The No. 7 train project, in comparison, is something of a success story. It is now expected to be completed by the end of this year, extending the line, which now terminates at Times Square, to 11th Avenue about a year behind schedule. It cost $2.4 billion — on budget, officials say, though plans for an additional station at 41st Street and 10th Avenue were scrapped. And Mr. Bloomberg did get to ride his train last December, pulling into 34th Street in a makeshift, one-day-only opening ceremony arranged by the transportation authority.

But the station, and its unusual elevator, provide a useful case study in the difficulties of capital construction in the city.

The idea for a diagonal elevator — two, actually, to go with the station’s escalators and vertical elevators — dates to the project’s genesis more than 10 years ago, the authority said. Angling the structures at an incline was thought to be less expensive than tunneling in relatively straight lines, down and across.

It would also prove a boon to wheelchair users, officials said. A traditional vertical elevator from the upper to the lower mezzanine would have left such passengers about 150 feet from a second elevator that could take them to the platform. But because the incline elevators run parallel to the escalators, Mr. Horodniceanu said, “you are providing a similar experience, irrespective of your handicap.”

At a recent transportation authority committee meeting, board members were assured that the technology underpinning their design was nothing new. The Eiffel Tower relied on an incline elevator as early as 1889. And since 1993, similar elevators have operated without major incident at the Luxor Las Vegas.

Before construction began, the transportation authority led an international search for elevator manufacturers, recommending two companies to Skanska, the project’s general contractor: Maspero and Huetter-Aufzuege, in Germany.