Each officer of the city shall before entering upon the duties of his office take the oath of office, and such as may be required to give bonds file the same, duly approved, within ten days after receiving notice of his election or appointment; or, if no notice be received, then on or before the date fixed for the assumption by him of the duties of the office to which he may have been elected or appointed; but, if anyone, either elected or appointed to office fails for ten days to qualify as required by law, or to enter upon his duties at the time fixed by law or the orders of the City Council, then such office shall become vacant, or if such officer shall absent himself from such city without the consent of the Council for three consecutive weeks or shall openly neglect or refuse to discharge his duties, the said Council may declare such office vacant: Provided, that the penalty for absence from the city shall not apply to such officers as serve without salary or without compensation. The City Council shall fix the amount of all official bonds, and may designate what officers shall be required to give bonds in addition to those required to give bonds by this Charter.