Gold for Weak Magnetic Fields. 79 



is given by 



/9Hi 



(°+E> 



where C is the current in the secondary system when the 

 magnetic field is zero : due to the inexact setting of H a and 

 H 2 . /3 is the Hall coefficient *. H is the magnetic field- 

 strength in C.G.S. nnits. i is the current flowing through 

 the primary, t is the thickness of the foil. Rn is the resist- 

 ance of the entire secondary circuit. g 2 is the constant of 

 the coil of the galvanometer included in the secondary 

 circuit ; and m is the equivalent magnetic moment of the 

 suspended system. 



This for the case of balance is equal and opposite to the 

 effect of the shunt-current, which is given by 



^— ffiin (approximately), 



where S is the resistance of the shunt included in the pri- 

 mary current; R r is the resistance of the box R when adjusted 

 to balance ; and c/i is the constant of those coils of the gal- 

 vanometer that are included in the shunt-circuit. 

 We have now 



When we reverse the magnetic field and readjust the re- 

 sistance in the shunt-circuit (to say R 2 ) for a second balance, 

 we have similarly 



(°- as )*=£*■ 



whence 



RnS/1 _ 1 \t £, 

 P~ 2 Ui R 2 /H'<7 2 ' 



the value of i being eliminated. A series of tests showed 

 that i might be as great as J ampere without bringing in 

 error from thermal effects ; this, of course, is largely in con- 

 sequence of the method of leaving the primary current closed 

 for short periods only. 



The quantities employed were: — 2=033 ampere. R : and 

 R 2 were of the order 1000 to 1500 ohms. R n = 0'801 ohm. 



S = 0-0178 ohm. £ =0*96. * = 2'05 x 10~ 4 cms. 



0-2 



* I. e. the transverse potential gradient for unit magnetic field and 

 unit current density in a plate of unit thickness. This reduces directly 

 to the "Rotary coefficient" definition given in Wiedemann's Electrhittit, 

 iii. p. 202, et seqq. (edition of 1898). 



