draw the three curves, as in Fig. 55,
wherein the abscissae are the values of time in seconds and the
ordinates the current. The faint vertical dotted lines mark the time
constants in the three cases. It will be seen that when rapid working
is required the magnetizing current will rise, during short intervals
of time, more rapidly if all the cells are put in series than it will
do if the cells are grouped according to the amateur rule.

|
5| .
| .
| .
4| MAXIMUM .
| OUTPUT \ .
| .
3| .
| . : ALL IN SERIES
| _-------------------:------------------------------
2| .- - :
| - - :
| -: - :
1| / : - : ALL IN PARALLEL
|. : . : _________--------
|- :__ : ----------
+-----------------------------:-------------------------------
0 1 2 3 4 5 6 7 8 9 10

FIG. 55.--CURVES OF RISE OF CURRENT WITH DIFFERENT GROUPINGS OF BATTERY.

When they are all put in series, so that the battery has a much
greater resistance than the rest of the circuit, the current rises
much more rapidly, because of the smallness of the time constant,
although it never attains the same ultimate maximum as when grouped in
the other way. That is to say, if there is self-induction as well as
resistance in the circuit, the amateur rule does not tell you the best
way of arranging the battery. There is another mode of regarding the
matter which is helpful. Self-induction, while the current is growing,
acts as if there were a sort of spurious addition to the resistance of
the circuit; and while the current is dying away it acts of course in
the other way, as if there were a subtraction from the resistance.
Therefore you ought to arrange the battery so that the internal
resistance is equal to the real resistance of the circuit, plus the
spurious resistance during that time. But how much is the spurious
resistance during that time? It is a resistance proportional to the
time that has elapsed since the current was turn