SECTION 40. Proceedings if initiative petition not properly signed

If an initiative petition is signed by registered voters equal in number to at least eight per cent but less than fifteen per cent of the total number of registered voters, and said measure is not passed without alteration within twenty days by the city council or the school committee, as provided in the preceding section, such proposed measure, without alteration, shall be submitted by the city clerk to a vote of the registered voters of the city at the next regular municipal election which occurs at least thirty days after the date of qualification. As used in this section and section thirty-nine, ''date of qualification'' shall mean the twentieth day after the date of the certificate of the registrars, or the day on which the city council or school committee finally decides not to pass the measure without alteration, whichever day occurs first. A proposed measure under this section or section thirty-nine shall become effective if it shall be approved by registered voters of the city equal in number to one third of the whole number thereof and also by a majority of the voters voting on such measure, but not otherwise.