The following Act of March 1819 gives the legal backing as to what information was gathered.
BE ENACTED That, if the master or other person on board any ship or vessel, owned in the whole or in part by a citizen or citizens of the United States the territories thereof, or by a subject or subjects, citizen or citizens, of any foreign country, shall, after the first day of January, next, take on board of such ship or vessel, at any foreign port or place. -.or shall bring or convey into the United States, or the territories thereof from any foreign port or place; or shall carry,. convey, or transport from the United States, or the territories thereof to any foreign port or place, a greater number of passengers than two for every five tons of such ship or vessel, according to the custom-house measurement, every such master, or other person so offending, and the owner or owners of such ship or vessel, shall severally forfeit and pay to the United States, the sum of one hundred and fifty dollars for each and every passenger so taken on board of such ship or vessel, over and above the aforesaid number of two for every five tons of such ship or vessels to be recovered by suit in any circuit or district court of the United States, where the said vessel may arrive, or where the owner or owners aforesaid may reside; Provided nevertheless, that nothing in this act shall be taken to apply to the complement of men usually and ordinarily employed in navigating such ship or vessel.
SEC. 2. That if the number of passengers so taken on board of any ship or vessel as aforesaid, or conveyed or brought into the United States, or transported therefrom as aforesaid, shall exceed the said proportion of two to every five tons of such ship or vessel by the number of twenty passengers, in the whole, every such ship or vessel shall be deemed and taken to be forfeited to the United States, and shall be prosecuted and distributed in the same manner in which the forfeitures and penalties are recovered and distributed under the provisions of the act entitled "An Act to regulate the collection of duties on imports and tonnage."
SEC 3. That every ship or vessel bound on n voyage from the United States to any port on the continent of Europe, at the time of leaving the last port whence such ship or vessel shall sail, shall have on board, well secured under deck, al least sixty gallons of water, one hundred pounds of salted provisions, one gallon of vinegar, and one hundred pounds of wholesome ship bread for each and every passenger on board such ship or vessel, over and above such other provisions, stores, and live stock, as may be put on board by such master or passenger for their use, or that of the crew of such ship or vessel, and in like proportion for a shorter or longer voyage; and if the passengers on board of such ship or vessel, in which the proportion of provisions herein directed shall not have been provided, shall at any time be put on short allowance, in water, flesh, vinegar, or bread, during any voyage aforesaid, the master and owner of such ship or vessel shall severally pay to each and every passenger who shall have been put on short allowance as aforesaid the sum of three dollars for each and every day they may hare been on such short allowance, to be recovered in the same manner as seamen's wages are or may be recovered.
SEC. 4. That the captain or master of any ship or vessel arriving in the United States, or any of the territories thereof, from any foreign place whatever at the same time that he delivers a manifest of the cargo, and, if there be no cargo then at the time of making report or entry of the ship or vessel, pursuant to the existing laws of the United States, shall also deliver and report to the collector of the district in which such ship or .vessel shall arrive, a list or manifest of all the passengers taken on board of the said ship of Vessel at any foreign port or place; in which list or manifest it shall be the duty of the said master to designate, particularly, the age, sex and. occupation of the said passengers, respectively; the country to which they severally belong, and that which it is their intention to become inhabitants; and shall further set forth whether any, and what number have died on the voyage; which report and manifest shall be sworn to by the said masters in the same manner as is directed by the existing laws of the United States, in relation to the manifest of the cargo; and that the refusal or neglect of the maker aforesaid, to comply with the provisions of this section, shall incur the same penalties, disabilities, and forfeitures, as are at present provided for a refusal or neglect to report and deliver a manifest of the cargo aforesaid.
SEC. 5. That each and every collector of the customs to whom such manifest or list of passengers as aforesaid shall be delivered, shall, quarter yearly, return copies thereof to the Secretary of State of the United States, by whom statements of the same shall be laid before Congress at each and every session. . March 1819. approved. JAMES MONROE
Microfilm copies of many of the ship passenger arrival records are held in US National Archives. Some for Philadelphia predate the 1820 act but the rest are from 1820, though there are significant gaps in many records.
Some of the major ports are indexed - Baltimore (1820-1952), Boston (1848-1891 & 1902-1920), New Orleans (1853-1952), New York (1820-1846 & 1897-1948) and Philadelphia (1800-1948). Other minor ports may also be indexed. Note the large gap in the New York index.
You can request a search of these indices (for a fee) by the National Archives and Records Administration - requests on form 'NATF form 81' to General Reference Branch (NNRG), National Archives and Records Administration, 7th and Pennsylvania Avenue NW, Washington, DC 20408, USA. (Copies of the form can be requested from same address).
Although many names are readable and easily transcribed, it is obvious from the manifests I have seen than many names will be miss-indexed and thus will be not be found - Manx names, being unfamiliar to most English speakers, are particularly error prone.
Copies of the manifests of all ships arriving at New York 1820 to 1897 are available in National Archives Microfilm Publications Microcopy No. 237. Roll 10 covers the period 1 Jun1827 through to 6 November 1827.