On Current Curves. 257 



3. This method is not applicable to the case in which the impressed 

 E.M.F. is sinusoidal, on account of difficulties of integration. But 

 both cases can be treated in another way : Take a series of points 

 on the (B, H) curve of the iron core, such that the chords joining them 

 practically coincide with the curve itself. Let B K , H and B K+1 , H K+1 

 be the coordinates of two consecutive points. The equation to the 

 curve between these points is approximately 



B = n? K+1 H + constant (9), 



where W|t+l = c+1 ""^ c , 



-tl/c + i H/c 



and therefore between these limits 



During the time that the current rises from i K to 4+i, and B and 

 H rise from B K and H K to B K+1 and H K+1 , and t rises from t K to t K + lt 

 we have 



and therefore 



which is true to a very close approximation for any simultaneous 

 values of t and i between the above limits. From this equation, 

 since t and i' are both zero, we can determine in succession the times 



TT TT 



at which the current has the known values 0, , , ... &c., 



L L 



using that value of m which applies to that particular value of H 

 under consideration. In this way the current curve can be plotted. 



On making E = in the original differential equation, and 

 observing the proper limits, we get 



as the equation to the curve representing the dying away of the 

 current when the E.M.F. is withdrawn; m, m, l+ i being determined 

 from the descending (B, H) curve. 



Fig. 1 and Table I give the results of calculation for a circuit with 

 the following constants: Resistance, 1 ohm; E.M.F., O4315 volt; 

 self-induction (without iron core), 0'0004- henry. 



