The superintendent of streets, or the engineer, if the legislative body has by resolution directed that the work be done under his direction and to his satisfaction, shall, when in his judgment it is necessary, appoint a suitable person to take charge of and superintend the construction and improvement of any work authorized by this division, whose duty it shall be to see that the contract made for the doing of the work is strictly fulfilled in every respect and in case of any departure therefrom to report the same to the officer who appointed him. Such person shall be allowed for his time actually employed in the discharge of his duties such compensation as shall be just and the rate thereof shall be fixed by the legislative body conducting the proceedings. The sum to which the party so employed shall be entitled shall be deemed to be incidental expenses within the meaning of those words as used in this division.