49$ CONSTANTS OF COILS. 



The length of the wire is determined either directly or by 

 measuring the diameter of the coil before and after coiling each 

 layer, or by two corresponding circumferences. A flexible metal 

 band, wound on the coil, measures the circumference with great 

 approximation. We may assume that the mean line of the band 

 retains the same length, notwithstanding its curvature ; so that, if a 

 is the radius of the cylinder, the observed length corresponds to 

 the radius a, added to half the thickness of the strip, and from it 

 will be deduced the length of the circumference of radius a. 



It must, however, be observed that if the coil contains several 

 layers, separated by an insulating substance, a measurement of the 

 diameters or circumferences before and after the coiling of a layer 

 does not give the exact value of the mean diameter, for the pressure 

 of the wires crushes the insulating substance. 



On the other hand, we cannot, without special precautions, 

 deduce the length of a wire from a measurement made before 

 winding, because the wire elongates to a varying extent during 

 winding, especially in consequence of the strain which it must 

 undergo to obtain regular layers. According to Werner Siemens,* 

 this elongation may, with fine wires, amount to 5 or 6 per cent. ; 

 it is less, but still considerable, even with thicker wires. If we 

 wish to measure the wire before winding, it ought to be subject 

 to the same strain as during the winding; the change of length 

 due to the fact of winding itself, may be neglected if the radius 

 of curvature is very large in comparison with the diameter of 

 the wire. 



All formulae for coils imply the condition that the current is 

 uniformly spread in each section of the wire, or, what amounts to 

 the same thing, that the current may be considered as concentrated 

 on the axis of the wire itself. This condition is not rigorously 

 fulfilled, especially with variable currents ; the calculation will only 

 give then a first approximation, and the error cannot be neglected 

 with rather thick wires. 



There is, lastly, an evident condition, but one which experiment 

 shows cannot be easily realised, which is, that the different windings 

 be completely insulated from each other. In order to ascertain 

 whether a coil is properly insulated, Lord Rayleighf interposes its 

 two insulated ends between the two coils of a Hughes' induction 



* WERNER SIEMENS. Pogg. Ann., Vol. cxvir., p. 327. 1866. 



f Lord RAYLEIGH and Mrs. SIDGWICK. Transactions of the Royal Society 

 for 1884, p. 419. 



