1082 



Physics. — ''On tlie Imv of partition of energij" V. By Prof- 

 J. D. VAN DKK Waals Jr. (Communicated bv Prof. J. 1). van 



UKR Waals). 



(Communicated in the meeting of March 28, 1914). 



§ 10 bis. In ^ 10 of this series of oommunications^) I have drawn 

 up a formula for the dissociation equilibrium of a di-atomic gas. 

 This formula, however, requires emendation. In the tirst place, namely, 

 the Co of the gas woidd not correspond with 5, but witli 7 degrees 

 of freedom on the suppositions introduced 1. c. And besides the 

 vibrations of the atom would consist of three equivalent degrees of 

 freedom, and there was no occasion to ascribe the ordinarj- equi- 

 partition amount to two of them (together representing a rotation 

 round the othei- atom), and the amount V of Planck's formula to 

 the third (the vibration in the direction of the radius vector). 



To correct this we shall have to take care that the degrees of 

 freedom do not remain e(|uivalent. Then it will no longer be permis- 

 sible to consider one atom as a point which moves in the quasi 

 elastic region of the other. We shall then introduce the following 

 sup[)OSitions. Every atom will have a point P, which we shall call 

 the pole. The line from the centre J/ to the j)ole will be called a.x'W. 

 There will be a quasi elastic region (t round the pole. Two atoms 

 will now be bound when they lie with their poles in each other's 

 regions (i. The potential energy will be minimum when the poles 

 coincide, and when moreover the axes are one another's continuation. 



We shall introduce the following coordinates for the diatomic 

 molecules : 



1. The th)-ee coordinates of the centre of gravity Xz,yz,z~. The 



3 

 kinetic energy corresponding to them will be - 6. 



2. The distance of the centres of the atoms, or rather the displace- 

 ment in the direction M^ 3/, of the points P^ and P^ out of the 

 state of equUibrium (in which they coincided). This displacement 

 will be called r ; it will give rise to vibrations with the frequency v, 



in which the potential and the kinetic energy are both equal to ~ U. 



3. Displacements of P^ and P.^ with respect to each other normal 

 to il/i M^, or what comes to the same thing rotations of the axes 

 out of the position M^M^, These coordinates will give rise to rotative 



1) These Proc. XVI, p. 88. 



