what was the function of the Roman cavalry?

[Felix]

Ardant du Picq says this about very deep formations:

"There is a point beyond which man cannot bear the anxiety of combat in
the front lines without being engaged. The Romans did not so increase
the number of ranks as to bring about this condition. The Greeks did
not observe and calculate so well. They sometimes brought the number
of files up to thirty-two and their last files, which in their minds,
were doubtless their reserves, found themselves forcibly dragged into
the material disorder of the first ones."

He wrote in the mid 19th century, out of a background of Napoleonic warfare, and in his opinion the disorder propagates all the way to the back of a deep formation.