For a simple example let m=1 and n=1. Consider a horizontal beam on which two points have been defined: point 1 and point 2. First we apply a vertical force P at point 1 and measure the vertical displacement of point 2, denoted Δ Δ P 2 . Next we remove force P and apply a vertical force Q at point 2, which produces the vertical displacement at point 1 of Δ Δ Q 1 . Betti's reciprocity theorem states that: