( 397 ) 



Fig. 2. 

 time at a distance 2jr from each other, woiikl tiiiallv have to 

 become constant. Tliis, however is only possible if the n umber 

 of • terms of this sum becomes at last infinitely large, which is bv 

 no means the case. Every vertical distance within the extension 

 remains, namely, of the same length, so that the nnmber of elements 

 within each vertical area which are to be taken together, remains, 

 always finite. Only when the occurring oj's extend over a finite 

 distance, the jinmber of terms of the sum for t = a:) can also 

 become infinitely large. 



A second partial ejitropy, that w'dJt. regard to the vdocitlc.s is 

 obtained l)y taking these elements of the extension together Avhich 



give the same velocity. So this is here ^S 



'=P' 



io(j F" cko, in which 



'1 

 P" = I Fdl is integrated along the vertical areas. This entropy, is 



indeed, also smaller than the "entropie fine", bnt the difference 

 remains constant, and so also >S' constant. 



§ 3. A transition case from that of the planets to that of the gas 

 molecnles is furnished by the case of a gas of one dimejision. By 

 this PoiNCAKÉ understands a gas, all the molecules of which move 



