He made an abstract of this manuscript at the time, and this abstract is now preserved in the British Museum.
Comparing the abstract with the edition published in 1758, there is no doubt that the learned doctor had copied from a manuscript which, if it were not genuine, was certainly the text of the work published in 1758 as "The History of the Four Last Years." But Dr.Birch's language suggests that he believed the manuscript he examined to be in Swift's own handwriting.

If that be so, there is no doubt whatever of the authenticity.

Birch was a very careful person, and had he had any doubts he could easily have settled them by applying to the many friends of the Dean, if not to the Dean himself.

Moreover, it is absurd to believe that a forged manuscript of Swift's would be shown about during Swift's lifetime without it being known as a forgery.

Mrs.Whiteway alone would have put a stop to its circulation had she suspected of the existence of such a manuscript.
Finally, it must be remembered that when the History was published in 1758, Lord Orrery was still living.