When any expenditure is made on account of any separate or single lot, parcel of land, or lands, or premises, which, by the provisions of this Charter or by law, the City is authorized to charge and collect as a special assessment against the same, and which assessment is not of that class of special assessment required to be made pro rata upon lots or parcels of land in a special assessment district, a statement of the labor or services for which such expenditure was incurred, verified by the City Manager, with a description of the lot and the name of the owner or person chargeable therewith, if known, shall be reported to the Council in the manner prescribed by it. The Council shall determine the part of such expenditure that shall be charged, and the person against whom, if known, and the premises upon which the same shall be levied, as a special assessment. As often as the Council deems expedient, the Clerk shall give notice of the several amounts so determined and reported to the several persons chargeable therewith. Such notice shall be sent by first class mail to the last known addresses of such persons as shown on the assessment roll of the City, or by publication. Such notice shall state the basis of the assessment, and the amount thereof, and shall give a reasonable time, not less than thirty days, within which payment shall be made to the Treasurer. In all cases where payment is not made within the time set, the fact shall be reported by the Treasurer to the Assessor, who shall charge such amounts, together with a penalty of ten per cent of such amounts, against the persons or real property chargeable therewith, on the next tax roll.