Section 274. Extension of the district

A county district may be extended so
  as to include territory not previously included within its boundaries in
  the   same   manner   as   hereinbefore   prescribed  for  the  original
  establishment of the district.   If the cost  of  establishment  of  the
  original district and of providing the improvement therein was assessed,
  levied  and  collected pursuant to the provisions of section two hundred
  seventy, then the cost of the extension and of the improvements  therein
  shall  be  assessed,  levied and collected pursuant to the provisions of
  said section. If the cost of establishment of the original district  and
  of  providing  of  the  improvement  therein  was  assessed,  levied and
  collected pursuant to the provisions of section two hundred seventy-one,
  then the cost of the extension and of the improvement therein  shall  be
  assessed,  levied  and  collected  pursuant  to  the  provisions of said
  section. The cost of the extension shall include such proportion of  the
  cost  of the system of the original district as the board of supervisors
  shall determine.