The trustees of said Village shall have power to, and may appoint such number of police officers within said Village, as said trustees may judge necessary for the interest of the inhabitants of said Village, by writing under their hands, which shall be recorded in the office of the Village Clerk; and such appointment may be revoked at any time. Said trustees may specify their duties as watchmen and patrols, and agree with them for their compensation, which shall be paid by the said corporation. Each of said police shall be sworn, and shall have the same powers, within the limits of said Village as constables, in serving criminal process and in criminal matters, and when on duty shall wear conspicuously a badge of office, and shall hold their office for one year, unless sooner discharged as aforesaid.