The three-phase line in a type V phase diagram starts with a lower critical end point (LCEP), where the two liquid phases merge, and ends with a upper critical end point (UCEP), where the vapor and liquid phases merge. Along the phase line no indication is seen as to why the situation is so different at the end points. If however one considers the complete set of V(x) or p(x) plots, i.e., including all the unstable and metastable binodal lines, it can be seen that a 'dramatic' rearrangement takes place somewhere between the ends of the three phase line at the 'plait point' transformation. I unearthed many figures showing this transformation and although one obtains the impression that van der Waals and Korteweg were aware of this behavior, no explanation was given in their work. Korteweg described the general rules for special points on the binodals, but no thorough calculation of the plait point transformation seems to exist. This paper is confined to the description of this transformation; the full mathematical treatment will be given in a later publication.