546' Mr, W. Sutherland on a 



Now at absolute zero our collection of molecules is supposed 

 to be practically incompressible, so that Q=3N, and o-=%; 

 hence for N we have the two values, the limit of 



1 JD_ /SDie e \ 



*<?(e-E)\8g D e-E /' 

 and the limit of 



V(e-E)V SfB e-E r )' 



These two forms and the value of BD 2 ; above, which at abso- 

 lute zero is given by 2eSD 2 '/D8£' = l — e/(e— E), suggest that 

 both eSDyS^D and eBDi/B^'J) are nearly equal to ej(e— E). 

 If in the case of Young's modulus the condition for constant 

 temperature were that the mean of the effective kinetic 

 energies in all directions is constant or 



8(D/ + D 2 ' + D 3 ')=0, 



then, from the values of 5D 2 / and &D S ' we get 



eSD/ / 2<re 



% 



D = U-^E +2 - 6 4 



which at absolute zero would make q vanish, and therefore 

 cannot be quite correct, but proves at all events that at ab- 

 solute zero e8D i /~DSlj' is nearly equal to ej{e— E). The two 

 expressions for N show that at absolute zero we may put 



eSD/ _ 'e 

 DSf'"" e-E + > 



where A is a constant the same for all bodies, and 



DSf ~6-E +J ^ 



where B is the same for all bodies, and , - 

 B + l=f(A + l), 



A and B are both numbers not large compared to 1. Then 

 N is the limiting value of 



i P(B + l) 



3 e 2 (e-E) ' 



which, with D=zJcm0 and e— E = 750E O , gives 



N Jcm(B + l) m 



2Um/p > U ° j 



