A method for constructing envelopes and the period-amplitude relation of Cepheids.

Summary. We derive a statistically sound method to construct envelopes to point diagrams. We give a procedure to define points of equal probability, to which curves can be fitted by least squares. Empirical envelopes thus defined can be compared with each other or theoretical predictions and their difference can be statistically tested. We apply the method to the period-amplitude relation of Cepheids in M 31 and in our Galaxy. Using the data of Schalterbrand and Tammann (1971) for the Galaxy and Baade and Swope (1963, 1965) and Gaposchkin (1962) in M 31 upper envelopes are derived for both galaxies. They seem to be not significantly different, although we do not regard the question as settled. Key words: envelopes - Cepheids period-amplitude relation galaxies - cosmology