Whenever any such proposed subway will reach within the limits of any city, if the governing body of each such city and the board of supervisors of the county in which each such city is situated first so agree, the board of supervisors may call an election and submit to the electors of the county, in the manner provided in this article, the question whether bonds of the county will be issued and sold for the purpose of constructing such a subway in the manner prescribed in this article.