60 Trans. Acad. Sci. of St, Louis. 



to a sphere of radius r, and it is then a perfect gas in equilib- 

 rium, we must have the same mass 



.^„ = ^i^.^, (20) 



or T/, = Tr, 



Tr 



or r=_^«. (21) 



Equation (21) leads to the conclusion that no contraction 

 can take place without a rise in the temperature. These 

 directly opposite conclusions to which we are led by equations 

 (19) and (21) leave us but one way of escape from contra- 

 diction : — 



Since no automatic contraction can take place without a fall 

 in the temperature, and since no contraction from any cause 

 can take place without a rise in the temperature, it follows 

 that no automatic contraction can take place at all ; and finally 

 this last conclusion would appear to lead to one more, viz. ; 

 that a mass of isolated gas in equilibrium can undergo no 

 change of temperature. 



The writer does not hesitate to admit that his investigations 

 have led him into unexpected fields and that the conclusions 

 he has reached are not entirely free from suspicion ; but he 

 submits them to the examination of his fellow investigators. 



In this paper he makes no claim that the formulae given 

 apply to imperfect gases, or vapors. He has discussed an 

 ideal problem, and does not wish his results to be interpreted 

 except in close connection with his assumptions. 



IsmeA, April 28, 1899. 



