The Distance Machine
Here are a few nineteenth- and early twentieth-century texts that we have run through the Distance Machine. All of these give good examples of how the program can find words that were not yet common at the time the texts were published. These include some words that became more common because their meanings became more general, some slang words that later became more accepted in formal writing, and some cases where a text was simply on the leading edge of the adoption of a new word.

Charles Babbage - “On the Economy of Machinery and Manufactures” (1832; UK English)
Charlotte Brontë - “Jane Eyre” (1847; UK English)
Thomas Carlyle - “Signs of the Times” (1828; UK English)
Wilkie Collins - “The Moonstone” (1868; UK English)
James Fenimore Cooper - “The Last of the Mohicans” (1826; US English)
Charles Darwin - “On the Origin of Species” (1859; UK English)
Charles Dickens - “Great Expectations [1867 edition]” (1867; UK English)
Frederick Douglass - “Narrative of the Life of Frederick Douglass, an American Slave” (1845; US English)
George Eliot - “Middlemarch” (1874; UK English)
Nathaniel Hawthorne - “The Maypole of Merry Mount” (1836; US English)
John Keats - “Poems Published in 1820” (1820; UK English)
Karl Marx - “The Communist Manifesto” (1848; translated by Moore & Engels, 1888; UK English)
Herman Melville - “Moby-Dick” (1851; US English)
Herman Melville - “Bartleby, The Scrivener” (1853; US English)
Mark Twain - “The Adventures of Huckleberry Finn” (1884; US English)
Mark Twain - “A Connecticut Yankee in King Arthur's Court” (1889; US English)
Mark Twain - “What Is Man?” (1906; US English)
Walt Whitman - “Leaves of Grass [1855 edition]” (1855; US English)

All of these texts were taken from Project Gutenberg with the exception of “Signs of the Times,” which is taken from here.
A more contemporary example is Barack Obama's 2015 State of the Union Address. Try moving the slider back to see which words were uncommon in 1800. (For comparison, here is the 2014 address.)
The Distance Machine also includes data from the EEBO-TCP Phase I corpus, which includes about 25,000 books published from 1500-1700. Here are a few texts from that collection:

Andrew Marvell - “Miscellaneous Poems” (1681)
John Milton - “Paradise Lost” (1667)
William Shakespeare - “Macbeth” (c. 1606)
William Shakespeare - “Shakespeare's Sonnets” (1609)

Comparing these examples to the ones from the nineteenth century shows how the patterns in language change differ from one time period to another. Since spelling was not yet standardized at that point, many of the changes that the Distance Machine identifies in this period have more to do with spelling than with usage; for instance, it seems that around 1560, people stopped using the spelling “tyme” in favor of “time.”
In addition to analyzing texts, the Distance Machine is also useful for examining the sets of words that are included in dictionaries and lexicons. As an example, here are the lists of headwords from the three dictionaries that are incorporated into the program: Webster's Compendious Dictionary (1806); Webster's American Dictionary (1828); and Webster's 1st International Dictionary (1913).
Of course, you can try the Distance Machine out on your own texts, too!