302 Mr. J. Frenkel on the Surface Electric 



assumed that p = ^=0ana ***.= *&*. The exact 

 oy o? ox o% 



solution of the question about the error introduced by such 

 an assumption presents great analytical difficulties, but it i& 

 clear without any calculations that this error is the smaller 

 the more tightly the atoms are packed together,— or, in other 

 words, the greater is the overlapping o£ the separate atomic 

 fields. If the interatomic distances were large compared 

 with the atomic dimensions, each atom would form a closed 

 system, not interacting with the others and exerting no 

 influence on the free electrons (if any). Thus there can be 

 no question about the intrinsic potential of an ideal gas *.. 

 In solid and liquid bodies, where the atoms (or molecules) 

 are very tightly packed together, the interatomic distances 

 being of the same order of magnitude as the atomic diameters, 

 the interatomic forces are very intense and the overlapping 



of the atomic fields very complete. This reduces ^ y and 



oT ^ 



-— -^ inside the double-layer to a negligible value (they are 



° z PT . . 



equal to zero, as well as -^—^ , inside the double-layer where 



p x =0), as clearly seen from the examination of the extreme 

 case when e tends to zero and n to infinity (the product ne 

 remaining constant). Another important effect of the 

 condensation of the atoms is the increase of regularity in 

 the surface electric field, the diminution of the deflexions 

 in the value of the intensity E, acting on the free electrons 

 in different points of each plane, from the corresponding 

 mean value E. 



Returning to our hydrogen-like atoms, we see that when 



the mean distance between them 2R— —~ is comparable 



with their diameter 2r, the electric double-layer at the 

 surface of the solid or liquid body is effective in producing 

 the field E x (and consequently the intrinsic potential Y r ) 



determined by the equation --—- t=4:7rp x , and also that this 



field is sufficiently regular to absorb from each escaping 

 electron an approximately constant amount of energy equal 

 to eY r . 



* But whenever there is some interaction between the gas-niolecules r 

 there must also exist an intrinsic potential; formula (G) cannot, how- 

 ever, hold for a gas with any degree of accuracy. 



