Should the monthly cost and expense of such engineering inspection amount to more than said estimate, the person, firm, or corporation concerned shall thereupon be immediately notified and required to make an additional deposit with the Director of Public Works of an amount sufficient to complete the monthly cost of said inspection as estimated by the Director of Public Works, which sum when paid shall be deposited as aforesaid, and no further engineering inspection service shall be performed or furnished until such additional deposit is made with the Director of Public Works.