Harvard and Yale played a rugby challenge match in 1875. The second meeting came in 1876 and was played a few days before the formation of the Intercollegiate Football Association, which established the first standard rules for American football. Freshman Walter Camp played for Yale in the 1876 game and had not yet fathered football. Still, there are some interesting elements in the game reports.
Based on the photo and the description of Yale placing the ball on the ground before the goal-from-field during open play, I assume they were playing with a round soccer like ball.
I also read years ago that pre-1876, a goal from the field (field goal) wasn't even permitted, that the try-at-goal after a touchdown was the only way to score, though I haven't found much else about this since the rules during that era are murky.