If the certificate of the clerk so attached shows the petition to be insufficient, he shall within ten days cause notice in writing, setting forth the fact that the petitions are found to be insufficient, to be served upon one or more of the persons designated in the certificate attached by him to the petition as the persons who filed the petition in his office. Additional signatures, properly verified, may be filed with the clerk at any time within fifteen (15) days from the date of the service of such notice. The city clerk shall attach his certificate to such additional petitions and shall cause them to be entered in the record book. The clerk shall within five days after the filing of such additional petitions make like comparison of the additional signatures with the registration books and attach his certificate of the result. If the number of signatures are still shown to be insufficient, or if no additional signatures are so filed, the clerk shall, upon demand, return the petition to any of the persons designated as filing it, without prejudice to the filing of a new petition for the same purpose.