46 Dr. L. Silberstein on the Quantum 



Summary. 



(1) On the assumption that van der Waals' a varies with 

 temperature, a relation is derived between a T , surface energy, 

 and molecular v<flume. 



a T d . 



This equation is valid only at low temperatures. 



By assuming that a T diminishes linearly with temperature 

 to the critical value a c , latent heats are calculated by the use 

 of Bakker's equation for several liquids. a 



(2) Recognition of the fact that the ratio — at the 



boiling-point is the same for many liquids results in the 

 derivation of Trouton's Constant. 



(3) Walden's empirical relationships between surface 

 energy and latent heats and the Ramsay-Eotvos law are 

 deduced. 



V. Contribution to the Quantum Theory of Spectrin n Emission : 

 Spectra of Atomic Systems containing a Complex Nucleus*. 

 By L. Silberstein, Ph.D., Lecttirer in Mathem. Physics 

 at the University of Rome f. 



1. TTTHEREAS in all investigations hitherto published, 

 T? or at least in all those which have come to my 

 knowledge, the atomic nucleus (positive charge) is treated 

 as a homogeneous sphere or, equivalently, as an ordinary 

 point-charge, the purpose of the present paper will be 

 to investigate, on the lines of the quantum theory, the 

 spectrum corresponding 1o an atomic system with any 

 differently shaped nucleus which will shortly be called 

 a complex nucleus. Such would, for instance, be a nucleus 

 consisting of two point-charges, acting as two fixed centres, 

 — or any other axially symmetrical distribution of positive 

 charge. The most general " complex " or aspherical nucleus 

 would be a charge distribution having no axis and no plane 

 of symmetry. 



If —e be the charge of an electron proper, it is generally 

 assumed hy the followers of Rutherford's and Bohr's 

 theories that the nucleus of a hydrogen atom has the 

 (net) charge e, that of a helium atom the charge 2e, and 



* A summary of tlie results of the present investigation and some 

 illustrating examples were given by the author at the Bournemouth 

 meeting of the British Association, September 1910, Section A. 



t Communicated by the Author. 



