We learn from Cordelia that Lear has run off from his caretakers and was last spotted in a wheat field, covered over with all sorts of plants.
Cordelia sends a century (literally, 100 soldiers) to find him, and confers with a doctor to figure out if there's any way to cure Lear's madness. The doctor promises a long sleep will do the trick (but as we know in Shakespeare, sleep is a hair's breadth from death, so this doesn't bode too well).
Cordelia prays for her father's recovery.
Cordelia explains that she has brought an army from France in furtherance of her father's wishes, and not because she wants power for herself. "Not blown ambition doth our arms incite / but love, dear love, and our aged father's right" she says.
A messenger then abruptly informs Cordelia that her sisters' British troops are marching towards the French army. Sibling rivalry is about to be played out through full scale civil war.