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Embarked: 256 men
Voyage: 158 days
Surgeon's Journal: no
Previous vessel: Lady Juliana arrived 3 June 1790
Next vessel: Neptune arrived 28 June 1790
Master Nicholas Anstis
Surgeon William Waters
Surgeon's Mate John Harris
Second Fleet convict ships Surprize, Neptune and Scarborough departed Portsmouth in January 1790. Many of the prisoners were already ill when they left England and by the time they reached the Cape of Good Hope, thirty five prisoners had died. 
Captain William Hill of the New South Wales Corps commanded the guard on the Surprize. In July 1790 he wrote to Mr. Wathen telling in part some of the misery of the voyage.
They sailed from Cowes Harbour 17th January and arrived in False Bay Cape of Good Hope on 13th April......
We met so violent a tempest, which continued for six and thirty hours, that left us no room even to hope an escape from a watery grave. It being the winter season at our arrival was the reason of our anchoring in False Bay as the safest harbour, otherwise Table Bay in fine weather or in the summer season, is much to be preferred, being contiguous to the Cape Town
Here I had some conversation with the unfortunate Mr. Riou of the Guardian; the loss of his ship will be severely felt by this colony, and I much fear the Dutch are taking every advantage of his situation, charging enormous sums for warehouse room and fresh provisions for the men, so that the cargo must, ere now, be insufficient to defray the cost. 
We left the Cape on 29th April. Would I could draw an eternal shade over the remembrance of this miserable part of our voyage - miserable, not so much in itself, as rendered so by the villainy oppression and shameful speculation of the masters of two of the transports. The bark I was on board of was, indeed unfit, from her make and size, to be sent so great a distance; if it blew but the most trifling gale she was lost in the waters, of which she shipped so much; that, from the Cape, the unhappy wretches, the convicts, were considerable above their waists in water, and the men of my company whose berths were not so far forward, were nearly up to the middles. In this situation they were obliged, for the safety of the ship, to be penned down; but when the gales abated no means were used to purify the air by fumigations no vinegar was applied to rectify the nauseous steams issuing from their miserable dungeon. Humanity shudders to think that of nine hundred male convicts embarked in this fleet, three hundred and seventy are already dead and four hundred and fifty are landed sick and so emaciated and helpless that very few, if any of them, can be saved by care or medicine, so that the sooner it please God to remove them the better it will be for this colony which is not in a situation to bear any burthen, as I imagine the medicine chest to be nearly exhausted, and provisions are a scarce article.
The irons used upon these unhappy wretches were barbarous. The contractors had been in the Guinea trade, and had put on board the same shackles used by them in that trade, which are made with a short bolt instead of chains that drop between the legs and fasten with a bandage about the waist, like those at the different gaols; these bolts were not more than three quarters of a foot in length so that they could not extend either leg from the other more than an inch of two at most; thus fettered, it was impossible for them to move but at the risk of both their legs being broken.
My feelings never have been so wounded as on this voyage, so much so that I never shall recover my accustomed vivacity and spirits; and had I been empowered, it would have been the most grateful task of my life to have prevented so many of my fellow creatures so much misery and death...26th July 1790 
The Fleet arrived at Port Jackson in June 1790, a voyage of 158 days.
David Collins in An Account of the English Colony wrote of the arrival of the Second Fleet.....
.....And on the following day the Surprise transport, Nicholas Anstis master (late chief mate of the Lady Penrhyn) anchored in the cove from England, having on board one captain, one lieutenant, one surgeon's mate, one serjeant, one corporal, one drummer, and twenty three privates of the New South Wales corps; together with two hundred and eighteen male convicts. She sailed on the 19th January from Portsmouth in company with two other transports with whom she parted between the Cape of Good Hope and this place. We had the mortification to learn that the prisoners in this ship were very unhealthy, upwards of one hundred being now in the sick list on board. They had been very sickly also during the passage and had buried forty two of these unfortunate people
A hospital was said to have been established a little north of the present alignment of Argyle Street, on the west side of Sydney Cove in July 1788. 
The Surprize departed Port Jackson bound for Norfolk Island on 1st August 1790 with provisions and 35 male and 150 female convicts, two superintendents and one deputy commissary. The arrival of Surprize and the storeship Justinian brough relief to the isolated island. Marine Ralph Clark wrote of his joy at seeing the familiar face of Surprize's master Anstis, - A little after Sun Set I got on board of her and found her to be the Surprize of London, Captain Anstis from Port Jackson and Convicts for this Island and that the other Ship which was but just in Sight from the mast head of the Surprize was the Justinian Store Ship also with Provisions but no Convicts for this Island..... Anstis was first Mate of the Lady Penryn when he came out with us - he was very glad to See me I much more So him on Account of his bringing us Some thing to eat.
Justinian and Surprize standing into Sydney Bay, Norfolk Island, 23 August 1790
Surprize left Norfolk Island for Canton on Sunday 29 August, arriving on 26 October 1790.
NOTES AND LINKS
1). This was the same vessel that made the voyage in 1794
2). On 29th September 1794 the Belfast Newsletter reported of the fate of Captain William Hill...The following melancholy circumstance is mentioned in a letter, received from the Shah Hormuzear, dated the 20th ult. lately arrived at Tellicherry from Botany Bay....'A most unhappy occurrence befell us in a newly discovered island near New Holland. Mr. Carter a young gentleman late of Calcutta and Captain William Hill of the New South Wales corps, with six other Europeans, who had gone ashore with one of our boats were cut off by the natives, and were devoured by these animals'
3). Jasper Harris arrived as a convict on the Surprise. He died in July 1800 and was buried in the Old Sydney Burial Ground, as was William Waller who died in April 1806 and Thomas Holt who died in November 1807 and Henry Todd who died in September 1807
4). Convicts and passengers arriving on the Surprize in 1790
5). National Archives - Company's packet, repaired by Calvert, measured 1789, 3 decks, length 107ft 9in, keel 85ft 8in, breadth 29ft 5in, hold 13ft 3in, wing transom 17ft 8in, waist 1ft 1in, between decks 6ft 9in, 394 tons. Voyages: (1) From Bengal 1783. Capt David Asquith. Left Bengal 22 Apr 1783 - 11 Sep River Shannon - 17 Oct Downs. (2) 1783/4 Bengal. Capt David Asquith. 23 Jan 1784 - 16 May 1785. (3) 1785/6 Madras and Bengal (to remain). Capt David Asquith. Downs 10 Jul 1785. (4) From China 1790. Capt N Anstis. Whampoa 4 Feb 1791 - 29 Apr Anger - 8 Jul St Helena - 6 Sep Downs. (5) From Bengal 1795. Capt Patrick Campbell. Calcutta 16 Nov 1795 - 16 Feb 1796 St Helena - 21 Apr Kinsale - 9 May Downs.
6). The detachment of New South Wales Corps on the Surprize was sent to replace the Marines.
A list is included in the Historical Records of Australia Vol.1, p.193 dated 24 July 1790 -
Captains Nicholas Nepean, William Hill
Lieutenants - at Sydney - John McArthur, Edward Abbot, at Rose Hill - John Townson, Ensign John Thomas Prentice
Surgeon's Mate John Harris, (born at Moneymore, County Londonderry, Ireland in 1754 and trained for the medical profession at the University of Edinburgh. )
Privates 93. Three privates had died since October 22 1789. One drummer and six privates had deserted.
7). Convict Ships departing England for New South Wales in 1789 - 1790 - Lady Juliana, Guardian, Surprize, Neptune and Scarborough.
1. Central Queensland Herald 4 April 1935
2. Historical Records of NSW Vol 1., p. 366
3. Times [London, England] 31 July 1790: 2. The Times Digital Archive. Web. 9 Mar. 2013.