Section 18. The directors may make such assessments on each share as they find necessary; and, upon the default of a proprietor for thirty days after notice thereof to pay an assessment, they may sell by public auction so many of his shares as will be sufficient to pay the assessment and the necessary charges, such sale being first advertised three weeks successively in a newspaper published in the county, or notices thereof being posted thirty days at least before the sale in public places in the town. The surplus proceeds arising from the sale shall be paid to the owner of the shares sold.