The Nadir, the Imum Coeli or lower meridian, is the point of the ecliptic exactly opposite the Midheaven. Like the Midheaven and unlike the ascendant and descendant, it is a function of sidereal time and the obliquity of the ecliptic alone: the geographic latitude does not enter the computation.
That is worth holding beside the ascendant. A chart of known time and unknown birthplace still has a meridian axis, because only the longitude is needed to fix the sidereal time, and it has no horizon axis at all. Everything an astrologer can say about the Midheaven and the Nadir in such a chart is on firmer ground than anything said about the ascendant, descendant or houses.
Its rate is the Midheaven's: one full circuit per sidereal day, advancing between about 0.92 and about 1.09 degrees of ecliptic longitude for every four minutes of clock time, the variation coming from the 23 degree 26 minute tilt between the ecliptic and the equator.
A terminological caution belongs here. In observational astronomy the nadir is the point directly beneath the observer's feet, the opposite of the zenith, and it has nothing to do with the meridian intersection of the ecliptic. The astrological Nadir and the astronomical nadir are different points and coincide only by accident. Where precision matters, the older term Imum Coeli, the bottom of the sky, is the unambiguous one.