Each supervisor before entering upon his official duties shall take and subscribe to an oath before some officer authorized by law to administer oaths, that he will honestly and impartially perform the duties devolving upon him in office as supervisor of the drainage district in which he was elected, and that he will not neglect any of the duties imposed upon him by this article. Any supervisor-elect who fails to qualify by taking such oath and filing the same in the office of the secretary of the drainage district within ten days after his election shall be deemed to have declined such election, and the vacancy shall be filled as herein provided.