454 The Expression for Electrical Conductivity of Metals. 



Problem (2). 



To show that x—v\ H -~ + fS -^ 9 tan 2 ilr X cos yjr. 



(. mv* 2mv 2 T J T 



From (4) we have 



„ X<? f ., Xe.r ") - 



a? = y cos 6/ H 2 = -{ 1 H s ^ > v cos 0. 



m ( ??itrcos"t/ J 



Replacing cos 6 by its value in terms of cos yjr as found 

 from Problem (1), we have 



#== ^ H s ^ ~ -: — „tair > v cos ilr 



( mv" cos~ 2mtr ) 7 



{., ~Ke% . Xex , „ , ") , 



1 + — if + o — 2 tan ^r cos ^*- 

 mir 2mv 2 T ) T 



The University of Sheffield. 

 July 30th, 1913. 



Note added Dec. 26th, 1913. 



Since the above paper was written, certain further matters 

 in relation to the history of expressions (1) and (2) have 

 come to my notice. 



Before Drude published the expression (1), and as early as 

 1898, E. Eiecke (Wied. Ann. Bd. lxvi. pp. 353 et seq., 1898), 

 in a paper in which both positive and negative carriers were 

 included, obtained an expression which when interpreted in 

 terms of the modern electron theory would amount to 



ne "\jV 

 g— * . In the same year, and still before the publi- 

 cation of Drude's paper, Riecke found it necessary to 

 introduce a correction into his calculation which actually 



results in the expression <r= ? ^g- deduced above (see Wied. 

 Ann. Bd. lxvi. p. 1199, 1898). In spite of this fact, Drude's 

 result g—-~t-^ is still quoted in all the well known books 



1«C7 A 



dealing with the subject ; and this fact is the more re- 

 markable since the difference between the two formube is 

 not the outcome of any difference in the fundamental 

 assumptions in the two methods, but is simply due to an 

 error in Drude's work, which, as is shown in the present 

 paper, is of a purely mathematical nature. 



