220 SCIENCE PROGRESS. 



of a very rare medium the whole mean kinetic energy of a 

 molecule, and therefore in that case the measure of tempera- 

 ture. In the case of a vertical column of gas I understand 

 Professor Tait to assert that the constancy of temperature 

 throughout (when the column is in equilibrium) is an axiom. 

 Anyhow it is certain that in case of a rare gas the mean 

 kinetic energy of a molecule is constant throughout the 

 column, and if kinetic energy and temperature are the same 

 thing no question arises. But when the gas becomes 

 denser can it be accepted as an axiom that the tempera- 

 ture is constant ? 



Assuming it to be so, then if E is also constant through- 

 out, we have sufficient grounds for taking E as the measure 

 of temperature, that is, the mean kinetic energy during free 

 path, instead of the whole kinetic energy. But the propo- 

 sition that E is constant seems to me to require more proof 

 than is given to it in the above extract. Then it may be 

 asked what becomes of the temperature when the gas is so 

 compressed that there remains no free path, which must 

 surely be a possible condition above the critical tempera- 

 ture. Perhaps Tait would say that the substance must 

 now be regarded as liquid. He goes on to say that 

 for a liquid the temperature is not E but E + C, C being a 

 quantity which is zero at the critical point, and increases 

 with diminishing temperature. 



Finally he says (part iv., p. 268) : " What has been said 



above leads us in the succeeding developments to write (so 



long as we are dealing with vapour or gas) E = R^ where 



R is now the increase of pressure with temperature under 



v ,. . r™ . ^ dp dp E 



certain ordinary conditions. That is E = t-jz or ~,- = ^ , ^ 

 J at at E + C 



We must now dismiss this subject in the hope that Tait 



will throw some more light on it in his forthcoming papers. 



■$$. On a dense medium of elastic spheres. 



Tait's molecules are elastic spheres, although their 

 motion is much affected by the assumed attractive force 

 between them. It does not appear that any physicist 

 has yet worked out the problem of the motion of a system 

 of elastic spheres as such, when their aggregate volume 

 comes to bear an appreciable proportion to the space in 



