That line ended up becoming the 9th avenue elevated line, which became known for having the worst accident in the history of NYC's elevated lines.
His company had been chartered the year before under the name of the West Side and Yonkers Patent Railway Company, with subscribed capital of $100,000, to build a 25 mile elevated railroad from the southern extremity of the city northward through the city and thence to the village of Yonkers.
The half-mile line was dubbed the “one-legged railroad,” because the single track ran above the street on a single row of columns. The cable was a loop, driven by a stationary engine, that ran between the rails for propulsion of the cars, then returned under the street.
The concept was similar in many respects to that used by the San Francisco cable cars five years later—the primary difference being that Harvey's patent called for the car to be secured to the cable by a sort of claw that would grab onto metal collars woven into the cable
The system broke down frequently and stopped running some time in 1870. A contemporary magazine article says "The Greenwich Elevated Railway, which at first was a total failure as long as several stationary engines were used, moving the cars by means of a wire rope, has become a decided success since the employment of small locomotives, each pulling two or three quite long cars."
Another article describes the technology and its problems in more detail: "...the main trouble by which the first management lost considerable money, (and probably the cause of the breaking of the company financially,) were the costly experimental contrivances intended for the propulsion of the trains. They consisted in an endless wire rope of about a mile long, and of which one-half moved over pulleys between the rails, while the returning half moved through a small tunnel underground, along the base of the columns.
A magazine article about another proposed cable-driven system concluded "If this inventor were acquainted with the drawbacks connected with the system of drawing trains by endless ropes, and had seen how it has been gradually abandoned in every case where it was possible to apply the motive power in another way, he would not think of applying it in a case like this. Does he not know that this was the plan upon which the Greenwich street elevated railroad was first worked; that it was given a fair trial, and that after so many thousands of dollars had been spent in experimenting as to bankrupt the whole concern, it was finally abandoned as valueless for the purpose?" ("An Absurd Rapid Transit Plan", [Manufacturer and Builder, Volume 11, Issue 5, May 1879)