( 241 ) 



VII. — On the Relation betiveen the Variation of Resistance in Bismuth in a Steady 

 Magnetic Field and the Rotatory or Transverse Effect. By J. C. Beattie. (With 

 a Plate.) 



(Read 17th June 1895.) 



Kundt # has shown that the transverse effect in iron, cobalt, and nickel is proportional 

 to the magnetisation. Such an effect, where the magnetisation appears in the first power, 

 we shall call a Hall effect. In applying the same method to bismuth, he found that no 

 transverse effect was given by the thin plates of the electrolitically deposited metal used 

 by him. That this absence of transverse effect is not characteristic of all bismuth so 

 prepared has been shown experimentally. The question is, What relation, if any, exists 

 between it and the magnetisation ? To settle this it is necessary to compare the 

 transverse effect in any given plate with some other effect in the same plate whose 

 relation to the magnetisation is known. Such an effect is the variation of resistance. 

 GoLDHAMMERt has shown that this latter is proportional to the square of the magnetisa- 

 tion. 



The current sent through the plate is called the primary. A thick copper wire was 

 placed in the primary circuit, so that two fixed points in it could be inserted in the 

 galvanometer circuit ; the reading thus obtained was used as a measure of the strength 

 of the current. This brings in no error, since the measurements are throughout relative. 



By the rotatory or transverse effect is meant the ratio of half the galvanometer 

 deflection (with proper sign), which is obtained when two equipotential or approximately 

 equipotential points on opposite sides of the plate are inserted in the galvanometer 

 circuit, to the strength of the primary current. The numerical value of this effect is 

 denoted by E. 



To measure the resistance of the plate, two fixed points or lines in it were inserted in 

 the galvanometer circuit ; the reading thus obtained divided by the strength of the 

 primary current was taken to be proportional to the actual resistance of the plate. By 

 this means it is rendered independent of the current strength. 



The resistance n + A n of a plate in a steady magnetic field, minus its resistance (n), 

 when no field was there, — that is, An can be taken as proportional to the square of the 

 magnetisation. 



If the transverse effect is a pure Hall, we shall have 



c 1N /A»=±E ... (1) 



Evidently this cannot hold for plates where E attains a maximum value : in such we 

 must use a formula 



c 1 (Ara)* + c 2 (A»)2=±E . (2) 



In the following experiments a d'Arsonval galvanometer was used. The electro- 

 magnet was ring-formed, and was wound with a wire capable of carrying a thirty ampere 



* Wiedemann's Annalen Neue Folge, Bd. 49, 1893. t Ibid., Bd. 36, 1889. 



VOL. XXXVIII. PART I. (NO. 7). 2 K 



