Final answer:
The third party with the greatest importance in the late nineteenth century was the 3) Populist Party, known for advocating reforms such as the regulation of railroads and direct election of U.S. senators. Their support for Democratic candidate William Jennings Bryan in 1896 and their eventual disappearance after 1908.
Step-by-step explanation:
The third party with the greatest importance in the late nineteenth century was the Populist Party. This party, also known as the People's Party, was formed in 1892, largely in response to concerns about the dominance of big business and the decline in the power of farmers and rural communities.
The Populist Party advocated for various reforms including the regulation of railroads, the implementation of an income tax, and the direct election of U.S. senators. Although the party did not achieve electoral success in presidential elections, with its candidate James B.
Weaver not performing as well as the major party candidates, its influence was felt during the 1896 election when it supported the Democratic candidate William Jennings Bryan. The Populist Party nominated their own candidates in subsequent presidential elections but eventually disappeared from the national scene after 1908.
Nonetheless, the party's legacy lived on as their ideas were absorbed into the platforms of other, more successful parties.