PROPERTIES OF A COIL. 71 



CHAPTER IV. 

 PROPERTIES OF CIRCULAR CURRENTS. 



722. Before entering on the investigation of electromagnetic 

 instruments, it will be desirable to examine generally the properties 

 of conducting circuits, and especially of circular coils. 



We will consider principally cylindrical bobbins, or coils, which 

 are formed of a metal wire enveloped in an insulating substance, and 

 coiled in a channel of rectangular section. These coils are most 

 easy to construct ; they lend themselves best to measurements and to 

 calculation, and are therefore those which are most convenient for use 

 in apparatus for absolute measures. 



A cylindrical coil formed of equidistant windings which has an 

 even number of layers, or which has a return wire if the number is 

 odd, is equivalent to a system of equidistant circular currents perpen- 

 dicular to the axis. The action of such a coil traversed by a current, 

 is equal to the magnetic induction of a uniformly magnetised cylinder 

 of the same form. We shall assume that the conditions of regularity 

 of winding which the similarity presupposes are exactly fulfilled, and 

 that when the coil is constructed of several successive layers,. the 

 radii of these layers vary in arithmetical progression. 



The winding of a wire is homogeneous when the spirals of each 

 layer are equidistant as well as the successive layers, and the winding 

 is uniform when the distance of the successive layers is equal to that 

 of the individual windings. 



We shall suppose that in each wire the current is concentrated on 

 the axis of the conductor. The results calculated on this hypothesis 

 are sometimes exact, and are always closely approximate as long as 

 the diameter of the wire is very small compared with the radius of 

 curvature of the circuit, and that we do not consider the action at a 

 point too near the wire. 



723. The properties of a coil must be deduced from the various 

 data, which are defined by its dimensions and the mode of its 

 construction. 



