If one proprietor or his predecessor in title makes the whole fence and the adjoining proprietor afterwards encloses his land, such adjoining proprietor shall purchase and maintain half of the divisional fence. If the parties do not agree in dividing and appraising it, either may call on the selectmen of the town in which such fence is situated, who may set out, to each, his proportion of such fence and determine how much shall be paid to the party erecting or owning the same by the other; a certificate of which determination, under the hands of the selectmen, shall be sufficient evidence for the recovery of the amount so determined. No action therefor shall be maintained unless the proprietor, who, or whose predecessor in title, first occupied his land and made the whole of the divisional fence, has caused such fence to be so divided and appraised within six years after the adjoining proprietor, or those under whom he holds, has first enclosed his land by particular enclosure, nor unless such action is commenced within one year after such division and appraisal have been made.