Whenever the city, county commissioners, and the said railroad, street railway and other companies, and others interested, or any of them, have entered into a contract or contracts for the construction of said bridge or viaduct, as is hereinbefore provided, it shall be lawful for the said city and the said county commissioners to have prepared plans or specifications of the entire work, and thereafter to advertise for bids, and to award the contract to the lowest responsible bidder. The contract for the said work shall provide that the county shall pay for its certain part of said bridge or viaduct, and the city shall contract for the other part of the said work; but the said contract, as to the city's part thereof, shall be based upon the appropriation made by the city for the part of the work for which it had agreed to pay, and the remaining part of the contract price shall be based upon the amounts the other parties have agreed to pay; and the contractor shall have a right of action against each party uniting in said contract, for the part thereof agreed to be paid by each party, respectively, as set forth in the contract or contracts in which all the parties unite, as aforesaid.
53 P.S. § 2508