November 20, 1903.] 



SCIENCE. 



649 



initial and final states of the substance 

 which undergoes the sweep, inasmuch as, in 

 a simple sweep, no outside substance is 

 affected in any way, no work is done on 

 or by the substance which undergoes the 

 sweep, and no heat is given to or taken 

 from it. 



In a trailing sweep the degeneration may 

 lie partly in the i-elation between the 

 initial and final states of the substance 

 which undegoes the sweep, partly in the 

 direct conversion of work into heat and 

 partly in the direct transfer of heat from 

 regions of high temperature to regions of 

 low temperature. 



In a steady sweep the substance which 

 undergoes the sweep remains entirely un- 

 changed as the sweep proceeds, and the 

 degeneration lies wholly in the direct con- 

 version of work into heat, in the direct 

 transfer of heat from a region of high 

 temperature to a region of low tempera- 

 ture, or both. 



A substance which has undergone a 

 sweeping process may be brought back to 

 its initial state, or regenerated, by a revers- 

 ible process; but when a substance is 

 regenerated by a reversible process, the ex- 

 ternal action necessary to bring about the 

 reversible pi-ocess involves an equal degen- 

 eration of some external substance ; that is, 

 the regeneration of a substance by a revers- 

 ible process always involves the creation 

 of an equal external regeneration. This is, 

 in fact, a statement of the second law of 

 thermodynamics. 



The entire subject of thermodynamics, in 

 so far as it does not have to do with the 

 specific thermal properties of particular 

 substances, is based upon the consideration 

 of the two kinds of thermodynamic degen- 

 eration which are involved in steady 

 sweeps, that is, upon: (a) The thermo- 

 dynamic degeneration which is represented 

 by the direct conversion of work into heat, 

 and the thermodynamic regeneration which 



is represented by the conversion of work 

 into heat by a reversible process; and (b) 

 The thermodynamic degeneration which is 

 represented by the direct transfer of heat 

 from a region of high temperature to a 

 region of low temperature, and the thermo- 

 djTiamic regeneration which is represented 

 bj' the transfer of heat from a low tem- 

 perature region to a high temperature re- 

 gion by a reversible process. 



The following two propositions concern- 

 ing the two kinds of thermodynamic degen- 

 eration (o) and (6) follow at once from a 

 consideration of steady sweeps. 



Proposition (A).— The thermodynamic 

 degeneration represented by the direct con- 

 version of work into heat at a given tem- 

 perature is proportional to the quantity of 

 work so converted. 



Proo/.— Consider a steady flow of electric 

 current in a wire. This process being 

 steady, the amount of degeneration occur- 

 ring in a given interval of time must be 

 proportional to the time. The amount of 

 work converted into heat is also propor- 

 tional to the time. Therefore the amount 

 of degeneration is proportional to the 

 amount of work converted into heat. Of 

 course the temperature must be invariable, 

 or the process can not be thought of as 

 remaining identically the same from in- 

 stant to instant. The dependence of this 

 kind of degeneration upon temperature will 

 be considered later. 



Corollary.— The thermodynamic regener- 

 ation which is represented by the conver- 

 sion of heat at a given temperature into 

 work by a reversible process is proportional 

 to the heat so converted. 



Proposition (B).— The thermodjTiamic 

 degeneration represented by the direct 

 transfer of heat from a given high tem- 

 perature 1\ to a given low temperature T, 

 is proportional to the quantity of heat 

 transferred. 



Proo/.— Consider a steady flow of heat 



