It turns out the Morrill Land Grant Act, enacted in 1862 during the Civil War, included some vague language about military training. It's language on the purpose of colleges with the money athorized reads:
the endowment, support, and maintenance of at least one college where the leading object shall be, without excluding other scientific and classical studies, and including military tactics, to teach such branches of learning as are related to agriculture and the mechanic arts, in such manner as the legislatures of the States may respectively prescribe, in order to promote the liberal and practical education of the industrial classes in the several pursuits and professions in life. [emphasis added]
The language is awkward, but the reasonable interpretation is the colleges is to focus on agriculture and mechanic arts but also including classics and science, including military. Apparently the phrase was added late, as earlier versions of the act preceded the Civil War.
The meaning of "industrial classes" is "working people", a little more expansive than "working class".