The United States federal 1890 census was destroyed.
Only about 6000 counted people appear on what's left of it.
The years between 1880 and 1900 were ones of major immigration in the United States and major changes in society and culture. So that's 20 years for which the researcher must use alternative methods to find their ancestors, especially if they immigrated into the United States during that time. It's a long period of time and millions of people who at first, when you depend on census, appear to be missing.
Among the records that can be used are County Histories (books often put together by and paid for my the citizens which include photos and bio/profiles which are more like yearbooks as well as more literary efforts by professors and historians), City Directories (pre phone book listings that individuals paid for, though there were advertisers and sponsors), STATE CENSUS, ship manifests that record the destination location or address, Military Records that show an individual enlisted, served, or received a pension or benefit as well as draft records, NATURALIZATION RECORDS that begin with the Declaration of Intent, newspaper articles (such as one's I've found that list the names of the men who recently were sworn in as citizens) that may contain wedding announcements, business advertisements, as well as obituaries), and so on.
So many local historical society volunteers take pride in knowing about families in small towns especially I think its worth trying to talk to them. (I met one man whose family had been in Los Angeles for 6 generations beginning with Andras Pico, one of the founding fathers, at a celebration event at a local historical site.)
The Declaration of Intent (to become a citizen) and the Ship Manifest (document of arrival in the United States at any one of several port, New York being the busiest) are two documents I always attempt to find for immigrants of the Industrial Age. On the Declaration the person states how and where and on what date they entered the country. So they will say the name of the ship and between these two you are likely to find one or two addresses for them in their early years in this country. Sometimes Ship Manifests, despite the Ellis Island, Ancestry databases, and so on are difficult to find because they appear missing but are perhaps not showing up where they should be kept digitally. So if you find the name of the ship and harbor and date of arrival in the Declaration of Intent you may be able to find it using one of the alternative search features provided by stephenmorse.org (http://stevenmorse.org/). If the ship manifests still appears to be missing, try for records that document passengers leaving a port or arriving at a port in another country such as Germany or The United Kingdom.
There's a romance to the era of the big steam ships and images of the ship and reading through the manifests to get a feeling for the passengers on the ship besides your ancestor makes for interesting reading and history, but perhaps the addresses and relationships give you the most information to go on with.
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