The Allen and Greenough is still under construction;
so some links may not work quite the way you would expect.
USES OF THE ABLATIVE AS INSTRUMENTAL.
408. Means, Instrument, Manner, and Accompaniment
are denoted by the Instrmental Ablative (see §398), but some of these
uses more commonly require a preposition. As they all come from one
source (the old Instrumental Case) no sharp line can be drawn between
them, and indeed the Romans themselves can hardly have thought of any
distinction. Thus, in omnibus precibus
órábant, they entreated every [kind of]
prayer, the ablative, properly that of means, cannot be
distinguished from that of manner.