November 20, 1903.] 



SCIENCE. 



647 



therefore, a sweeping process can not be 

 arrested nor reversed by any means. 



Note l.—A fluid not in thermal equi- 

 librium has no definite pressure, tempera- 

 ture or volume. The volume of a turbulent 

 gas pertains only to the containing vessel. 

 Any one, for example, who i-eads the re- 

 ports of the measurement of the Holton and 

 St. Albans base lines by the U. S. Coast 

 and Geodetic Survey will appi-eeiate the 

 necessity of the projection of a region of 

 thermal equilibrium into a space which is 

 to be measured, and any one of course 

 knows that the reality of the results of 

 these measurements depends upon the fact 

 that the earth's crust is approximately in 

 thermal equilibrium. 



One error in Mr. Swinburne's discussion 

 of thermodynamics is in the extension of 

 the notions of volume, pressure, tempei-a- 

 ture and entropy to substances not in 

 thei'mal equilibriimi. Points in Watt's 

 diagram can represent only states of equi- 

 librium, and lines in Watt's diagram can 

 represent onlj'' reversible processes. I shall 

 indicate in a subsequent paper the method 

 which must be used when one wishes to ex- 

 tend engine calculations, for example, so 

 as to include sweeping processes. 



Note 2. — Writers on thermodynamics 

 who are obliged to deal with irreversible 

 processes or sweeping processes, that is to 

 say, steam engineers, frequently introduce 

 the notion of the integration of entropy 

 and temperature. Thus Mr. Swinburne 

 enlarges upon this procedure. lie would 

 assign a definite entropy and a definite 

 temperature to each volume element of 

 turbulent steam, and by integration arrive 

 at the notion of total entropy and mean 

 temperature. Now in the first place, when 

 this method appears to give results a 

 legitimate mode of calculating sweeps is 

 really u.sed, and the legitimate ideas in- 

 volved are illogically expressed in terms 

 of temperature and entropy. In the sec- 



ond place, temperature and entropy have 

 no meaning as applied to the elements of 

 volume, even of a substance in thermal 

 cqnilihrium, not to mention the question of 

 their application to the volume elements of 

 a turbulent substance. This is a limita- 

 tion of the ideas of thermodynamics which 

 is indicated by the ideas of statistical me- 

 chanics. "Wliether this limitation can be 

 justified independently of statistical me- 

 chanics I am not prepared to say with 

 certainty. Thermodynamics has to do 

 only with finite portions of matter, and 

 infinitesimals have no meaning except as 

 increments of finite quantities. 



4. SIMPLE SWEEPS. 



Tlie settling of a closed system to 

 thermal equilibrium is called a simple 

 sweep. 



Example.— The equilibrium of a mixture 

 of oxygen and hydrogen in a closed vessel 

 may be disturbed by a minute spark, and 

 the explosion and subsequent settling of the 

 aqueous vapor to a quiescent state without 

 loss of heat constitute a simple sweep. The 

 equilibrium of a gas confined under high 

 pressure in one half of a two-chambered 

 vessel may be disturbed by opening a cock 

 which connects the two chambers, and the 

 rush of gas into the empty chamber con- 

 stitutes a simple sweep. 



5. TRAILIKG SWEEPS. 



When external influences chaijge con- 

 tinuously, a substance in its tendency to 

 settle to equilibrium never catches up, as 

 it were, with the changing conditions, but 

 trails along behind them, and we have what 

 is called a trailing sweep. 



Examples. — The rapid expansion or com- 

 pression of a gas in a cylinder is a trailing 

 sweep. So long as the piston moves at a 

 perceptible speed, the gas, in its tendency 

 to settle to equilibrium, never catches up 

 with the varying conditions. This is evi- 



