If objects of weights x and w1 are suspended from the balance in Figure 13(A), the cross-beam is horizontal if bx = aw1. If the lengths a and b are known, we may use this equation to determine an unknown weight x by selecting w1 such that the cross-beam is horizontal. If a and b are not known precisely, we might proceed as follows. First balance x by w1 on the left as in (A). Then switch places and balance x by w2 on the right as in (B). The average ¯x = 12(w1 + w2) gives an estimate for x. Show that ¯x is greater than or equal to the true weight x.

FIGURE 13