Upon conviction of any person under any of the provisions of Sections 16-19-40, 16-19-50 or 16-19-90, the court before whom such conviction shall take place shall commit such offender to the common jail of the county in which such conviction shall happen for a period not exceeding the time for which such offender has been sentenced, unless such offender shall sooner pay the fine or fines herein imposed, together with the cost of prosecution.