The Lot of Necessity, kleros anankes, is the lot of Mercury in the Hermetic set, built on the Lot of Fortune and therefore on the side of circumstance rather than of will. Paulus Alexandrinus gives it for constraint, subordination, struggle and the conditions a person cannot argue with, and it stands in deliberate opposition to Eros: what one wants against what one must accept. The Greek ananke is a heavy word, the impersonal necessity that binds even the gods in some Greek thought, personified as a goddess in Orphic cosmology, and the choice of it for a lot is not casual. Later medieval and Renaissance handbooks reduced the lots to a long undifferentiated list of parts, and the structural opposition between Eros and Necessity, which is the point of both, tends to be lost in that presentation.
The day formula takes the arc from Mercury to Fortune and projects it from the Ascendant, Ascendant plus Fortune minus Mercury; by night the terms reverse, Ascendant plus Mercury minus Fortune. Necessity's construction from Fortune, rather than from Spirit as Eros is, is itself part of the opposition the two lots are read against each other: Eros, built on the mind's lot, measures what is wanted, while Necessity, built on the body's and circumstance's lot, measures what is imposed, and the choice of which principal lot each is built from is not arbitrary but encodes the very distinction the pair is meant to illustrate.