Definition of "rivulet"

Yes Madam I think you will like them—when you shall see in a beautiful Quarto Page how a neat rivulet of Text shall meander thro' a meadow of margin—'fore Gad, they will be the most elegant Things of their kind—

1777, Richard Brinsley Sheridan, The School for Scandal, I.i

The struggle with ways and means had recommenced, more difficult now a hundredfold than it had been before, because of their increasing needs. Their income disappeared as a little rivulet that is swallowed by the thirsty ground.

1918, W[illiam] B[abington] Maxwell, chapter XXIII, in The Mirror and the Lamp, Indianapolis, Ind.: The Bobbs-Merrill Company

Rills running down the steepest slopes develop into rivulets.

1945, Charles Cotton, Geomorphology: An Introduction to the Study of Landforms