By Professor Fell. 19 



except perhaps under great pressure. If heated it would pass at 

 once from the solid to the vapourous state. It would shew no 

 bright lines in the spectrum at any temperature. In a state of 

 vapour no heat could be consumed in internal vibrations, so that 

 Maxwell's factor /3 would in this case be unity. I am not aware 

 that there is any substance possessing these properties, but at all 

 events we may presume from the complicated constitutions which 

 molecules appear to possess, that p is generally considerable and 

 4/ therefore small. The above equations give us 



p -^ jLt \|/ cot 4/ 



S jU, represents the range of jw, in the prevalent heat, and for 



J. 

 heat of considerable intensity, — is small, and -^ being small 



-r- does not differ much from — . If for any substance 



^ . . . 



\|/ were small enough, ^p might exceed unity, even within 



the range of heat of considerable intensity, in which case 

 there would be different values of ^ for different wave lengths. 

 The molecular arrangements of such a substance would dis- 

 play great instability. A molecule formed under one wave 

 length would be decomposed, and otherwise arranged by heat of 

 a different kind. As we have every reason to believe that this 

 kind of instability does not exist in the case of simple substances, 

 we may infer that \|/ is not very small : the general conclusion 

 being that for ordinary substances \I/ is small but not very small. 



The particular value of \J/ which for any substance is equal to 



— IS not the one which produces the greatest effect in arranging 



the atoms into groups. The greatest effect is caused by the value 

 of vf/ which makes (2 n + 1) -^ equal to an odd multiple of 



- ; and when n is large, such a value must exist. In this case 



the expression for the relative displacement becomes infinite. 

 This does not indicate that there would necessarily be a 

 rupture of the system, but merely that the displacement cannot 

 be expressed exactly in the manner supposed. The best way of 

 stating the case is that a vibration of that exact wave length 

 cannot be propagated through the system at all. By the effect 

 of the factor c, by which in the second approximation, it becomes 

 necessary to multiply jx, the time of vibration and the wave 

 length are increased, so that if \J/ be continuous, this particular 



