form the dimmest conception 
of what I have had the honour to do, will cry out ogrpaidg 
fieri. The mere proposal of these two prize-questions has 
been to me a piece of rare good fortune. And I am more 
than content with the undivided glory, whatever that may be. 
