The Minerva was a merchant ship built in Bombay and launched in 1773. According to the Shipping List for Port Jackson she was owned by Robert Larnock, was 578 tons and carried 12 guns and a crew of 42.  She traded for over 20 years before being chartered by the East India Company under which she transported convicts from Ireland to Australia in 1799 - 1800.
The Minerva departed the Downs, on 6 August 1799 bound for Cork. She sailed from Cork in convoy on 24 August. There were on board, 165 male and 26 female convicts, together with three children belonging to convicts. Many of the prisoners were United Irishmen transported for their role in the 1798 rebellion including General Joseph Holt.
The Military Guard comprised a detachment of the 102nd regiment commanded by Lieutenant William Cox who had particular charge of the political prisoners. Lieutenant Cox was accompanied by his wife and four sons.
Surgeon John Washington Price
John Washington Price's Journal of the voyage is held in the Wellesley Collection at the British Library in London. It was transcribed and edited with an introduction by Pamela Jeanne Fulton in 2000
....From the Cover - John W. Price was only twenty-one years old and a recent graduated from Dublin's College of Surgeons when he commenced the journey. He was well educated, with a keen awareness of the world around him. His journal is lively copious and detailed. It covers the entire voyage both to and from Sydney. Price was an acute observer of people and his journal is full of minutiae about convicts, sailors and soldiers, and the flora and fauna encountered along the way.
The Minerva Journal contains a list of the Ship's Company; a list of the detachment of the N.S.W. Corps; a list of those who went as free passengers as well all the convicts, their occupations and date and place of trial.
The Ship's Company included :
Joseph Salkeld, Commander;
Henry Harrison, Chief Mate;
William Howe, 2nd Mate;
William Huggett, 3rd Mate;
John Washington Price, Surgeon;
Joseph Compton, Boatswain;
William Bolton, Carpenter;
William Winters, Gunner;
Thomas Harris, Cook;
Isaac Anstey, Steward;
Timothy Gurnel, Cooper;
John-Guy Johnson, sailmaker;
James Ward, Boatswain's Mate;
George Feversham, Carpenter's Mate;
James Nixon, Quarter Master;
Robert Douglass, Quarter Master;
John Thompson, Quarter Master;
Richard Marsden, Quarter Master;
William Cato, Cabin servant;
Joseph Hunter, Cabin Servant;
George Waft, seaman
Peter Downey, seaman
John Burr, seaman
James Hart, seaman
Joseph Berry, seaman
William Taylor, seaman
William Robinson, seaman
George Heath, seaman
John Baker, seaman
Richard Thomson, seaman
Charles Ferris, seaman
Robert Warren, seaman
John Walter, seaman
David Gleming, seaman
Benjamin Ellis, seaman
John Howe, seaman
Henry Thorpe, seaman
Jacob Nuteson, seaman
John Jack, seaman;
Daniel Kelly, boy;
Henry Aylmer, boy;
Margaret Bolton, carpenter's wife.
The wife of Captain Hugh Reed of the Friendship accompanied her husband on the voyage to New South Wales during which time she kept a journal:
'24th August. The signal for sailing was made from his Majesty's ship Dryad, and repeated by the Revolutionaire frigate, who was to convoy us; and the ship Minerva, Captain Salkeld, who also had prisoners on board for New South Wales. We left Cork harbour with a large fleet who were bound to America and the West Indies. On the third day after leaving Ireland, the different convoys separated. '
The Minerva and Friendship kept company until 14th September.....
'The commodore made the signal that he would part company that evening, but would lie to until four o'clock for our letters; in consequence of which all were busy preparing to write to their friends. Sent the letters on board (the Minerva) and parted with them. We kept company with the Minerva until next day, when as she sailed much faster than the Friendship, and Captain Salkeld thought it eligible to make the best of his way and left us to pursue the voyage alone. '
One hundred and sixty-three male convicts and 26 female convicts arrived in the Minerva on 11 January 1800. Three prisoners had died on the passage out. The convict indents particularly noted some of the men who had been involved in the rebellion in Ireland and who had been transported for life - Thomas Maxwell, William Mahony, Edward Gibbons, Thomas Higgins, Nathaniel Connaghan, Martin Haden, Edward O'Hara, Peter McIvers, Bryan Connor, Florence McCarty, William Henry Alcock, Joseph Holt, Samuel Culley, Bryan Daly, James Harrold and Andrew Byrne*, Joseph Holt.
Governor Hunter in correspondence to the Duke of Portland dated 15 January 1800 reported the arrival of the Minerva:
The Minerva having touched at Rio Janeiro, has brought many articles for sale as well from thence as from England, many of which are greatly wanted by the people here; but, my Lord, the prices in general, altho' not so much in this ship, are such as drain the colony of every farthing the people can gather together, and serves to keep them in a continual state of beggary. It is not possible, my Lord, that we should prosper under such circumstances. 
Governor Hunter later remarked about some of the convicts of the Minerva and Friendship:
With respect to laborers, it becomes necessary to assure your Grace that, notwithstanding the number of people brought from Ireland by the last two ships, we have receiv'd no great accumulation of strength. Many of those prisoners have been either bred up in genteel life, or to professions unaccustomed to hard labor. Those are a dead weight on the public store ; and really, my Lord, convicts. notwithstanding we cannot fail to have the most determin'd abhorrence of the crimes which sent many of them here, yet we can scarcely divest ourselves of the common feelings of humanity so far as to send a physician, a formerly respectable sheriff of a county, a Roman Catholic priest, or a Protestant clergyman and family to the grubbing hoe or timber carriage.
Amongst these, Bryan O'Connor was a physician, who was emancipated on the 12th of August, 1801, in order that he might practise his profession; the Reverends James Dixon and James Harold were Roman Catholic priests, who had arrived in the Friendship and Minerva respectively; the Reverend Henry Fulton was a Protestant clergyman who had been transported in the Minerva. 
Departure from Port Jackson
The Minerva departed Port Jackson bound for Bengal in April 1800. Hidden in the hold was an escaping convict by the name of Thomas Parnell who had arrived on the Ganges in 1797. He was found by Captain Salkeld and returned to the colony. A copy of the Verbal statement and examination of Thomas Parnell is held in the British Library and is part of the Joint Copying Project. Mfm M 1888-1889-Papers of Richard Wellesley, 1st Marquess (as filmed by the AJCP) [microform] : [M1888-1889], 1793-1805./Series Add MS 13713/Item ff.50-53/
Convicts from the Minerva identified in the Hunter Valley:
BRADY, THOMAS - Tried Co. Wicklow March 1798. Sentenced to transportation for life. Find out more about rebel Thomas Brady
HAFFARD, WILLIAM - Tried Co. Kildare 1797. Sentenced to transportation for life. Sent to Newcastle penal settlement in October 1813
MACKINLEY, JOSEPH - Tried Co. Monaghan March 1798. Sentenced to 7 years transportation . Age 30. Sentenced to three years at Newcastle penal settlement in 1811. Employed as a constable at Newcastle in 1814. Applied for a grant of land but this was cancelled because of his being a receiver of stolen goods.
Notes and Links
1). *Andrew Byrne died in April 1863 and was buried in the old Devonshire cemetery. Epitaph: 'He was a native of the County of Wicklow, Ireland, and arrived in this colony as a patriot of his country in the year 1800. (Sydney Morning Herald 7 February 1901)
2). James Bull arrived as a free passenger on the Minerva. (CSI)
4). Edward McRedmond.....George Rude in Protest and Punishment: The Story of the Social and Political Protesters Transported to Australia traced the life of Edward McRedmond - from being an illiterate labourer in King's county who came to Australia at the age of 32, had by middle age become a wealthy landowner and highly respected citizen of Sydney. He started as a small dealer in the city around 1803 and in 1809 acquired a wine and spirit license as well as a grant of 135 acres of land. In 1815 in partnership with Patrick Cullen, he leased the profitable tolls between Sydney and Parramatta. A year later, he became one of the original shareholders of the Bank of New South Wales. He extended his holdings in land and when he died in 1840 he left his widow and children farms at Bathurst, Bingham, Annandale and on the Hawkesbury River as well as houses at Windsor and Liverpool and three at Sydney. More about Edward McRedmond at Australian Dictionary of Biography