72 PROPERTIES .OF CIRCULAR CURRENTS. 



Assuming that the winding is uniform, we shall call 



y, the radius of the wire, 

 y =y + Zy the external radius of the wire covered with its insulating 



coating. 



/, the length of the wire measured along its axis. 

 d, the specific gravity of the metal. 

 #', the radius of the channel of the coil. 

 a", the outer radius of the coil. 



2<r, the thickness of the channel along the radius 2c = a" -a. 

 26, the length of the channel along the axis. 

 W, the section of the channel : w = 2b (a" a') ^bc. 

 a, the distance from the axis to the centre of gravity of the 



section of the channel. 



U, the volume of the channel : U = 2ir (a" 2 - a" 2 ) b = 27r#w. 

 V, the volume of the metal. 



V, the total volume of the wire together with the insulator. 

 , the total number of windings. 

 n v the number of windings for unit length along the axis of 



the coil. 



2 , the number of windings for unit length along the radius of 

 the coil. 



These data will enable us to determine the other elements, 

 such as the length, the volume and the weight of the wire, the 

 volume of the insulator, and lastly the electrical properties of 

 the coil. 



Neglecting for a moment the effects of induction, we shall have 

 to calculate : , 



i st. The total resistance R of the wire. 



2nd. The total surface that is to say, the sum of the surfaces 

 bounded by the different windings, or the magnetic moment of 

 the coil for unit current. 



3rd. The electromagnetic action G of the coil, or the intensity 

 of the magnetic field for unit current. 



724. LENGTH OF WIRE. MEAN RADIUS. The thread of each 



winding is equal to ; the length of a winding whose projection on 



n \ 

 a plane perpendicular to the axis is a circumference of radius r, is 



