Electrons concerned in Metallic Conduction. Ill 



Thus even excluding the effect o£ resonance electrons the 

 present form of theory would give a value of 1ST about twice 

 that deduced by Nicholson. It is, however, just the re- 

 sonance electrons which render the result too indefinite to 

 be of any real assistance in the determination of N, unless 

 we have sufficient information to enable us to accurately 

 determine the factor 1—aA or, its equivalent, the reciprocal 

 of {l + a(yLt p 2 — 1)}. An error in the assumed value of this 

 factor will result in a corresponding error in the estimation 

 of N. 



More accurate formulae may be obtained by successive 

 approximation, as, for example, the next approximation to 

 N 2 is 



N 2 = 



97r 3 c z ?n 2 /jLK(T . an fi i 6w7**c(l — «A) 



2eW 



( l-„A)[l + ^^], 



so that even the correction term for the next approximation 

 will depend on the values of a and A. There appears, 

 however, very little necessity at the present stage for using 

 anything more than the first term as representing a suitable 

 approximation to the quantity required. 



The second equation can be used, after Nicholson, to 

 determine the value of fxp 2 when the values of N, /x, and k 

 are known; but here again the calculation is considerably 

 modified by the presence of the resonance electrons, which 

 introduces the factors (1 — a \ ) , which are themselves functions 

 of /jp 2 . Very little weight can, therefore, be attached to the 

 exactness of Nicholson's calculations on this basis. 



The conclusion must therefore be stated at the outset. 

 The theory is too complex for any very definite results to be 

 obtained from it until our knowledge of the behaviour of 

 the metals is equally complex. Until then we must content 

 ourselves with very rough approximations to the numbers 

 required. 



Of course any great precision in the results on the basis 

 of the present theory is necessarily nullified by the fact that 

 the basis adopted is obviously only a first order approxima- 

 tion to the actual state of affairs ; so that even though full 

 information were at hand, the theory would probably not fit 

 the facts very well*. If we are prepared to regard the basis 

 of the present theory as the correct one, there are other and 

 apparently better and more direct means of obtaining an 



* It is known for instance that the assumption that the electrons and 

 atoms are elastic spheres is not in agreement with all the facts and that 

 a more general type of dynamical interaction is necessary. These points 

 are discussed in detail in separate communications. 



