the Electrical Conductivity of Metals. 443 



Part I. — Deduction of the expression <r= Q . 



oac/ 



Let OS (fig. 1) represent the axis o£ x, and let the field X 

 act from right to left so that the electrons are urged from 

 left to right. We shall proceed to find the flow per square 

 centimetre through the plane perpendicular to the paper and 

 represented by the line MP. 



Fig. l. 



Direction of force on electrons 

 due lo field 



OS - x. 



1y is tfie au^le between OS and OE 



dy " 0£ " QD 



p 6 - OS - OT 



&8 " OT " OM 



If <£ is measured about OS in the plane perpendicular to 

 the paper, the number An of electrons starting out from an 

 element dco at having suffered collisions therein, and which 

 are contained within the solid angle sin 6 dB dcp is 



Arc = -— — sin 6 dO deb dco. 

 47rX r ' 



where 6 is the angle between OS and the radius vector OT 

 drawn from 0, X is the mean free path, and v is the velocity. 

 When the field is off, those of the above electrons which 

 succeed in getting far enough without collisions will strike 

 the plane on the area indicated by MT, but when the field is 

 on they will be bent round. They will travel along paths 

 contained within the dotted lines 01) and OE, and those which 

 get far enough will strike the plane on the area represented 



by DE. R 2 *in^ 



In the notation of fig. 1 this area amounts to — -- . deb d\lr 

 ° cos y ' 



