of the Coefficients of Induction. 471 



15. The curves are very readily drawn on squared paper, and 

 yield some remarkable results. If the impressed electromotive 

 force E and the resistance B, are constant quantities, the 

 curve C will be a straight line parallel to the axis of time 

 cutting the current axis in a point R. The inclination of the 

 line joining R to any point T on the curve T will represent 

 the rate at which the current is increasing when it has the 

 value corresponding with the point T. Now, if the self- 

 induction is constant or nearly constant, this rate of increase 

 will be great at first but will continually diminish as time 

 goes on. If, however, the self-induction be very variable, the 

 result may be quite different and dependent to a great extent 

 on the value of C . Suppose the self-induction to increase at 

 first, and then to diminish. Unless C be very small, there 

 will now be points of inflexion on the current curve. The 

 current will increase very rapidly at first, slower afterwards, 

 then more rapidly, and will finally attain its maximum slowly. 

 If C be such as to magnetize the iron far beyond saturation, this 

 effect may be very marked, and the time taken for the current 

 to rise to a small fraction of its final amount may exceed that 

 taken to rise through the remainder. The writer is indebted 

 to Prof. Silvanus Thompson for the information that this fact 

 has actually been observed when accumulators have been con- 

 nected in series with the field-magnets of a dynamo and with 

 an Ayrton and Perry dead-beat ammeter. The needle has 

 been noticed to move very slowly at first, and then with great 

 rapidity through the larger portion of the ultimate deflection. 

 The greater the value of C , the quicker will the current 

 attain a given fraction of its final value. This may be roughly 

 accounted for by the fact that the mean value of the coefficient 

 is less the greater the value of the final current. 



16. When the electromotive force E is alternating, the coeffi- 

 cient L will not only be variable but two-valued. It will 

 depend not only on the value of the current, but also on 

 whether the current is increasing or diminishing. The curve T 

 will therefore consist of two parts — one for increasing current, 

 and the other for decreasing current. Although E and 

 may be pure sine functions, C will not be a simple sine 

 function if the coefficient L varies. Suppose a current curve 

 C, drawn on the assumption that there is a constant coefficient 

 of self-induction equal to the mean of the different values. 

 The true curve will, roughly speaking, differ from the 

 curve (7 in rising more rapidly when L is less than the 

 average, and in rising less rapidly when L is more than the 

 average. The general effect of the variation of the coefficient 

 will therefore be to introduce ripples into the current curve. 



212 



