162 PROCEEDINGS OF THE AMERICAN ACADEMY. 



If now ft (T) be accurately plotted against T, the area under this 

 curve from T\ to Ti is equal to the time in seconds which elapses while 

 the excitation is growing from T\ to T 2 . If a large number of these 

 areas be measured by aid of a planimeter, it is easy to give a graphical 

 representation of T (and therefore of ii and i 2 ) in terms of t, and we 

 may expect the current curves thus obtained to correspond closely 

 with the oscillograph records for the same case. If r 2 , r 2 , m, n\, and E\ 

 are all increased in a given ratio X, the quantity ft ( T) and therefore, 

 dt, will be increased in the same ratio. 



Application to Transformer with Fine Wire Core. — It will be 

 instructive to apply the foregoing theory to a certain transformer 

 (DN), in which magnetic leakage and eddy currents were negligible. 

 This transformer was constructed in the form of a toroid, about 41 

 centimeters mean diameter, the core of which was made of about 25 

 kilograms of fine, soft, varnished iron wire. 



After the core of the transformer had been thoroughly demagnetized 

 the magnetic flux through the core, due to an ascending series of steady 

 currents in the exciting coil, was determined. The results of the long 

 series of measurements, which were taken with a slow period ballistic 

 galvanometer, are given in Table VI. The full curve, OK, Figure 8, 

 reproduces the table graphically: one vertical unit corresponds to 

 fifty thousand maxwells, and one horizontal unit to a thousand ampere- 

 turns. The ordinates of the dotted curve exhibit, on an arbitrary 

 scale, the corresponding slopes of the other. A few values of the slope,. 

 dN/dT, are given in Table VII. 



From the foregoing theoretical discussion, and the numbers given 

 in Tables VI and VII, it is always possible to predict under fixed condi- 

 tions the growth of the excitation in the core, the march of the current 

 in the primary and secondary coils, and the manner of increase of the 

 flux of magnetic induction in the core of the transformer in question. 

 It will be seen from equation (11), when E = 10, n 2 = 1000, n\ = 

 100, r-i = 10, and n = 1, that if the slope of any point of the curve, OK, 

 is multiplied by 11/10 4 (1000- T), the result is the value of ft (T) for 

 the given value of T. A few values of ft (T) are shown in Table VIII. 

 If now ft (T) be plotted as a function of T, and the area from T = 

 to T = T\, for a number of different values of T be measured in terms 

 of the unit square of the figure, this area gives the time in seconds for 

 the excitation in the core to attain the value T. 



The curve, VWSZ, bounding the shaded area (Fig. 9), reproduces 

 the first two columns of Table VIII graphically; that is, ft (T) as a 

 function of T. For convenience 10 4 ft (T)/5 was taken as the vertical 



