Castigliano's theorems apply if the strain energy is finite. This is true if m − − i > n / 2 . It is m = 1 , 2 the order of the energy (= the highest derivative in the energy), i = 0 , 1 , 2 , 3 , is the index of the Dirac delta (single force, i = 0 ) and n = 1 , 2 , 3 is the dimension of the space. To second order equations, m = 1 , belong two Dirac deltas, i = 0 , force and i = 1 , dislocation and to fourth order equations, m = 2 , four Dirac deltas, i = 0 force, i = 1 moment, i = 2 bend, i = 3 dislocation.