74 ELECTRICAL MEASUREMENTS 



current is taken to it by two mercury cups, the leads being as 

 far as possible concentric, to avoid disturbing effects. 



A torsion head is used in reading, so any effect due to the angu- 

 lar displacement of the axes of the coils from the perpendicular 

 position is avoided. The suspension wire is the most troublesome 

 feature of the instrument, for its torsional properties must be so 

 definite that they can be determined to a high degree of accuracy. 

 A well-aged phosphor-bronze wire is the most satisfactory. 



The force, in any given direction, which acts on a circuit carry- 

 ing a current I M , when it is placed in a magnetic field, is equal to 

 the product of the current and the space rate of change of flux 

 through the circuit when the circuit is displaced in the given 

 direction. If the flux is due to a second circuit, its value will 

 be I F m, where I F is the current in the second circuit and m is 

 the coefficient of mutual induction of the two circuits. Conse- 

 quently, the force in the direction x is 



F -!,!*% (61) 



Similarly, the turning moment acting between the coils of an 

 electro-dynamometer and tending to change the angle 6 between 

 their axes is given by 



M = I F l u ~ (62) 



To use these relations it is necessary to have expressions for m 

 in terms of the numbers of turns in the coils, their dimensions, 

 and their distance apart; in general, m must be expressed in the 

 form of a series, examples of which may be found in Maxwell's 

 "Treatise on Electricity and Magnetism," and in Gray's "Abso- 

 lute Electrical Measurements." 



In accordance with the above, if a plane circuit of area A, 

 which is traversed by a current I M , is suspended in a uniform mag- 

 netic field of strength, H f , it will experience a turning moment 

 - M = AI M H f sin where 6 is the angle between the perpen- 

 dicular to the coil and the direction of the field H r . This simple 

 relation cannot be used in connection with the electro-dynamom- 

 eter except as a first approximation, for the field due to the fixed 

 coil is not uniform throughout the space occupied by the movable 

 coil. 



