Origin and earliest recorded use of 'fungo'
Solution 1:
The Eleventh Collegiate Dictionary is mistaken about "fungo bat" being only from 1926.
There is an ad in the 1916 Spalding's Official Base Ball Record :
No. F Hardwood "Fungo" Bat. 38 inches long, thin model.
An early meaning of "fungo" is given in the 1874 Chadwick's base ball manual, which has a section titled "Terms" in which there is an entry on page 54:
FUNGO.
This is a style of batting useful only in affording out-fielders a chance for practice in taking long, high balls on the fly. It, however, gets the batsman out of good batting form, for he has to hit the ball as it falls perpendicularly, and not as it comes to him in pitching, nearly horizontally.
An earlier use of the word "fungo" is from the 31 May 1871 Brooklyn Daily Eagle, page 4:
This is not skillful batting-it is little else than "fungo" hitting
And even earlier from the 2 April 1870 New York Clipper page 413:
They should certainly stop "fungo" batting, for nothing gets a batsman's sight out of training sooner than batting at a ball which drops perpendicularly, as in fungo
As to the origin, The Dickson Baseball Dictionary discusses 5 different theories of word origin.
One unresolved issue is whether or not "fungo" or "fungoes" is the original form of the word. Dickson and others cite to Chadwick's 1867 The Base Ball Player's Book of Reference which gives a short list of "Technical Terms to Base Ball" and includes on page 138:
FUNGOES.—A preliminary practice game in which one player takes the bat and tossing the ball up hits it as it falls, and if the ball is caught in the field on the fly, the player catching it takes the bat. It is useless as practice in batting, good for taking fly balls.
"Fungoes" and "fungo" also referred to a game played of its own right, no just as practice for baseball.
In fact, according to the 1893 The Eagle and Brooklyn... volume 2 :
fifty years ago ... Schoolboys played a sort of ball game they called "old cat" or "fungoes," a kind of apology for the base-ball of to-day
There is also the 1887 short book Jack Winthrop of Old 15:
The scene of this story is the Old Fifth Street school. It is a truthful narrative, without any exaggeration, of the career of a former pupil from his entrance into the Primary to the day of his graduation... 40 years ago... He could play "Fungoes" before he knew the alphabet
and the October 1888 Cosmopolitan article Our National Game says the game fungo preceded baseball:
Naturally the first form of play was what we now call “fungo-hitting;” that is, he hit the ball in the air for his companions to catch.