What does it mean to beat one's hands together?
Solution 1:
I have never seen or heard this expression before. However the sentence ...
He grew quite hysterical, and raising his open hands, beat his palms together in a perfect agony of grief.
... seems pretty clear. I think that it must be a clapping motion but with the fingers bent back rather than cupped and the hands perfectly aligned rather than slightly crossed. That way there would not be much sound.
I don't recall ever seeing anyone doing this. Maybe I've just never seen anyone in an agony of grief.
Update
Clapping Hands as a Gesture of Anguish and Anger in Mesopotamia and Israel
Whaddaya know?