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William and Ann was built at the King's Yard in 1759.
It was reported on February 18, 1791.... Mary Anne, bound to Botany Bay sailed from Gravesend with near 100 women convicts on board. The Matilda also sailed at the same time to receive convicts at Portsmouth. Two other ships have sailed within these nine days, the William and Anne, and Britannia, both with men convicts, supposed to have on board about 200 each. The other ships still lying at Gravesend, to receive the men convicts from Newgate, are the Albermarle, the Barrington, and the Active. 
On 17th March at twelve o'clock, two of the transport ships from Portsmouth appeared off the harbour at Plymouth and made a signal to the Atlantic, Salamander and William and Anne vessels lying in Cawsand Bay; on which they weighed anchor, and got under sail immediately. 
Below is a list of transport vessels provided by Messrs. Camden, Calvert and King contractors for the Commissioners of the Navy for the conveyance of convicts to New South Wales
William and Ann
The Mary Ann departed England in February 1791 and the rest of the fleet departed in March 1791 and later met with the Queen from Cork at Madeira.
Active,Admiral Barrington, Albemarle, Britannia and Matilda departed from Portsmouth; their naval agent was Lieutenant Robert Parry Young. HMS Gorgonsailed from Portsmouth on 18th March 1791.
Atlantic, Salamander, and William and Ann departed from Plymouth; naval agent: Lieutenant Bowen.
Queen departed from Cork, Ireland; naval agent, Lieutenant Samuel Blow.
The New South Wales Corps formed the Guard on the vessels of the Third Fleet. The guard on the William and Ann consisted of a sergeant and thirteen privates, and several of their wives and children 
The William and Ann anchored in Sydney Cove on the 28th August 1791
DEPARTURE FROM THE COLONY
Some of the vessels of the Third Fleet were to proceed to the Southern Whale Fisheries after unloading the prisoners; the rest were bound for Bengal where they were to be freighted back to England with cotton. The sailors on board the Nootka ships were to have nine guineas for the run to Botany Bay after which they were to share as whale fishermen do. The other sailors were paid twenty five shillings per month.
Thomas Rainbow arrived free on the William and Anne (1825 muster)
NOTES AND LINKS
1). Eber Bunker (1761-1836), sea captain and farmer, was born on 7 March 1761 at Plymouth, Massachusetts, United States of America, son of James Bunker and his wife Hannah, nee Shurtleff. On 16 November 1786 at St George-in-the-East, Middlesex, England, he married Margrett, daughter of Henry Thompson
2). Captain Bunker on the William and Ann and Thomas Melville on the Britannia were two of the first men who embarked on whaling voyages in 1791. (1) In 1791 a fishery for spermaceti whales on the coast of New South Wales was commenced by Captain Melville, commander of the Britannia, a ship belonging to Messrs. Enderby and Sons, the first British merchants who adventured in the southern whale fishery. Having discovered in his passage to Port Jackson with a load of convicts, that the spermaceti whales are more abundant in the seas adjacent to that country than near the coasts of South America, he sailed from that port on a whaling expedition, and was followed by several other vessels, which, like his own, were fitted for the whale fishery, and according to the original destination of their voyages, were to have stretched across the Pacific ocean to the coast of Peru on that pursuit. Captain M. got only one out of four whales that he killed, nor were the other vessels more successful, owing to the very tempestuous weather while they were out. But they were sufficiently encouraged to consider those seas as very favourable for the prosecution of the most valuable branch of the whale fishery. Read more........ A Treatise on the Laws of Commerce and Manufactures By Joseph Chitty
3). Success of the Whaling Industry
4). Denis Reardon a convict who arrived on the William and Ann was killed by lightning in 1793. He was buried in the Old Sydney burial ground
5). Convict George/John Bevin is the only prisoner of the William and Anne so far identified at Newcastle
 Eber Bunker - Wikipedia
 The London Times 21st March 1791
 The London Times 28 March 1791
 Historical Records of Australia, Vol.1, p225
 John Hunter's Voyage. - An Historical Journal of the Transactions at Port Jackson and Norfolk Island
 The Times 15 March 1791
 The Lady's Magazine, Volume 22, by National American Woman Suffragettes