Provision shall be made in the annual budget and in the annual appropriation ordinance for a reasonable contingent fund for use in any of the administrative departments of the city. Such contingent fund shall be under the control of the city manager and distributed by and with the approval of the City Council. In case of emergency, upon written request by the head of any department, stating the facts constituting such emergency, the city manager shall bring the same to the attention of the City Council and, if approved by him and by the council, he shall in writing authorize the transfer from the contingent fund to the credit of the department making such request of a sum sufficient to meet the proposed emergency expenditure. He shall transmit a copy of such written authority to the city controller and likewise to the department making such request. Upon the receipt by the city controller of such copy, the said fund shall be available for the purposes aforesaid, and shall be charged against the appropriation set apart for such department.