Section 17. In every city, other than one having a board of election commissioners or an election commission, which, by vote of the city council, approved by the mayor, accepts the provisions of this section, or has accepted corresponding provisions of earlier laws, or which is now subject to similar provisions of law, there shall be a board of registrars of voters, consisting of four persons, who shall be appointed by the mayor with the approval of the board of aldermen. When a board of registrars is first appointed after the acceptance of the provisions aforesaid, two registrars shall be appointed in February or March following such acceptance for terms respectively of three and four years, beginning with April first next ensuing. The city clerk of such city shall cease to be a member of the board of registrars on April first, but the remaining two members of the existing board of registrars whose terms do not then expire shall continue to hold office for their respective terms of one and two years. In February or March of every year after such first appointments, there shall in like manner be appointed one registrar of voters for the term of four years, beginning with April first following. The board so constituted shall annually in April organize by electing one of its members as clerk, who shall perform all the duties of a city clerk when acting as clerk of the board of registrars.