'Tis certain, that not only in philosophy, but even in common life, we may attain the knowledge of a particular cause merely by one experiment, provided it be made with judgment, and after a careful removal of all foreign and superfluous circumstances. Now as after one experiment of this kind, the mind, upon the appearance either of the cause or the effect, can draw an inference concerning the existence of its correlative; and as a habit can never be acquir'd merely by one instance; it may be thought, that belief cannot in this case be esteem'd the effect of custom. But this difficulty will vanish, if we consider, that tho' we are here suppos'd to have had only one experiment of a particular effect, yet we have many millions to convince us of this principle; that like objects placed in like circumstances, will always produce like effects; and as this principle has established itself by a sufficient custom, it bestows an evidence and firmness on any opinion, to which it can be apply'd.
Treatise 1.3.8.14 (SBN 104-105)
I've been recently searching for a topic for a paper on Hume and Shepherd; currently I'm leaning toward something on their views of the singular experiment. Unfortunately I'm not sure it can be done without going into some length about Thomas Brown's views on the subject -- I say 'unfortunately' not because Brown's views are uninteresting, but because I really would rather write about Hume and Shepherd themselves without any major detours, particularly since both of them are tangle enough on the question without adding more tangles. I think I can do it. But reasonable completeness of research requires that I compare them both to Brown, anyway, and papers have a way of not doing what you intend them to do.
