What was a "protracted sojourn?"
From 1882 to 1903, ship manifests of alien passengers to the United States included in column 10 a designation as "transient, in transit, or intending protracted sojourn."
It is the last designation that we see on the early Eilertsen manifests. Indeed, not just the Osmundsens but seemingly every one of the passengers and crew on those sailings was intending a protracted sojourn in America.
At this time in American history, immigration to the United States was still relatively unrestricted, especially for Europeans. While the passenger manifest itself was not an immigration document, the "protracted sojourn" designation was used for those planning to immigrate.
Or in the case of these early Eilertsen crossings, the PS also covered coming over for a few months or years, getting the lay of the land, making some money working on the ships and docks, and then returning home to Norway.
The forms changed after 1903 and then the laws became much more restrictive in 1924.
Three waves of immigration between 1850 and 1924 brought about 1 million Norwegians to the United States. Most settled in the upper midwestern states but there were important Norwegian enclaves in other locations such as Brooklyn, New York.
