157 





da 



. (23) 



Substituting for— — its value according- to (22), 'it is immediately 



da '' 



found that : 



oh = 0, 

 hence Ik is an adiabatic invariant. 



SUMMARY. 



If a mechanical system possesses the following properties : 



1. every momentum pk can be expressed as a function of the 

 corresponding coordinate qk (supposition B) ; 



2. the motion of every coordinate qic is Silibi'ation {supposition A'); 



3. no relations of commensurability exist between the mean motions 

 uiJ^ of the "a-ngular variables" (supposition C) ; 



then the "phase integrals" 



Vk 

 Ik =z2 j dqk . pk 

 §k 

 are invariant against an adiabatic disturbance of the system. 



Remark. Those cases of degeneration in which supposition C is 

 not satisfied will be treated separately in a subsequent communication. 



