Why does Marcellus tell Horatio to speak to the ghost in Hamlet?
Marcellus wants Horatio to see the ghost because Horatio does not believe that there is one; also, Marcellus believes that if Horatio, a scholar, speaks to this specter, it will respond.
The play Hamlet opens with the changing of the guard on the ramparts of Elsinore Castle on a cold winter's night. Bernardo relieves Francisco, and they speak of "Not a mouse stirring" (1.1.10).
Then, Marcellus and Horatio enter. When asked if the guards if they have seen anyone, Bernardo replies that he has seen nothing. Marcellus tells them,
Horatio says ’tis but our fantasyAnd will not let belief take hold of himTouching this dreaded sight twice seen of us. (1.1.20-22)
Just then the ghost enters, and Marcellus urges everyone to be quiet. Bernardo notices that it resembles King Hamlet. He remarks upon this resemblance to Horatio. Horatio replies that it does, indeed, and it frightens him. Further, Marcellus urges Horatio to question the ghost. Horatio speaks to it:
What art thou that usurp'st this time of night
Together with that fair and warlike form
In which the majesty of buried Denmark
Did sometimes march? By heaven I charge thee, speak. (1.44-47)