support points) the edge of the mirror will be flexed upward over the two support points, and downward under the other two points, midway between. In going once around the edge of a mirror so loaded we will encounter two high areas (maxima) and two low areas (minima). Although the curve may not be a perfect sine-curve, it will be a fair approximation to such a curve.
The first warping harness to be constructed was designed to apply flexure forces to the edge of the mirror blank in just this way - two "pushes" and two "pulls". Tests of this device in the optical shop showed it to do a fairly good job on a 6-inch-diameter mirror everywhere except in the immediate vicinity of the the pressure-points, where the flexure was found to be too great. This is just the opposite of what might be expected from a consideration of just the Z2 and Z3 features of the flexure curve. It indicates that other factors are acting to increase the curvature of the mirror blank in the areas where the simple beam formula says the curvature might be found to be a little too small.
Another way of looking at the problem is to consider the actual flexure curve as we go around the edge of the mirror (in contrast to going across the face of the mirror). From this point of view the actual flexure curve peaks too sharply at the maxima and minima (as compared with the desired sine-curve shape). A rather obvious solution to this difficulty is to distribute the loads at the edge of the mirror as compared with the single-point design. To carry out this idea, a short bar was placed under each of the four pressure members and each of these divided the load equally and distributed it to two points separated 30° apart around the edge of the mirror.
The original warping harness was modified to employ this stratagem and then tested on a 6-inch-diameter mirror. The final design of this warping