434 



[1} = frequency of the rotationiil movement, h and /• the constants 

 in Planck's radiation-formula). The connection between U and T, 



assuming v independent of the tempera- 

 ture, is then approximately as indicated 

 by curve 2 in the figure. The straight 

 line 1 gives the relation according to the 

 original assumption: U^kT. 



The form (1) gives for T—0 a value 



1 

 J^ of U differing from 0, viz. = — liv. If 



the zero-point energy is left out, the term — hv in (1) disappears 



Li 



and the dependence of U on T is represented by curve 3. 



If we may assume that the proportionality of the susceptibility with 



— holds [ks 2) and, therefore, that — is proportional to U^),— will 

 U ^^ ' X X 



show the same law of dependence on temperature as U, and it will 

 be possible by measurements of the susceptibility of paramagnetic 

 substances at different temperatures to obtain an insight into the 

 changes of the rotational energy of the molecules for these substances. 



§ 4. Starting from this assumption it can be concluded at once 

 from the measurements of the susceptibility, that a curve as given 



by 3 is unable to represent the changes in -- or U. In fact all the 



A 



observations at low tem|»e)'atures which give deviations from Curie's 

 law always show that the product y^T has smaller values at lower 

 temperatures than at higher, whereas according to curve 3 the pro- 

 duct X T would continually increase towards lower temperature. The 

 assumption of a zero-point energy (curve 2 and also 4, see lower 

 down) on the other hand leads to deviations from Curie's law in 

 the same sense as found experimentally. According to a remark in 

 the paper by Einstein and Stern. quoted above Weiss had arrived 

 at a similar view and had inferred the existence of a zero-point 

 energy from Curie's measurements of the susceptibility of gaseous oxygen. 

 According to curves 2 and 4 Vx '^i^^^' X ought to approach a con- 

 stant finite value at low temperatures; this is actually the case for 



1) In this case also U is the rotational energy for two degrees of freedom and 

 is, therpfore, given by the expression (f), because the dependence of the suscepti- 

 biiily on the temperature is determined solely by the rotation about axes at right 

 angles to the magnetic axis of the molecule; for the sake of simplicity the moment 

 of inertia — and therefore v — is taken equal for those axes. 



