1324 
noticing that in the deduction of (8) the fact that we have a homo- 
geneous system has not been used. The given relation holds also in 
a capillary layer. However f,- will depend on a parameter in the 
d, 
direction of the layer (for Ee depends on i) The consideration may 
9 
easily be extended to the case of a mixture and the capillary layers 
in a mixture. It will be possible then to develop MANDELSTAMM's *) 
considerations on the diffuse reflection at the layer of contact between 
two liquid phases in the critical point of mixture more exactly 
than he himself has done. 
Utrecht, Mei 1916. 
Physics. — “The dilatation of solid bodies by heat” By Prof. 
H. A. Lorenz. 
(Communicated in the meeting of October 30, 1915.) 
When in the theory of specific heat the idea had been worked 
out that the heat motion of solid bodies consists in vibrations of 
the particles under the influence of the same forces that give rise 
to the phenomena of elasticity, Desyn*) successfully attacked the 
problem of thermal dilatation. In his theory, which has been further 
developed by M. J. M. van EvERDINGEN®), it is shown that this phe- 
nomenon may be accounted for in a satisfactory way by adding in 
the expression for the potential energy of the body terms which 
are of the third order with respect to the displacements of the 
particles. 
In the present paper considerations similar to those of DrBre and 
VAN EVERDINGEN are presented in a form that is perhaps somewhat 
simpler. 
§ 1. We shall suppose the body to be isotropic or erystallized in 
the regular system. Let S be its surface and v its volume at the 
temperature 7’ and under a uniform pressure p. We can imagine 
that the particles lying on the surface are kept fixed in the positions 
about which they vibrate and that, when this has been done, the 
1) Ann. der Phys. 42. 
2) P. Depye, Zustandsgleichung und Quantenhypothese, Wolfskehl-Vorträge, 
Göttingen, 1913, p. 17; Leipzig, Teubner. 
3) M. I. M. van Everpincen, De toestandsvergelijking van het isotrope, vaste 
lichaam. Proefschrift, Utrecht, 1914. 
