Both have since been destroyed, though a replica of the lighthouse replaced the original at Vaucluse. ”That’s one of the reasons we are so keen to restore the design motif at Hyde Park Barracks, because the domes are very representative of Greenway,” Mr Hill says.

The larger, reconstructed dome of Greenway’s north-west pavilion, now part of the barracks restaurant, gives some clues about how the missing domes were made. Its companion, on the Hyde Park side, was demolished in 1918 to accommodate trams – described by the architectural historian Morton Herman as ”the wanton ruin of Greenway’s one example of planning in the grand manner”.

Some drawings show the missing domes as relatively shallow, others more prominent – ”like bosoms”, Clark says.

Mr Hill believes he has found the correct shape in a rare book in the trust’s collection. In 1795 a British architect, John Plaw, published a ”pattern book”, Ferme Orne (or Rural Improvements). Such volumes were the 18th-century equivalent of today’s display villages, says Mr Hill, showing designs from which customers selected.

Mrs Macquarie brought to Sydney a copy of a similar pattern book, Edward Gyfford’s Designs for Elegant Cottages, which was used to build the colonial secretary’s house in Macquarie Place, now demolished. John Macarthur, the colony’s richest man in the early 19th century, had a copy of Plaw’s book and used it for the design of Belgenny Farm at Camden.

Mr Hill was flicking through Plaw’s designs recently but stopped at a remarkably familiar design – a ”hunting box”, a large lodge surrounded by an elegant wall. The proportions of the distinctive domed gatehouses and corner pavilions were strikingly similar to Greenway’s.

”It is highly probable that Macquarie showed Plaw’s design to Greenway as an example of what he wanted at Hyde Park Barracks,” Mr Hill says.

So is it architectural forgery? Not at all, Mr Hill says. Architects constantly reference the past.

The Historic Houses Trust Foundation wants a major sponsor for the domes. See http://blogs.hht.net.au/domes/.