The Captain Cook was built at Whitby in 1826. Convicts were transported to New South Wales on the Captain Cook in 1832, 1833 and 1836. 
The Guard consisted of 1 sergeant, 1 corporal and 8 privates of the 4th regt., 8 privates of 17th regt, 3 women and 2 children under the orders of Lieut. Gibbons of 49th regiment. Passengers included Mrs. Gibbons and three children.
After embarking the Guard at Deptford on 10 September 1831 the Captain Cook proceeded to Dublin where 200 male prisoners were embarked on 27th October 1831.
The prisoners came from cities and towns throughout Ireland - Antrim, Dublin, Wicklow, Cavan, Tyrone, Meath, Monaghan, Armagh, King's County, Queens County and Fermanagh. They were held in county prisons before being transferred to the hulk to await transportation.
In May 1832 after complaints were made as to the state in which prisoners were transmitted from the county gaols to the hulks, New Orders were issued regarding the transfer of prisoners and it was expected that they would be free of disease and fit to embark and that they would be clean, adequately clothed with their hair cut close. There were to be no transfers on Sundays, no spirits or tobacco would be allowed on the road and knives and other dangerous articles were taken from them, however when the prisoners of the Captain Cook were transferred in October 1831 the old system was still in place and they probably arrived at the hulk poorly clothed and already ill.
Their crimes were mostly of theft, assault, house robbery, vagrancy, forgery and embezzlement. There were no prisoners convicted of white boy crimes on the Captain Cook.
On the 5th November they departed Dublin and shortly afterwards experienced very bad weather and being unable to keep to sea were obliged to put into Milford Haven on the 8th where they remained wind bound until 27th November 1831.
SURGEON EBENEZER JOHNSTONE
Ebenezer Johnstone kept a Medical Journal from 28 October 1831 to 15 April 1832.....
He remarked that the general health of the convicts was extremely good, having a better diet than they usually were accustomed to while they were in port. Quite a few suffered from catarrh which the surgeon attributed to the defective clothing they were supplied with in Dublin. (1)
Ebenezer Johnstone was also employed as surgeon on the convict ships William Miles in 1828 (VDL) and Manlius in 1830 (VDL).
As they entered the Tropics the prisoners suffered severely from seasickness and constipation, several of the cases from seasickness being old men becoming very reduced and debilitated required cordials and additional diet. During January the men continued extremely healthy, diseases chiefly from exposure of the head to the sun, and vertigo, which was relieved by the use of lancet, free evacuation and cold applications, several of the elderly prisoners began to show scorbutic symptoms and complained much of debility. In February and March 1832 there was hazy drizzly weather and several days of heavy rain.
Two prisoners died on the passage out - Francis McCormick and Joseph Murphy. The surgeon attributed the death of one of them to an addiction to gambling his provisions - the prisoner's health had at first improved under the surgeon's care, however the man managed to obtain an opportunity of either losing his allowance or obtaining a double or triple quantity which invariably aggravated his complaints. 
The Captain Cook arrived in Port Jackson on 2 April 1832.
The prisoners were mustered by the Colonial Secretary on 6th April 1832. Indents include name, age, religion, education, marital status, family, native place, trade, offence, date and place of trial, sentence, prior convictions and physical description. There is no information in the indents as to where and to whom the prisoners were assigned on arrival. There is occasional information about colonial crimes, deaths, pardons, etc.
There were ten very young convicts on the voyage - James White, James Murray, Hugh McGurdy, Arthur Finn and Michael Dunn were all sixteen years of age; John Kelly was fifteen; Adam Ballantyne and Thomas Cox were both thirteen years of age. The youngest two were only 12 years old - James Corcoran and Michael Clancy, both errand boys from Dublin convicted of stealing; both in following years were punished severely for colonial crimes.
Prisoners were landed on Monday 16th April 1832 and inspected by the Governor before being assigned to various settlers and government employment.
DEPARTURE FROM SYDNEY
The Captain Cook departed Sydney for Launceston 15th May 1832 and departed there on 8th August and St. Helena 1st September arriving back in England late January 1833.
1). Seventy-seven prisoners who arrived on the Captain Cook in 1832 have so far been identified as residing in the Hunter region in the following two decades. Select here to find more about Hunter Valley convicts/ passengers of the Captain Cook.
2). Belfast Sessions - Sentences -William John Bell, George Saunders, John Gurney, Archer Finn, and Hugh McGrady, all for larceny, sentenced to seven years' transportation each - Belfast Newsletter 26 July 1831
3). Bushranger John McIntyre (McTeer) also arrived on the Captain Cook
4). Dublin - Recorder's Court - Patrick Donohoe, for felony, sentenced to 7 years transportation - Freeman's Journal 28 June 1831.
5). Convict Ships bringing detachments of the 4th (King's Own) Regiment
Jane departed Cork 29 April 1831. Commander of the Guard Captain George Mason
Surry departed Portsmouth 17 July 1831. Commander of the Guard Captain Charles Waldron 38th regt.
Asia departd Cork 6 August 1831. Commander of the Guard Captain Richard Chetwode
Norfolk departed 15 October 1831. Commander of the Guard Lieut. David William Lardy 4th regt.
Captain Cook departed Dublin 5 November 1831. Commander of the Guard Lieut. Gibbons 49th regt.
Isabella departed Cork 27 November 1831. Commander of the Guard Captain William Clarke 4th regt.
Bussorah Merchant departed Dublin 14 December 1831. Commander of the Guard Lieut. William Lonsdale 4th regt.
John departed the Downs 7 February 1832. Commander of the Guard Lieut. George Baldwin 31st regt.,
Lady Harewood departed Portsmouth 15 March 1832. Commander of the Guard Lieut. Lowth 38th regt.,
City of Edinburgh departed Cork 18 March 1832 . Commander of the Guard Lieut. Bayliss
Clyde departd Portsmouth 9 May 1832. Commander of the Guard Lieut-Colonel Mackenzie
Eliza departed Cork 10 May 1832. Commander of the Guard Lieut. Hewson
Planter departed Portsmouth 16 June 1832 under command of Lieuts. Bullin & Irvine of 38th regt.
Hercules departed the Downs 19 June 1832. Commander of the Guard Lieut. Gibson 4th regt.
Dunvegan Castle departed Dublin 1 July 1832. Commander of the Guard Lieut. Thomas Faunce 4th regt.
Parmelia departed Sheerness 28 July 1832 under Command of Captain Young 38th regt.
Waterloo departed Sheerness 12 March 1833 under Command of Captain Mondilhan 54th regt.
5). National Archives - Reference: ADM 101/16/1 Description: Medical journal of the Captain Cook, convict ship from 28 October 1831 to 15 April 1832 by Ebenezer Johnston, surgeon and superintendent, during which time the ship was employed in making a passage to New South Wales.
6). NewOrdersfor prisoners transmitted from county gaols to hulks and depots - 1832.... Circular Notice from the Inspectors General of Prisons to the Medical Officers of the Gaols in Ireland, with reference to Medical Certificates for Convicts. Dublin, 25th May 1832. -
Complaints being made by the Superintendent of the Convict Service of the State in which Prisoners are transmitted from many of the County Gaols to the Hulks and Depot, his Excellency the Lord Lieutenant has been pleased to direct that the following Regulations be circulated to the Gaols of the several Counties, and strictly obeyed :—
I.—Convicts, prior to their Transmission to the Hulks or Depot, are to be inspected by the Medical Officers of the County Gaols from which they are respectively removed, and certified by them to be free from Itch or other Disease; and any Prisoner who is unfit for the Journey and Voyage is to be detained until further Orders. Every auch Case is to be reported by the Local Inspector of the County Gaol to Government, supported by the Affidavit of the Medical Officer, who is to transmit, by the Person in charge of the Convicts, a general Certificate of the Health and Freedom from Itch.
II.—On the Arrival of the Convicts at the Hulk or Depot, and Examination being made by the Medical Officer there appointed to inspect them, if it shall appear that any Prisoner is labouring under Disease, and unfit to embark, or affected by Itch, a Report of the Case is to be made to Government by the Superintendent of the Convict Service, specifying the Name, the Disease, the County, and the Name of the Medical Officer by whom the Certificate was signed.
III.—In the Event of any Prisoner being so reported an Investigation will be immediately ordered, and a serious Responsibility will attach to Medical Officers if it shall appear that a careless Inspection has taken place, or that Itch or other curable Disease shall appear to have been neglected in the County Gaol. Attention to the cleansing and Use of the Bath for all Prisoners, on their Committal to a County Gaol, would afford much Security on this Head.
IV.—All Convicts are to be clothed, on leaving the Counties, in strict Conformity with the Orders of Government, according to the Schedules which accompany the Warrants for their Removal; they are to be in a cleanly State, and their Hair cut close.
V.—No Children, except those on the Breast, are to be permitted to accompany the Convicts.
VI.—No Prisoners to be removed on Sundays. No Spirits or Tobacco to be allowed on the Road. Knives and other dangerous Articles to be taken from the Convicts. All Money to be taken in charge by the Governor of the County Gaol, and transmitted by the Person in charge of the Convicts to the Superintendent of the Hulk or Depot.
VII.—All the Governors of Gaols and Keepers of Bridewells, at which the Escorts may stop, are called upon to observe closely the Conduct of the Convicts, and of those in charge of them upon their Route, and to report any Irregularity to the Inspectors General of Prisons. If any Omission of such Report shall be discovered, the Governor or Keeper will be held responsible.
VIII.—A printed Copy of these Regulations is to be posted up at all Times, in a conspicuous Place, in every Gaol and Bridewell in Ireland.
 Journal of Ebenezer Johnstone. Ancestry.com. UK, Royal Navy Medical Journals, 1817-1857. Original data: The National Archives. Kew, Richmond, Surrey.
 Bateson, Charles & Library of Australian History (1983). The Convict Ships, 1787-1868 (Australian ed). Library of Australian History, Sydney : pp.350-51.