The Prince of Orange was built in Sunderland in 1813 She was the next convict ship to leave England for New South Wales after the departure of the Hebe in July 1820.
The convicts were tried in counties in England - Norfolk, Lincoln, Warwick, Suffolk, Essex, Sussex, Bristol, Lancaster, Middlesex, Devon, London, Cornwall, Berks, Dorset, York, Stafford, Southampton, Surrey, Cambridge, Rutland and Oxford.
The guard consisted of a detachment of the 34th Regiment under orders of Lieut. James Oliphant Clunie of the 17th foot.
The Prince of Orange departed the Downs on 8th October 1820.
Surgeon George Shaw Rutherford
George Shaw Rutherford kept a Medical Journal from 1 September 1820 to 17 February 1821. He thought that many of the diseases were too trifling to write in a Medical Journal. The men suffered constipation, headache and distension of the stomach which he ascribed to change of diet and confinement on board, many of the prisoners being country men and accustomed to the use of vegetables and active exercise. 
The following men are mentioned in the Surgeon's journal:
John Venis, convict, aged 25,
James Horton, soldier, aged 18,
William Sprigs, convict, aged 20,
Henry Hancock, convict, aged 21,
John Neil, soldier, [aged not known],
Thomas Regell, convict, aged 26,
Thomas Easterbrook, convict, aged 19,
William Harris, convict, aged 16,
John Muston, convict, aged 29,
John York, convict, aged 36, . Died 29 October 1820 at 3 o'clock pm.
William Barber, convict, aged 26,
William Holden, convict, aged 28,
John Law, soldier, aged 23,
Joseph Lenny, convict, aged 24,
John Blackman, convict, aged 21,
Isaac March, convict, aged 19,
James Davis, convict, aged 29,
William Pepper, convict, aged 27,
Robert Long, convict, aged 48,
Peter Richardson, convict, aged 32,
Thomas Martin, convict, aged 28,
Samuel Goldsmith, convict, aged 19,
Robert Harmer, convict, aged 38,
Thomas Myall, convict, aged 23,
Corporal Collins, corporal, aged 25,
William Harris, convict, aged 17. 
The Prince of Orange arrived in Port Jackson on Monday 12 February 1821.
Inspection by Governor Macquarie
Lachlan Macquarie was still Governor when the Prince of Orange arrived. The Sydney Gazette reported - His Excellency the Governor and Commander in Chief this morning inspected the prisoners that arrived on Monday last, per the ship Prince of Orange; after which they were directed to be distributed to their variously assigned employments.
Notes and Links
1). George Rutherford was also surgeon on the convict ships:
2). Convict Henry Adams was born c. 1804 at Wrenthan Frostenden, Suffolk. He was convicted of lamb stealing on 24 July 1820 and sentenced to 14 years transportation. He married Elizabeth Clarke in January 1838 at All Saints Sutton Forest and died 17 January 1866 at Young.
3). James Clunie joined the 17th Regiment as an ensign in 1813 and was promoted to lieutenant the following year. In 1821 he was transferred to Madras, India on the Almorah. In 1830 he returned to NSW as senior officer of the Guard on the convict transport Forth. He succeeded Patrick Logan as Commandant at Moreton Bay and was stationed there from 1830 to 1836. He died in 1851. In the State Library of New South Wales there is a Transcript of a journal kept by James Clunie from 29 September 1820 - 16 February 1821 on this voyage of the Prince of Orange.
4). Convict ships bringing detachments of the 34th regiment included;
 Bateson, Charles, Library of Australian History (1983). The convict ships, 1787-1868 (Australian ed). Library of Australian History, Sydney : pp.344-345, 383
 Ancestry.com. UK, Royal Navy Medical Journals, 1817-1857. Medical Journal of George Shaw Rutherford on the voyage of the Prince of Orange in 1821. The National Archives. Kew, Richmond, Surrey.
 National Archives - Surgeon's Journal Reference: ADM 101/60/8 Description: Medical and surgical journal of the Prince of Orange convict ship from 1 September 1820 to 17 February 1821 during her passage to New South Wales.
 The Sydney Gazette and New South Wales Advertiser (NSW : 1803 - 1842) Sat 17 Feb 1821 Page 2