METEMPTOSIS (from μετα "post," and πίστω eido "I fall,") a term in chronology, expressing the solar equation, necessary to prevent the new moon from happening a day too late. By which it stands contradistinguished from proemptosis, which signifies the lunar equation, necessary to prevent the new moon from happening a day too soon.
The new moons running a little backwards, that is, coming a day too soon at the end of 312 years and a half; by the proemptosis, a day is added every 300 years, and another every 2400 years: on the other hand, by the metemptosia, a bisextile, is suppressed each 134 years; that is, three times in 400 years. These alterations are never made but at the end of each century; that period being very remarkable, and rendering the practice of the calendar easy.
There are three rules for making this addition or suppression of the bisextile-day, and, by consequence, for changing the index of the epacts. 1. When there is a metemptosia without a proemptosis, the next following, or lower index, must be taken. 2. When there is a proemptosis without a metemptosia, the next preceding or superior index is to be taken. 3. When there are both a metemptosia and a proemptosis,
or when there is neither the one nor the other, the same index is preserved. Thus, in 1600, we had D: in 1700, by reason of the metemptosia, C was taken: in 1800, there will be both a proemptosis and a metemptosia; so the same index will be retained. In 1900, there will be a metemptosia again, when B will be taken; which will be preserved in 2000, because there will then be neither the one nor the other. This is as far as we need compute for it: but Clavius has calculated a cycle of 301800 years; at the end of which period, the same indices return in the same order. See EPACT.