The Henry Wellesley was built in India in 1804.
Prisoners came from counties in England and Wales - London, Lancaster, Buckinghamshire, Lancastser, Devon, Worcester, Warwick, Salop, Cumberland, York, Surrey, Somerset, Hertford, Lincoln, Essex, Kent, Northumberland, Nottingham, Cambridge, Hereford, Berks, Southampton, Oxford, Gloucester, Sussex, Wiltshire, Norfolk, Denbigh, Flint, Pembroke, Glamorgan and Carmarthen. 
One hundred and forty women were received onto the Henry Wellesley between 26th June and 12th July 1837.
Mary Ann Bignell who was tried at the Old Bailey on 12th June was re-landed prior to sailing and Ann Platten who was suffering from venereal disease was returned to the keeper at Newgate for a time before being re-embarked.
Surgeon William Leyson
This was William Leyson's only appointment to a convict ship taking prisoners to Australia. He kept a Medical Journal from 2nd June 1837 to 3 January 1838 -
On the 26th June 1837 the first prisoners were received on board at Woolwich to the number of thirty-one with seven of their children from Newgate and from that time to the 12th July we almost daily continued to receive from the various prisons in England and Wales to the amount in all, of one hundred and forty-three prisoners and twenty nine children, the last eleven and one child arriving from Newgate. The general health of the prisoners on their reception was good when previous incarceration for six months in some instances is taken into consideration, and at the time the vessel sailed from Woolwich on the 20th July, a great improvement was visible in their appearance and condition. 
Marie Smith alias Caroline Bernard a widow in her 30's who was a native of France and had been convicted at the Old Bailey of stealing articles of jewelry, was employed as Hospital Matron on the voyage out.
The Henry Wellesley departed London on 20 July 1837.
William Leysom made note in his journal of the amusements and occupations he allowed the prisoners during the voyage:
On putting to sea the greater number of the prisoners were affected by sea sickness, some of them very severely and many of them continued to be so affected in heavy weather during the whole of the voyage; they were all notwithstanding daily sent on deck when the weather was dry, with the exception of those prevented by disease. We were detained in the Channel until the 9th August by contrary winds and occasional very heavy gales, in which the women suffered severely from sea sickness. As I consider that tranquillity of mind is most essential to bodily health, I set out in my superintendence of the convicts by having no more restrictions on them than their unhappy situation necessarily demanded, and I therefore caused them all to be let on deck from an early time of the morning until the close of the day, whenever the weather would permit and in showery days they were only sent below during the occurrence of the rain. They were allowed to amuse themselves by running about, dancing or in any innocent way whenever the duty of the ship would admit of it. Many of them were attentive to school and the attendance of the young ones there I insisted on. The patchwork and knitting served out, employed their attention most usefully. 
The prison deck was thoroughly cleaned daily after breakfast by dry holystoning with sand, and afterwards minutely inspected by myself and I found that the power afforded me of rewarding them for cleanliness etc by the allowance of a little tea and sugar very materially quickened their zeal. Hanging stoves when necessary were used and chloride of lime was frequently used. The beds were sent on deck daily, except when the weather was too bad, when they were rolled up tidily and stowed in the bed places and in fine weather the bedding was frequently aired. There was a constant washing day once a week, and I remark except in very few instances, that there was a general attention to personal cleanliness and attire.
I was particular in preventing fighting which was the most usual infringement of any regulation; improper language towards each other or in my hearing I always repressed and any attempt at theft or prostitution I punished by more than the usual restraint. 
The ship arrived within the heads of Port Jackson on the 22nd December 1837 in a gale of wind which prevented us from proceeding up the harbour, and it was not until the 25th that we anchored at Sydney Cove, being a period of one hundred and fifty-eight days since our departure from Woolwich.
There were no deaths of prisoners on the voyage however sixteen month old James Hemsley, son of Maria Hemsley died of encephalitis. He had been sickly prior to embarking according to the surgeon.
The convict indents include name, age, education, religion, marital status, family, native place, offence, date and place of trial and physical description. There is no indication in the indents as to where the women were assigned however there are occasional details of relatives already in the colony and sometimes other interesting details.
Isabella Arnett's brother Edward Arnett was a prisoner at Hobart per Recovery 1837
Ann Beresford alias Mary Lee - Husband Thomas Beresford, a prisoner, transported same time for same offence for life
Elizabeth Bottomley age 60 was the mother of Ellen Bottomley age 20, both convicted of the same crime.
Ann Capper - Husband Thomas Capper, prisoner for life per Prince George
Mary Edwards - Husband Joseph Edwards transported for the same offence
Elizabeth Gilthorpe - Husband William Millington a prisoner at Hobart per Elphinstone in 1837
Agnes Hamilton- Blind in the right eye.
Elizabeth Jackman alias Smith - Sister Maria Jackman arrived per Diana, prisoner for life.
Jane Laxton - Rather deaf, Sister Martha Tucker, prisoner at VDL.
Elinor Richards - Speaks Welsh only
Alicia Robinson - Sister Caroline McCarthy aged 16 years on board
Eliza Stephenson - Blind in left eye
Ann Tandy - Son James Tandy transported for 7 years 
The women spent their first Christmas in Australia on board the Henry Wellesley as they weren't disembarked until 3rd January 1838. Only one woman remained on the sick list and she was well enough to be assigned to a master the same day. The prisoners when landed were said to make a very decent appearance and the authorities at Sydney seemed to be well satisfied with the treatment which the prisoners had received and with their healthy state and condition on landing.
1). The Henry Wellesley called at the Cape of Good Hope on the voyage out. There was apparently also an extra passenger on the Henry Wellesley. In 1838 the Sydney Monitor and the Sydney Gazette reported that a woman, named Eliza Barnett or Shearer, was committed take her trial, for escaping from the colony. She had been tried at the Surry Quarter Sessions, on the 9th April, 1832, she was convicted and sentenced to seven years transportation.
This woman was Eliza Barrett, a needlewoman from London who was convicted man robbery and transported on the Fanny in 1833. Shortly after arrival she married a man named Thomas Shearer and as a matter of course was assigned to him. On 18th April, 1835, she absconded from her husband and lived for some time ashore under the protection of the Mate of a vessel about to sail to England. When the ship sailed, she was taken on board and concealed by the mate. After the vessel had been at sea she was discovered by the Captain who on the arrival of the vessel at St. Helena delivered her to the authorities there as a runaway convict. She remained at St. Helena until a vessel for the Cape of Good Hope arrived by which she was forwarded there and remained in custody for twenty months until the Henry Wellesley arrived when she was put on board and conveyed to Sydney. She had an infant in her arms about six months old. On her return to the colony she was sentenced to twelve months in the
Parramatta Female Factory. The question of punishment for prisoners who were returned to the colony after escaping was raised when it was found that consequences for male convicts was much harsher than for females.
2). The Henry Wellesley was one of four convict ships bringing female prisoners to New South Wales in 1837, the others being the Sarah and Elizabeth, Margaret and Sir Charles Forbes. A total of 533 female convicts arrived in the colony in 1837.
4). Catherine Johnson arrived as a prisoner on the Henry Wellesley. She married John Harrison (per Burrell 1830) at Newcastle in 1838. Catherine and John Harrison were murdered by Michael Bradley at Maitland in 1841.
5). The following Petitions have been transcribed by researcher Keith Searson in UK in conjunction with Colette McAlpine of the Female Convict Research Centre in Tasmania.....
Caroline Parker - Aged 29, York Lent Assizes, March 1837. Sentence commuted to transportation for life. Gaol Report - Thief for Several Years. Convictd before. Wheatly near Doncaster March 29th 1837. Source Home Office Criminal Petitions, Series 1, SERIES - HO 17 PIECE NUMBER - 80 ITEM NUMBER - OX 4
My Lord, Having served on the Grand Jury at York these spring assizes we beg to recommend to your Lordship the case of CAROLINE PARKER implicated in a highway robbery. Her superior education, her youth and unfortunate circumstances seem to us to render her a fit object for the commutation of punishment which has been so restored to substituting confinement in the Penitentiary for transportation. We believe Mr Justice Patteson will support our recommendation. We remain your Lordships obedient servants William B Cooke Richard M Milne - To the Right Honourable Lord Russell.
Ann Dixon, Norwich 1836. Stealing a Duck 7 years transportation. Source - Home Office Criminal Petitions. Series 1
SERIES - HO 17 PIECE NUMBER - 29 ITEM NUMBER - CX 1 GAOL REPORT - Character very bad, thrice before convicted.
To the Right Honourable Lord John Russell Secretary of State for the Home Department The Petition of FULLER DIXON of the City of Norwich - Coach Maker. Humble Sheweth That ANN DIXON (the Sister in Law of your Petitioner) who is of the aged of forty six years and convicted at the October Sessions 1836 held in and for the City of Norwich and county of the same city of a felony and sentence to be transported for the term of seven years and that she now remains in the gaol of the said city pursuant of such sentence. That since the conviction of the said ANN DIXON her husband suddenly expired of an apoplectic fit leaving three small children totally unprovided for. That from the contrition and penitence expressed by the unfortunate object of this Petition as also her conduct in gaol since her conviction and from the state in which her helpless family are left, YOUR PETITIONER MOST HUMBLY PRAYS that your Lordship will be pleased to take unto your merciful consideration and interest in her behalf for a mitigation of her sentence with the sincere hopes of your Petitioners that she may return to the path of honesty, industry and by her future good conduct make an atonement for having offended the Laws of her Country. And your petitioner as in duty bound will ever pray. Fuller Dixon
We the undersigned inhabitants of the City of Norwich well knowingly your Petitioner and the circumstances mentioned in this Petition beg to recommend the prayers therein contained: John Angell - Magistrate of the City of Norwich James Reynolds - Town Councillor Charles Turner - Major of Norwich at the time of the conviction Robert Worthly - Town Councillor John Cully - Wine Merchant To the King Most Excellent Majesty
The humble Petition of ANN DIXON the wife of JAMES DIXON Sheweth That your Petitioner was tried at the General Quarter Sessions of the Peace held at the Guildhall in and for the City of Norwich on Tuesday the 18th day of October 1836 on an indictment of stealing a duck the property of THOMAS SPINKS and convicted and sentenced to be transported for seven years. That your Petitioner is forty six years old and had a husband and three children. That your petitioner in consequence of her age and other causes, is fully convinced that if transported beyond the seas, her health would be much affected and her life probably endangered. Your Petitioner confidently relying on the Royal clemency anxiously prays that it may be extended to her on the present occasion and humbly trusts that His Most Excellent Majesty will cause the sentence to be commuted to that of imprisonment for such a term as he in his mercy may think proper to direct. And your petitioner will ever pray Ann Dixon We the undersigned having known the above named prisoner ANN DIXON many years, beg leave to recommend her to the merciful and gracious consideration of His Majesty as a fit object for the Royal clemency. John Sparrow - Master Baker Dawson Kent - Carter in General Robert Skeet - Master Bricklayer Henry Parfitt - Master Painter Henry Danials - Dealer George Hudon - Master Carpenter Peter Thompson - Dealer James Smith - Gent. I THOMAS SPINKS Prosecutor does hereby recommend ANN DIXON to your mercy James Moore - Churchwarden and Overseer for Norwich.
John Ward had a special commission from Lord John Russell to inspect a number of prisons. He visited Clerkenwell, the Westminster Bridewell, Aylesbury and Chelmsford and about 12 other gaols.
He gave evidence before Sir William Molesworth in February 1838....He enquired of convicts of their views with regard to transportation and whether they had any idea as to what the punishment meant. He found that they were generally very ignorant of what it would mean and of the place they were going or the punishment that awaited them but thought it could not be worse than prison in England.
In the female department of Aylesbury gaol, he spoke to Eliza Arran, who was under sentence of transportation, who was totally ignorant of her probable situation on arrival. In Chelmsford Gaol he examined Hannah Courtman, under sentence of seven years' transportation for a theft; she said,having lost my character, I shall be very glad to go. (Hannah later married John Anderson and raised a large family in New South Wales)