1124 
-“ 
L. S. ORNSTEIN and F. ZERNIKE: “Ibid. III. The equation of state of the isotropic solid.” (Commu- 
nicated by Prof. H. A. LORENTZ), p. 1304. 
L. S. ORNSTEIN and F. ZERNIKE: “The influence of accidental deviations of density on the equation 
of state.” (Communicated by Prof. H. A. LORENTZ), p. 1312. 
W. J. H. MOLL and L. S. ORNSTEIN: “Contributions to the research of liquid crystals”. (Communi- 
cated by Prof. W. H. JULIUS), p. 13/5. 
L. S. ORNSTEIN: “The clustering tendency of the molecules at the critical point”. (Communicated 
by Prof. H. A. LORENTZ), p. 1321, 
H. A. LORENTZ: “The dilatation of solid bodies by heat”, p. 1324. 
H. A. LORENTZ: “On EINSTEIN’s Theory of gravitation”. I. p. 1341, Ibid. II, p. 1354. 
Mathematics. — “Two null systems determined by a net of 
cubics”. By Prof. JAN pe Vries. 
(Communicated in the meeting of January 27, 1917). 
§ 1. A net [c°l of ecubics determines on an arbitrary straight 
line f an involution /,? of the third order and the second rank. 
This involution possesses three groups, in which the three points 
have coincided; f is therefore stationary tangent for three cutves 
c*. If the three points of inflection are associated tof as null points 
F, a null system N33 arises. For in the pencil (c’), which has a 
point /’ as base point, three curves occur, on which /’ is point of 
inflection; each point has therefore three null rays. In this null 
system we shall indicate the null rays by 7, their null points by J. 
The above mentioned /,? has further a neutral pair of points, 
consequently two points forming with any point of / a group of 
the /,°. This pair is of course formed by two base points of a 
pencil included in |[c*]|. If these two points are considered as null 
points B of fb, a null system Ngo arises; for to any point B 
are associated in that case the remaining eight base points 5* of 
the pencil (c°) determined by B, so that B is null point of eight 
null rays ’). 
§ 2. If ¢ is made to revolve round a point P, the three null 
points / describe a curve (P)°, which passes three times through P. 
Through P pass 18 tangents ¢, which touch the curve elsewhere. 
The /,? on ¢ has moreover a neutral double point in the point of 
contact D; for the coincidence of two triple points always goes 
together with the coincidence of the points of the neutral pair *). 
1) If c3 has 7 base points this null system is replaced by an N1,2. Cf. my paper 
“Plane linear null systems”. (These Proceedings XV, 1165). 
2) If the involution is represented by 
a @,0, Haler, desta) Febre, da) =0, 
