In case any person upon whom an assessment shall have been made, as is herein provided, shall be a non-resident of the county in which said water-power is located, or absent, so that personal demand cannot be made upon him by the treasurer for the payment of such assessment, then in such case the treasurer shall give notice of such assessment by inserting a notice in some daily paper published in the town or city where such canal is located, in each issue, for 4 successive weeks, if a daily paper be published therein, if not, then in a weekly paper published in the county where said canal is located, once in each week for 4 successive weeks, specifying the fact of such assessment, and the name or description of the interest so assessed, and the amount of the assessment: Provided, That in case the directors shall so direct, it shall be lawful to include 1 or more assessments upon the same person or interest in 1 notice, and by a notice by mail directed to the owners’ reputed place of residence, and the publication aforesaid, and the giving of notice by mail as aforesaid, shall be deemed equivalent to a personal demand in the cases specified in this section after the publication and mailing said notices as aforesaid.