Physics. — ''Adiahatic Invariants oj Mechanical Systems." I. By 

 J. M. Burgers. Supplement N". 41c to the Communications 

 from tiie Physical Laboratory at Leiden. (Communicated by 

 Prof. H. A. LoRENTz). 



(Communicated in the meeting of November 25, 1916). 



Introduction. 



During the past year ^) the theory of quanta has made great 

 progress by the study of a class of mechanical systems which are 

 characterized by the following property : the integral of action -. 



W^ C2T .dt 



{T: kinetic energy) separates into a sum of integrals each of which 

 depends on one of the coordinates only : 



w=:s fdqk\^~F^)') (1) 



k J 



In general each coordinate can only move up and down within 

 a certain interval (which is given by roots of the equation i^^k ^ 0) '). 



From the formula given for W it follows that the momentum 

 corresponding to the coordinate q^ is equal to : 



Pk = ^ ^\{qk)^ 

 hence : 



idqkVFk^ idqic.pk (2) 



For this class of systems Epstein and other investigators use the 

 following equation as the principle for the introduction of the quanta : 



Ik= \dqk ' Pk=^ nk . h (3) 



h = jdqjc ' Pk =^ '>Vc ■ /« 



1) K. SCHWARZSCHILD : Sitz. Ber. Bed. Akad. 1916, p. 548. 



P. Epstein: Ann. d. Physik 50 (1916) p. 490; 51 (1916) p. 168. 



P. Debije: Gött. Nachr. (1916) p. 142; Phys. Z. S. 17 (1916) p. 507, 512. 



A. SoMMERFELD, Ann. d. Physik 51 (1916) p. 1; Phys. Z. S. 17 (1916) p. 491. 



2) The radical sign has been written in accordance with the most common cases ; 

 the function Fk then becomes a rational function. 



3) Comp. note 2 p. 150. 



