106 Dr. J. E. Mills on the Relation of 



proportional to its mean distance from their common centime 

 of mass. 



If we designate the kinetic energy of motion in its orbit at 

 this mean distance from the centre of mass retained by 

 particle m x as Eio and the energy lost as Eil, ?»nd similarly 

 for particle m 2 , we shall have, when E« denotes the total 

 attractive potential energy obtained from the sether : 



E a = E 10 + E 1L + E 20 + E 3L = — '— 3 . . . (17) 



E 1L = E 10 = l/2 



E2L — E20 = 1/2 



s 

 km 1 m 2 2 1 



(18) 



m l -\-m 2 s I 

 kni] 2 m 2t 1 m f ' 



m 1 -\-m 2 s -> 



These equations govern the energy relations of two masses in 

 stable equilibrium under all circumstances. 



18. If we supply a given amount of energy, say E*, to a 

 system with a circular orbit, or in fact with any orbit, then the 

 exact orbit followed will depend upon the exact way in ivhich 

 the energy is added. Since the amount of "lost" energy is 

 decreased by this addition of energy to the system, and since 

 Eo = El, the amount of orbital energy must also be decreased. 

 That is to say, the major semi-axis, or the radius, must be 

 increased, and the potential energy must be increased by an 

 amount equal to 2E/ C , one-half of this amount being added to 

 the system and one-half coming from th* decrease of the mean 

 orbital velocity in the system. The mean orbital kinetic energy 

 of the system can only be increased by abstraction of energy 

 — not by addition of energy. This remarkable fact may be 

 a well-known mechanical consequence of the motion of two 

 bodies under the gravitational law of attraction, but its 

 significance does not seem to have been appreciated by those 

 trying to express the relationship between temperature and 

 molecular attraction. For the above fact leads at once to 

 the question : How can the temperature of a system of two 

 bodies be increased by the addition of energy, since addition of 

 energy seems to necessitate a loss of mean orbital velocity ? 

 We might as well go to the bottom of the trouble at once. We 

 have no generally accepted definition of temperature, or 

 better, perhaps, no generally accepted idea of temperature 

 that will apply to a system under the influence of attractive 

 forces. If there are no attractive forces then what we call 

 temperature is proportional to, and is measured by, the 

 kinetic energy of the moving particles (molecules). But if 

 attractive forces exist, this definition of temperature no longer 



