Heaps of falling powder and circular waves in a struck vessel
Granular piles twice as wide as high, dust circulating on a struck board, and waves in water
Several problems in the motion of particles and water share this page. A heap of powder or grain falling from a single hole h always spreads to a width (o m) twice its height (a n); a struck, dusted board sends its dust circulating around the right-angled triangle a m n; and the concentric circles at center illustrate the waves raised when a vessel of water is struck. Struck at the center the rings grow from small to very large; struck at the side or off-center they behave as an earlier proposition shows.
On this page
A poured heap is twice as wide as it is high
Powder or grain falling from a single hole h forms a heap whose width o m is always double its height a n. The figure shows o m going twice into n a.
Dust circulating on a struck board
Strike a dusted board and the dust gathers into little heaps that pour from the apex of each pyramid to its base, re-enter beneath, and rise again, circling the right-angled triangle a m n for as long as the striking lasts.
Circular waves in a struck vessel of water
Struck on one side, the water makes circular motions that fade at the center of its surface; struck at the center, the rings grow from smallest to very large. The concentric circles drawn at center picture this motion.