AND OF THE SECOND LAW 55 



From this functional equation / may be determined. After 

 successive differentiation there is obtained a differential equation 

 of the second order and its general integral is 



f(W) =k log W+ constant 

 or S = k log W+ constant, .... (10) 



which determines the general dependence of entropy on proba- 

 bility. The universal integration constant k is the same for a 

 terrestrial system as for a cosmical system, and when its numerical 

 value is known for either system it will be known for the other; 

 indeed, this constant k is the same for physically unlike systems, 

 as above, where concurrence between a molecular and a radiating 

 system was assumed. The last, additive, constant has no physical 

 significance because entropy has an arbitrary additive constant 

 and therefore this constant in (10) may be omitted at pleasure. 



Relation (10) contains a general method of computing the 

 entropy 5 from probability considerations. But the relation 

 becomes of practical value only when the magnitude W of the 

 probability of a system for a certain state can be given numerically. 

 The most general and precise definition of this magnitude is an 

 important physical problem and first of all demands closer insight 

 into the details of what constitutes the " state " of a physical system. 

 [This has been adequately done in the earlier part of this presen- 

 tation. Later on pp. 27, 28, permutation considerations led us 

 to define the probability W of a state as the number of com- 

 plexions included in the given state.] 



