whilst further 
( ?63 ) 
The result is therefore: 
The surface 
= —'f/i« 
±z=z(r~ < f ) 
\Z;f$r 
has the plane striction line r ~ rp t z = 0. 
The formulae deduced above hold for the surfaces (2). As was 
noticed the general types mentioned at the conclusion of 1 are not 
strictly separated, however, so that there are still amongst them 
scrolls with a right directrix, to which then the above formulae are 
applicable. 
Examples of this are: 
Of the type z =s* At sin (0 a)a0 F{r ) 
the surface z =^Ar sin (0 -f- «) + n0 -J- hr. 
Of the type l{z) = ad -f f(r) 
the surface l{z) = a0 -f- l (r -j- p); 
these have the 2-axis as directrix. 
Of the type r =f l {z)f t {0) the scrolls 
(£T 
x ■’ = (y - cx)z n or r = sec 0 ( tg0—c) n ~ l z n ~ l 
have still the //-axis as directrix. 
Physics. — “A new theory of the phenomenon allotropy ” By Prof. 
A. Smits. (Communicated by Prof. A. F. Holi.kman.) 
Introduction. 
In two short communications inserted in the “Chemisch Weekblad” 
7, 79 and 155 (19J0) I have already sketched the main lines of the 
theory, an extension and experimental confirmation of which follow 
here. 
Before passing on to this I may, however, be allowed to give the 
gist of this theory in a few words. 
In the investigation of the phenomenon tautomerism it has been 
possible to show by means of the process of solidification that the 
liquid phases of tautomeric substances are composed of two kinds 
of molecules. 
