Section 37. Each register shall keep a docket of all cases and matters in his court, and shall enter therein every case or matter by its appropriate title and number, brief memoranda of all proceedings had and papers filed therein, the dates of such proceedings or filing of such papers, and references to the places in which the proceedings or papers are recorded, if there is a record thereof. He shall also keep a separate alphabetical index of all such cases and matters which shall refer both to said docket and to the files of the court, and a separate alphabetical index of all public administrators seeking appointment or appointed to administer any estates, with the names of such estates. Such docket and indexes shall be open to public inspection at all reasonable times.