Differential ebulliometry is a powerful and rapid procedure for obtaining infinitely dilute activity coefficients with potentially very good accuracy. Tedious degassing procedures are not necessary, as in a static method, and from only a few measurements full system phase behavior can be evaluated. The principal problem, precise evaluation of the equilibrium liquid composition from the known composition of a prepared solution charged to the apparatus, is well known but has so far defied adequate resolution. A system of exact self-consistent equations was developed for the characterization of an ebulliometer through a dimensionless ebulliometer constant. Evaluation of this constant from typical data and its subsequent use are illustrated for a system of known phase equilibrium behavior. Remarkably, the equations permit evaluation of the effective "static" holdups in various parts of th equipment without any volume measurements. Since one equation is redundant to the main purpose, it can be used for a consistency check of measured and calculated data. The equations also furnish a guide for the operation of ebulliometers.