On Scenic USA, Ken Reese has some info about Black Slate Falls:
Gathering momentum on the slopes of Mount Arvon, Michigan’s highest peak, the Slate River drops northward into Lake Superior. At one time when slate was a predominant roofing material, Arvon Road led to the small town of Arvon and a slate quarry. Today the town has all but disappeared, and piles of waste slate mark the quarry site.
West of the Slate River, Arvon Road leads to this beautiful setting of Black Slate Falls. Here, tucked in the woods is a picturesque little falls as it drops over slate ledges. Quartzite and Black Slate falls are found at the end of Arvon Road. For those seeking more woodland waterfalls, this wild river leads down to Slate (the largest drop), Slide and Ecstasy falls, just three miles downriver. Hiker’s notes indicate it’s a lot easier to reach Slate Falls from Skanee Road, where Arvon Road gets its start.
GoWaterfalling adds that Black Slate Falls are one of several waterfalls on the Slate River.
Many more waterfalls on Michigan in Pictures.