Darwin conducted several experiments evaluating the effects of extremely small doses on an insect-eating plant (Drosera rotundifolia, commonly called sundew), a plant that also happens to be a commonly used homeopathic medicine.
He found that solutions of certain salts of ammonia stimulated the glands of the plant's tentacles and caused the plant to turn inward. He made this solution more and more dilute and observed that 1/4,000,000 of a grain had a demonstrable effect upon the Drosera and that 1/20,000,000th of the grain had the same affect.
Astonished by his observation Darwin wrote, “Yet this amount sufficed to cause the inflection of almost every tentacle, and often the blade of the leaf. … My results were for a long time incredible, even to myself, and I anxiously sought for every source of error. … The observations were repeated during several years. Two of my sons, who were as incredulous as myself, compared several lots of leaves simultaneously immersed in the weaker solutions and in water, and declared that there could be no doubt about the difference in their appearance. … In fact every time that we perceive an odor, we have evidence that infinitely smaller particles act on our nerves.” (Darwin, 1875, 170)
-- Darwin, C. Insectivorous Plants. New York: D. Appleton & Co., 1875.