82


SIMPLE  PERIODIC  CUERE!fTS,


Take  a  horizontal  line  (Fig.  26)  to  represent  the  uniform  flow
of  time.  At  successive  instants  let  ordinates  be  drawn  to  this
line,  representing  the  strength  of  current  flowing  past  that
section,  and  let  them  be  drawn  above  (  +  )  or  below  (-),
according  as  the  direction  of  the  flow  is  to  the  right  or  to  the
left.  Thus,  if  time  begins  to  reckon  from  0,  after  the  lapse
of  a  time  0  T  the  current  is  positive,  and  is  represented  by  a


line  TI.  After  the  lapse  of  a  time  OT'  the  current  is
negative,  and  is  represented  in  strength  by  a  line  T'  T.
This  current  curve  is  obviously  a  single-valued  function —
that  is  to  say,  corresponding  to  a  given  instant  of  time  the
current  can  only  have  one  value.  The  curve  can  never  cut
itself  or  double  back.
We  may  here  remind  the  student  of  the  distinction  between
single  and  multiple-valued  functions.     A  single-valued  func-


X

Fig.  27.
Single  valued  function.
Fig.  28.
Multiple- valued  functions.
tion  is  one  which,  when  represented  graphically  by  a  continuous
curve,  presents  only  one  value  of  the  ordinate  for  each  value
of  the  abscissa.
In  Fig.  27  is  represented  graphically  a  single-valued  function,
having  only  one  value  of  the  ordinate  X  Y  corresponding  to  a
given  value  of  abscissa  OX.  In  Fig.  28  is  represented  a  curve
such  that  there  are  five  different  values  of  the  ordinate  of  th©


SIMPLE  PERIODIC  CURRENTS,


83


curve  corresponding  to  one  value  of  the  abscissa  0  X.     This
curve  represents  a  multiple- valued  function.
