Definition of "rill"

[N]or yet beside the rill / Nor up the lawn, nor at the wood was he

1750 June 12 (date written; published 1751), T[homas] Gray, “Elegy Written in a Country Churchyard”, in Designs by Mr. R[ichard] Bentley, for Six Poems by Mr. T. Gray, London: […] R[obert] Dodsley, […], published 1753

So twice five miles of fertile ground / With walls and towers were girdled round: / And here were gardens bright with sinuous rills, / Where blossom'd many an incense-bearing tree; / And here were forests ancient as the hills, / And folding sunny spots of greenery.

1797, S[amuel] T[aylor] Coleridge, “Kubla Khan: Or A Vision in a Dream”, in Christabel: Kubla Khan, a Vision: The Pains of Sleep, London: […] John Murray, […], by William Bulmer and Co. […], published 1816, pages 55–56

The secret of success lies never in the amount of money, but in the relation of income to outgo; as if, after expense has been fixed at a certain point, then new and steady rills of income, though never so small, being added, wealth begins.

1860, R[alph] W[aldo] Emerson, “Essay III. Wealth.”, in The Conduct of Life, Boston, Mass.: Ticknor and Fields, page 101

And fainter, finer, trickle farTo where the listening uplands are;To pause—then from his gurgling billLet the warbled sweetness rill,And down the welkin, gushing free,Hark the molten melody;

1862, Gerard Manley Hopkins, Il Mystico, 81-86

Alladad Khan was panting hard, soaked in sweat, and his rolled-up sleeve was all blood, blood rilling down his arm.

1956, Anthony Burgess, Time for a Tiger (The Malayan Trilogy), published 1972, page 158