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



The range of values of p is nearly the same as before, but 

 no value exceeds 6. The general agreement of the two 

 values for any metal admits, at this stage, of the statement 

 that the number of free electrons in a metal can be fairly 

 accurately known under the conditions which have been 

 assumed, namely, that the temperature is about 18° C, and 

 that a periodic force, whose frequency is that of sodium 

 light, acts on the metal. 



We now proceed to another aspect of the subject, based 

 on the equation (32), and for this purpose we calculate certain 

 optical constants of the metals from the experimental measure- 

 ments of Drude. 



The experiments of Drude * on the optical constants of the 

 metals were very exhaustive, and the results obtained were, 

 for series of determinations with the same metal, remarkably 

 in accord. A critical study of Drude's results has convinced 

 the writer that the error in certain sets of entries in Drude's 

 tables can rarely be greater than about one per cent., and 

 that in the results of these experiments we have a means of 

 obtaining much more definite information, concerning the 

 atoms of metals, than has been attempted hitherto. The only 

 possible error is apparently a systematic one throughout the 

 results, and this does not seem likely to occur. 



Drude uses two constants n and ^, where n is the index of 

 refraction of the metal and is identical with v. The relation 

 between k, the coefficient of optical length, and Drude's % is 

 embodied in 



Mrt*a=n(l+ix), (42) 



so that v= n, and « = "%• Thus v/c=zri 2 x, and v 2 — K 2 ='n 2 (l— ^ 2 ). 

 The value of vie has appeared already in the first table, but 

 it is convenient to repeat it below. In the case of sodium 

 light, the values of these constants are exhibited below, the 

 first columns being taken from Drude's paper. The values 

 for cobalt are taken from a later paper f, as Drude made it 

 the subject of a special examination. 



The formula (32) becomes, to a higher order, 



_ „ 2 irmCW/- 3 5 \ 



aJN<r \ a 2a? ) 



The first approximation to a -1 or 7r 3 />iV 2 C 2 /lN 2 /W is 

 vyc/ACoo by (30), and the second is 



M> V 



XO , 



* Wied. Ann. xxxix. p. 537. 

 f Wied. Ann. xlii. p. 189. 



