The article discusses the limits of material economy in frame structures, focusing on the conditions under which a frame can achieve the minimum volume of material while sustaining given forces. Maxwell's principle is used to derive the relationship between the stresses in the bars and the volume of material required. The author, A. G. M. Michell, demonstrates that for a frame to be economical, the strains in all the bars must increase equally and by the same amount during a small deformation. This condition is satisfied when the bars form curves of orthogonal systems, such as tangents and involutes, equiangular spirals, concentric circles, or rectangular networks of straight lines. The article provides specific examples of minimum volume frames for various applied forces, including single forces, central loads, and couples, and calculates the necessary volume of material for each case. The results highlight the efficiency of certain frame structures in terms of material usage.The article discusses the limits of material economy in frame structures, focusing on the conditions under which a frame can achieve the minimum volume of material while sustaining given forces. Maxwell's principle is used to derive the relationship between the stresses in the bars and the volume of material required. The author, A. G. M. Michell, demonstrates that for a frame to be economical, the strains in all the bars must increase equally and by the same amount during a small deformation. This condition is satisfied when the bars form curves of orthogonal systems, such as tangents and involutes, equiangular spirals, concentric circles, or rectangular networks of straight lines. The article provides specific examples of minimum volume frames for various applied forces, including single forces, central loads, and couples, and calculates the necessary volume of material for each case. The results highlight the efficiency of certain frame structures in terms of material usage.