If you read the commentary on Diagram 2, that’s a kickoff formation. Later you find Diagram 6, which he calls “The formation of the side which has the ball in a scrimmage,” that is, a team lining up for a normal play. In this diagram, the backs are lined up in a triangle, and his references to a “goal tend” as the fullback make it quite clear that this deepest man is the fullback. Diagrams 8 and 12, the other ones of teams prior to a snap when they aren’t kicking, show a similar backfield.
Walter Camp also says this in that book, in a chapter titled “Development of the Names of the Various Positions:”
This seems to pretty conclusively show that the name “quarter-back” originates from position on the field, since Camp explains that the “three quarter back” was based on position on the field. I don’t think it’s much of a stretch to say he is implying the same about the quarterback.
In addition, the article that zut linked to says this:
I think it’s clear from this, as well, that the fullback is set deeper than the halfbacks.
Again, please note that the article in question is written much later, and that it makes that statement despite the fact that the book to which zut has given reference does not use the name “T” formation for it. A “T” formation, in every contemporary reference I’ve been able to find, refers to a formation where the “fullback” is lined up square with the “halfbacks”, thus making a “T” when the quarterback is considered the downstroke.
And as for the origin of the names, again, let’s point out that the term “quarterback” appears to have been involved in naming a position used in 20-a-side rugby football in Scotland even prior to the use in America, if the links I gave above are to be believed. It is likely the American use of the term derived from its already accepted usage in Rugby football, though confirmation of this fact would be nice.
Hum. I poked around some more, and the best I could do was Scottish Football Reminiscences, which was written in 1890. Talking about a 1872 rugby match, the author says in passing, “If ever a man could handle a ball and kick a goal as a quarter-back in a Rugby game, it was Chalconer.” There’s the clear implication Chalconer was playing a “quarter-back” position in 1872 (before the term was introduced in American football), but since the book was written 20 years later, that’s hardly conclusive.
Also, from 1901 Blackwood’s Edinburgh Magazine: “Sometimes three full-backs, invariably two, were played; sometimes there wer e two three-quarters, sometimes only one; and originally there was only one half-back–called “quarter” in Scotland, a position said to have been invented by a current occupant of the Scottish Bench, who played, and played well, in the first international.” Again, not conclusive, but suggestive.
ETA: “Three quarter back” was certainly used in rugby before “quarter back” wasa used in American football.: THe Gentleman’s Magazine, 1873
I think it is pretty clear that the concept of designating a back by what portion of the whole he is back from the line comes from Rugby. American football, being a Rugby offshoot, simply adopted the terminology. I suspect that the “quarter” back, being a term that was not universal in Britain (limited, perhaps, to Scotland), didn’t make it into the lexicon until around 1879, when someone used it to designate the position that Camp wanted to mandate the existence of (ball receiver on restarts).
