1913-14.] The Hall and Transverse Thermomagnetic Effects. 219 
The ratio ^ varies from metal to metal. It is positive for all the 
metals tested except copper. The values are given in the following table : — 
Field strength = 21 ,000. 
Metal. 
at 45° C. 
Jti 
-§at 100° C. 
JLV» 
Nickel 
Iron . . . 
Copper 
Zinc .... 
Aluminium 
+ 3'25 x 10 3 
+ l-39xl0 3 
- 0'68 x 10 3 
+ T07x 10 3 
+ 0-34xl0 3 
1 
+ 6 0 xlO 3 
+ 1T8 x 10 3 
- 0’73 x 10 3 
+ 1*40 x 10 3 
It may he of interest to consider these results in their relation to the 
electron theory. In the development of this theory some difficulty arises 
in explaining the variation of the signs of the transverse effects. Drude * 
in his investigation assumes the existence of positive and negative carriers 
both taking part in the transmission of the heat and electric currents. 
Drude finds the following expressions for the Hall and thermomagnetic 
transverse effects : — 
r t = 
\ x 1 + x 2 ) 
Q = — + °"2^2^/l) 
( T 
® = l2/2)’ 
CCT 
where 
„ „ _d(log »j) 
1 dt ’ 2 W~ ’ 
y 1 = eVj, y 2 = ev 2 , 
cr 1 = e 2 v l n 1 , cr 2 = e 2 v 2 n 2 , a = <r 1 + <x 2 . 
and n 2 are the numbers of positive and negative carriers respectively 
in each unit volume of the metal. 
e = the magnitude of the charge on each carrier. 
and v 2 are the average velocities impressed on the positive and 
negative carriers respectively by unit electric field. 
p and c are constants. 
Now if x 1 and x 2 have the same sign, R and S are both differential effects 
* Ann. d. Phys ., vol. i., 1901. 
+ The expression for R given by Drude has been multiplied by <r in order to make it 
applicable to the coefficient R as defined in this paper. 
