Simpson's rule(s) approximate of a function by fitting a polynomial through representative points. They are particularly useful for approximating the volume between three irregular shapes, when no other information is available on the transition between them. Because the length-volume relationship along a river is an irregular, but continuous function with periodic observations (cross sections), hydrographers often use Simpson's rule to compute the volume associated with a three-cross sections sequence. The simple insight of Simpson's result is that a parabolic fit weights the central observation (e.g. XS2) in a simple ratio to the bounding observations (the upstream and downstream cross sections). The version of Simpson's rule used in HEC-RAS (following HEC6) is sometimes calls Simpson's Second rule or the 3/8ths. It is actually designed to find the volume from four equally spaced observations, but is modified to account This approach was adopted from HEC6 and was developed by W. Tony Thomas for three irregular spaced cross sections. The veneer elevation change (applied to the wetted, movable width W) is: