(.297 ) 
invariant point exists, always arrange that these arcs do not cohere, 
and within 0 (see fig. 10) an arc of simple carve ? can be constructed, 
running from infinite to infinite, lying entirely outside its image 
and enclosing with f>' a new transformation domain u>. According to 
the Schonflies process of representation *) the domains to, to , u> >••••> 
determined bv a series of successive repetitions of the transformation, 
can then be represented on regions enclosed by straight lines x — na 
and t = (n + 1) a in such a way that a series of corresponding 
points in to, to', to'', to"',... answers to a series of points (p,q), (p+a,q), 
( i)+2a,o), (n+3«,o),...; furthermore, if no invariant point exists, we 
can arrange, that the just-mentioned series of images of to, continued 
indefinitely on both sides, covers the whole Cartesian plane, i. o. w. 
we have proved: . 
Theorem 3. An arbitrary continuous one-one transformation of the 
Cartesian plane in itself with invariant indicalru either leaves at 
least one point invariant, or is a continuous one-one image oj a 
translation. 
ERRATUM. 
In my paper: “ The force field of the non-Euclidean spaces with 
positive curvature ”, these Proceedings IX 1, p. 261, 1. 6 from top. 
for : The unilateral elliptic Sp n is enclosed by a plane bp n -\, 
read: The elliptic Sp n is enclosed by a unilateral plane Sp*-i- 
Chemistry. — “On the nitration of diethylaniline”. By Prof. P. van 
Romburgh. 
(Communicated in the meeting of September 25, 1909). 
A considerable time ago I communicated to the Academy the 
results of the action of nitric acid on dimetbylaniline dissolved m a 
large excess of sulphuric acid 2 ). The difference in behaviour w ic 
dimethyl- and diethylaniline exhibit when nitrated under other 
conditions induced me to study also the action of nitric acid on 
diethylaniline in presence of an excess of sulphuric acid, and indeed 
this amine and some of its nitro-derivatives Appeared to behave m 
many respects differently from dimethylaniline. 
If we dissolve diethylaniline in double its volume of concentrated 
sulphuric acid and pour this solution into an excess of nitric acid 
~blfetiiemy~Ann. 62, p. 319—824 ^ m 
2 ) Verslagen Akad. v. W. Febr. 23, 1895 and These Proc. Dec. 30, 1900. 
