■ oTrV 



258 Dr. J. W. Nicholson on the Number of 



where (a) denotes >?i/N<? 2 , and unity may be neglected in the 

 denominator for good conductors. When this is neglected 

 we obtain 



and finally 



p=5-6 1G- 12 ^f(K + y C 2 -^), . . . (47) 



which is less than the value of p in (44) by a factor ir. For 

 a given value of the dielectric capacity, accordingly, this 

 theory leads to a value of p only about a third of that of the 

 foregoing. We shall return to this formula shortly. 



There is a tendency, exemplified in Wilson's paper, to sup- 

 pose that K may be written equal to unity for a metal, so that 

 the polarization current is entirely aethereal. This cannot 

 be correct. Let us examine the value to be attached to K 

 in order that the formula (44) shall give the same value of p 

 as we found before. 



In the first place, we calculate p on the basis K = l, in 

 order to see how far this assumption fails. The formula 

 used is (44) and the results are exhibited in Table IV. The 

 value thus calculated is called pi and is placed beside p. 



Table IV. 



Metal. 



Nickel .... 

 €obalt .... 



Silver 



Copper .... 



Gold 



Magnesium 



Pv 



P- 

 1-87 



K. 



8-96 



•986 



1-43 



2-45 . 



1006 



2-35 



2-49 



1-81 



•84 



2-63 



16-82 



1-43 



2-52 



7-68 



4-29 



3-14 



-4-41 



Metal. 



Platinum . 



Lead 



Cadmium _. 



Tin 



Zinc 



Aluminium 



Pi- 



2-14 



P- 

 3-10 



7-59 



2-84 



4-48 



626 



5-15 



424 



-3-38 



6-82 



4-91 



-6-39 



4-07 



4-87 



6-27 



4-25 



5-89 



11-18 



The values of K, the dielectric capacity required to give 

 the value of p derived from Table II., are shown in the third 

 columns of the above table. They are calculated from the 

 formula. 



K+« i -i;*=( K *-v*)p/p l9 . ... (48) 



which follows immediately from (45) by the definition of p x . 

 Of these values of K three are negative, but small. The 

 range of the positive values of K is also small, and there is 

 no positive value which is unduly large in comparison with 

 known values for non-metallic elements. Thus, for example, 

 carbon, in the form of diamond, has a refractive index equal 



