243 
that it leads to the same results as the Gisps method of the canonical 
ensemble. Although the two methods can therefore be regarded in 
principle as equivalent, the Bo1rzmMann method seems to possess certain 
advantages over the other, e.g. its terminology can be more directly 
applied to the physical conception. *) 
As Suppl. N°. 23 is not yet published we may here give a short 
general account of this method, which forms the basis of the sub- 
sequent developments. 
§ 2. General formulation of the method of obtaining the equation 
of state of a single component substance from the BourzMANN entropy 
principle. In the general formulation of the method we shall follow 
BOLTZMANN, Gastheorie II. § 36, and determine the momentary state 
(PLANCK’s micro-state*)) of a system of molecules whose motions, 
under the influence of their mutual forces, can be regarded as 
determined by Haminton’s equations *) in terms of a finite number 
of generalised coordinates and the corresponding momenta for each 
molecule. We shall define a mzcro-complerion *) as a state in which, 
for instance, the coordinates q,...qs and the momenta p,...ps of 
the first molecule lie between the limits qi; and q:; + dq1;, qe; and 
qa: + dga: … gsi and qe: ++ Asi, pri and pi; + pri, poi and po; + dpa, … psi 
and ps: + dps, those of the second molecule between qij and 
qj + dq; ete. 
In this, the micro-differentials*) dqi; ete. must so be chosen that 
the specified distribution of molecules according to generalised coordi- 
nates and momenta is sufficient to fix the energy of each molecule 
in the micro-complexion as lying between definite limits which, in the 
problem under consideration, may be regarded as coincident, and 
also to enable one to ascertain if possible special conditions (e.g. 
mutual impenetrability, in the case of molecules supposed rigid) have 
heen inltilied, Werassume that dg), =... — dg,;—dq,, =... dq,s, 
Odi lp; — AP, ete. or, at least, that. the 
1) And also in this that by this method the most probable distribution of molecules 
according to definite coordinates or momenta is at the same time determined, and 
also an expression is found for the Botrzmann H-function for the particular case 
under consideration. 
2) M. PranckK. Acht Vorlesungen p. 47 sqq 
3) In the application to collisions between molecules which are regarded as rigid 
bodies we shall, if necessary, regard the collision as a continuous motion subject to 
very great accelerations. 
4) Derived from BOLTZMANN’s “Komplexion’’. Comp. L. BOLTZMANN. Wien Sitz. 
Ber. 76 (1877), p. 373; Wiss. Abh. 2, p. 164. 
5) M. PLANck. Acht Vorlesungen, p. 59. 
