634 Dr. J. E. Mills on 



molecules from each other is simply n times as great, or 

 probably with more exactness n/2 times as great, and we 

 have 



«E=^(VJ-VB)=-fev*-VB). . (i) 



v m \m 



O _ O 



If fi= v'mfi' (or 2 V^aOj this equation reduces very 

 simply to 



Mx=M^( V3- VD), .... (5) 



which is the law that we have above shown to be experi- 

 mentally true. 



III. Statement of the Fundamental Equation in a 

 Simpler Form. 



While it seems to the author that all of the above 

 assumptions are conditions that are probably fulfilled if the 

 equation 



MX=M/*'( l/d- t/D) 



is true, and I have shown that it is true, I do not mean at 

 all to say that the equation as stated really represents all of 

 those conditions. The equation re^ts upon those conditions 

 and was derived logically from them, but the meaning of the 

 equation itself is more restricted. Taking into consideration 

 the theory by which the equation was derived, it is certainly 

 probable that the equation will represent under all circum- 

 stances, the temperature remaining constant during the 

 expansion, the work done against the force of molecular 

 attraction in moving molecules further apart. Now, the 

 further the molecules are moved apart the less becomes 

 the value of D, and D will finally become zerc when the 

 molecules have been moved an infinite distance apart. 

 Making, therefore, D equal to zero, and remembering that 

 the distance apart of the molecules, s, is proportional to 



a — -, where n is the number of molecules and is therefore 

 \'tid 



a constant, we can write 



X^ s = constant, (6) 



as the very simple form for the law under discussion. This 

 statement means simply this : — 



In any normal substance the internal heat given out as the 

 molecules approach each other, multiplied by the distance apart 

 of the molecules, is equal to a constant. 



