rarefy v.

[thin, few, unusual] late 14c., "thin, airy, porous" (opposed to dense); mid-15c., "few in number and widely separated, sparsely distributed, seldom found, very infrequent;" from Old French rer, rere "sparse" (14c.) and directly from Latin rarus "thinly sown, having a loose texture; not thick; having intervals between, full of empty spaces" (antonym of densus). Sometimes reconstructed to be from a PIE root *ere- "to separate; adjoin."

"Having the particles not close together," hence "few in number," hence, "unusual." Sense of "remarkable from uncommonness," especially "uncommonly good" is from late 15c. (Caxton). Related: Rareness. In chemistry, rare earth is from 1818.

Rare implies that only few of the kind exist : as, perfect diamonds are rare. Scarce properly implies a previous or usual condition of greater abundance. Rare means that there are much fewer of a kind to be found than may be found where scarce would apply. [Century Dictionary, 1895]

*dhē-, Proto-Indo-European root meaning "to set, put."

It forms all or part of: abdomen; abscond; affair; affect (v.1) "make a mental impression on;" affect (v.2) "make a pretense of;" affection; amplify; anathema; antithesis; apothecary; artifact; artifice; beatific; benefice; beneficence; beneficial; benefit; bibliothec; bodega; boutique; certify; chafe; chauffeur; comfit; condiment; confection; confetti; counterfeit; deed; deem; deface; defeasance; defeat; defect; deficient; difficulty; dignify; discomfit; do (v.); doom; -dom; duma; edifice; edify; efface; effect; efficacious; efficient; epithet; facade; face; facet; facial; -facient; facile; facilitate; facsimile; fact; faction (n.1) "political party;" -faction; factitious; factitive; factor; factory; factotum; faculty; fashion; feasible; feat; feature; feckless; fetish; -fic; fordo; forfeit; -fy; gratify; hacienda; hypothecate; hypothesis; incondite; indeed; infect; justify; malefactor; malfeasance; manufacture; metathesis; misfeasance; modify; mollify; multifarious; notify; nullify; office; officinal; omnifarious; orifice; parenthesis; perfect; petrify; pluperfect; pontifex; prefect; prima facie; proficient; profit; prosthesis; prothesis; purdah; putrefy; qualify; rarefy; recondite; rectify; refectory; sacrifice; salmagundi; samadhi; satisfy; sconce; suffice; sufficient; surface; surfeit; synthesis; tay; ticking (n.); theco-; thematic; theme; thesis; verify.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dadhati "puts, places;" Avestan dadaiti "he puts;" Old Persian ada "he made;" Hittite dai- "to place;" Greek tithenai "to put, set, place;" Latin facere "to make, do; perform; bring about;" Lithuanian dėti "to put;" Polish dziać się "to be happening;" Russian delat' "to do;" Old High German tuon, German tun, Old English don "to do."