304 PROCEEDINGS OF THE AMERICAN ACADEMY. 



or at most 0.0071 X 2500 = 18 kilojoules. The actual evolution of 

 heat in excess of the free energy is, however, 170 kilojoules, a figure far 

 greater than the calculated value. Other cells yield the same result; in 

 no case in which osmotic phenomena cause no disturbance is the greatest 

 possible amount of heat displaced enough to correspond to the deficiency 

 of free energy. Two alternatives are now open, — either the free 

 energy does not fully represent the " attracting energy," or else the 

 heat evolved is too large to correspond to the "attracting energy," 

 even after correction for the change of heat capacity. 



Before going further it is well to define precisely one of the terms 

 employed above. The phrase "attracting energy" is used to represent 

 the sum of the work done by all those tendencies which exert a positive 

 attraction. These tendencies may be three in number, — purely chemi- 

 cal attraction or ^' ckemism" (such attraction as binds chlorine to itself 

 in chlorine gas), gravitation (which seems to be important chiefly in the 

 heavy metals), and electrical attraction ; but if any other attractive ten- 

 dencies exist, they too are included. 



In the preliminary study of the phenomena of changing atomic volume, 

 use was made of the possible analogy between an atom and an elastic 

 sphere of gas, in which every portion of the interior gas was supposed 

 to exert an attraction upon every portion of another similar sphere. 

 Further use of this analogy makes it jjossible to explain the relation 

 between free and total energy in a plausible manner. The illustration 

 must, however, be somewhat modified as it becomes more detailed and 

 concrete ; for while the temperature of a sphere of gas is supposed to be 

 traceable to the motion of molecules within it, we must imagine the 

 temperature of an atom to be due to the elastic bodily oscillation of 

 the greater part of its substance. 



Two such elastic balls colliding in space would compress one another. 

 Unless some adhesive tendency caused them to cling together, they would 

 immediately fly apart again with their original velocities, tending to absorb 

 as much heat in their consequent expansion as they gave out during com- 

 pression. Except for tlie change of diiection, their condition would be 

 the same as if they had never met, and no violation of either the first or 

 the second law of thermodynamics would be involved. 



If, on the other hand, some attracting or adhesive tendency caused 

 them to cling together, permanently and irreversibly, they would con- 

 tinue in internal oscillation, the additional energy* of which would be a 



* That is to say, the energy over and above their original energy of progres- 

 sion before they affected one another. 



