Whenever any person, firm or corporation desires and intends to do any work to make any improvement as described in Section 635 of this Article, such person, firm or corporation before performing any such contemplated work, shall in writing request the Director of Public Works to make engineering inspection. The cost of such engineering inspection shall constitute a charge against and be paid for monthly in advance by the person, firm or corporation performing said work or making such improvements in the manner hereinafter provided.