Resistance of Thin Metallic Films. 489 



it does not depart far from a straight line. If it were a 

 straight line we should have (BO)(AB) = wi£ 2 , and 

 (B0)(SP)=V«/2. 



Hence SP _ PO _ JU_ 



AB ~" OB ~ 2muV 



so that 



V _ (SP)(PO) _ 1 (Jf\ 2 



mu 2 ~ (AB) (OB) ~~ 4\mW ' 



and, in any case, this will be the order of magnitude of 

 2rj/mu 2 . 



Problem 2. Deduction, of the expression for i given 

 on page 478. 



We shall at first limit ourselves to the case where the gaps 

 arej perpendicular to the x axis. Let PM (fig. 7) represent 



Fiff. 7. 



T OT = T 



oe= R 



1> If/is ttc analt hdwtcri 0S<l«4 OE . 

 E dy. . . - OE - OD 



0- - - » OS > OT. 



d8- - • - OT • OH. 



be 



Zindwn. of fora. 

 due Ic fuld . 



the position of one of the gaps, and lot the electric force 

 in such a direction as to urge the electrons from left to right. 

 If (j> is measured about OS in a plane perpendicular to the 

 paper, and if Sn is the number of electrons per c.c. which in 

 the absence of the field are in the velocity range c to c + dc\ 

 the number in this range starting out from any element 8co at 

 per second, and contained within the solid angle sin 6 d6 d<p, 



is , 



con 



47rX 



sin 6 dd d(f> 8co, 



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

 drawn from 0, and \ is the mean free path. 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 represented by TM, but when the field is on they 

 will be bent round, and will travel along paths contained 

 within the dotted lines OD and OE, and those which get far 



